Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 978420 10 pageshttpdxdoiorg1011552013978420
Research ArticleImproved Pilot-Aided Channel Estimation forMIMO-OFDM Fading Channels
J Mar12 Chi-Cheng Kuo1 and M B Basnet1
1 Department of Communications Engineering Yuan-Ze University 135 Yuan-Tung Road Jungli Taoyuan 320 Taiwan2 Communications Research Center Yuan-Ze University 135 Yuan-Tung Road Jungli Taoyuan 320 Taiwan
Correspondence should be addressed to J Mar eejmarsaturnyzuedutw
Received 2 July 2013 Accepted 11 August 2013
Academic Editor Ai Bo
Copyright copy 2013 J Mar et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
An improved pilot-aided channel estimation scheme is proposed to enhance the channel estimation accuracy of multiple-inputmultiple-output-orthogonal frequency divisionmultiplexing (MIMO-OFDM) fading channels Based on the adaptive path numberselectionmechanism the number of paths can be scalable and adaptively changed with the characteristics of MIMO-OFDM fadingchannels The fine channel estimation formulas for all data subcarriers are derived The 2 times 2 space-frequency block code-OFDM(SFBC-OFDM) system and a six-path fading channel model are considered as an example of the high mobility MIMO-OFDMwireless communications system Through simulations it is shown that 2 times 2 SFBC-OFDM system using the proposed approachcan satisfy the performance requirements over frequency selective and frequency nonselective fast fading channels
1 Introduction
The cellular mobile communications industry has recentlybeen one of the fastest growing industries of all time withthe number of users increasing incredibly rapidly Orthog-onal frequency division multiplexing access (OFDMA) waschosen as the spectrum access technology of the 4G cellularsystems because its orthogonality eliminates intracell inter-ference The high mobility OFDM wireless communicationsystem will operate in a fast fading channel where thenonnegligible fluctuations of the channel gains are expectedwithin eachOFDMdata block Fast fading involves variationson the scale of a half-wavelength and frequently introducesvariations as large as 35ndash40 dB [1] The channel estimationin OFDM systems over time-varying fading channels isgenerally based on the use of pilot subcarriers in givenpositions of the frequency-time grid [2] It is advisable toplace pilot subcarriers in each OFDM data block in orderto ensure adequate estimation accuracy In [3] the effectof pilot power on the performance of 16-QAM OFDMsystem operating in two-ray Rayleigh slow fading channel ispresented The optimum pilot-to-data power ratio (PDR) isanalytically derived As an alternative the channel estimationalgorithm based on subspace tracking has been presented in
[4] for OFDM systems which can effectively reduce channelestimation error by tracking the dominant delay-subspacespanned by the frequency responses
Increasing demand for high performance 4G broadbandwirelesses is enabled by the use of multiple antennas atboth base station and user equipment ends Multiple-input-multiple-output (MIMO) is one of the best ways to combatchannel fading using transmit diversity and receive diver-sity The use of MIMO technique in OFDM system is anefficient solution to meet the growing demand for highspeed spectral efficiency and reliable communication [2]in future-generation wireless networks The MIMO-OFDMwireless communications have the inherent signal variabilitygenerated from the multipath fading channelThe aim of thisstudy is to investigate the channel estimation algorithm in theMIMO-OFDM fading channels In [5] it is shown that thespace-frequency block code-(SFBC-) OFDM system exhibitserror floors caused by imperfect channel state estimation overfrequency selective fading channels Hence we need a morerobust frequency and phase synchronization technology forfast MIMO-OFDM fading channels The optimum pilotallocation in terms of overhead and channel estimation erroris analyzed in reference [6] that maximizes the channel
2 International Journal of Antennas and Propagation
capacity for MIMO-OFDM system operating in frequencyselective fading channel Both perfect interpolation and non-perfect interpolation for pilot-aided channel estimations areconsidered In [7] the sequential decision feedback sequenceestimation with an adaptive threshold equalizer techniqueand pilot tone plus interpolation channel estimation schemeare used to design the Alamouti coded small constellation(BPSK and QPSK) OFDM receiver in fast fading channels
An adaptive path number selection mechanism is pro-posed for channel estimation over MIMO-OFDM fadingchannels to provide the suboptimum system performancewhenever the high order modulation MIMO-OFDM systemis operated either in frequency nonselective fast fading or infrequency selective fast fading channels The 2 times 2 SFBC-OFDM system and a six-path fading channel model areconsidered as an example of the MIMO-OFDM system inthe simulations to prove that the acceptable bit error rate(BER) can be achieved by employing 16-QAM and 64-QAM modulations in time-varying fast fading channelsWe consider the vehicle speed of 200 kmh resulting inthe Doppler frequency of 1093Hz to satisfy the fast fadingcondition for MIMO-OFDM channel [8 9]
The rest of this paper is organized as follows The pro-posed MIMO-OFDM channel estimation algorithm isdescribed in Section 2 where the fine channel estimationfor all data subcarriers is derived The adaptive path numberselection mechanism for the MIMO-OFDM fading channelis presented in Section 3 The BER performance of theMIMO-OFDM system using the proposed suboptimalchannel estimation approach is simulated and discussed inSection 4 Finally concluding remarks are given in Section 5
2 MIMO-OFDM Channel Estimation
We consider a generic downlink multiuser MIMO-OFDMchannel model Let the number of transmit antennas be 119899
119879
and the number of receive antennas 119899119877 One OFDM symbol
of each user is transmitted across 119873 subcarriers To simplifythe formula derivations the data vector X for each user canbe expressed in polyphase representation as
X = [1198830
1198831
sdot sdot sdot 119883119873minus2
119883119873minus1
]119879 (1)
where 119879 denotes the transpose of the vector Thus the demo-dulated signal vector is given by
Y = HX + V (2)
where H is a diagonal matrix whose diagonal elements arethe 119873-DFT of the channel impulse response h and V isthe 119873-DFT of the channel noise With reference to theconventional channel estimation approach of a given OFDMsystem [9] ten short OFDM training signals are used forpacket detection coarse frequency offset estimation andtiming synchronization Two periods of the long trainingsignals are used for improving channel estimation accuracyof the short training symbols A phase-locked loop is adoptedin the receiver for estimating and compensating the carrierfrequency offset Each OFDM data block contains 119871 pilotsubcarriers which are used to track the carrier phase
A typical 2 times 2 SFBC-OFDM model which consists oftwo transmit antennas and two receive antennas is used todescribe the theoretical analysis and the proposed channelestimation scheme User data vector X is first encodedinto two spatial vectors X
1and X
2by the space-frequency
encoder Denote the transmitted signal vector of each user ina space-frequency block as
X1= [119883
0minus 119883
lowast
1sdot sdot sdot 119883
119873minus2minus 119883
lowast
119873minus1]119879
X2= [119883
1119883lowast
0sdot sdot sdot 119883
119873minus1119883lowast
119873minus2]119879
(3)
where X1is the data transmitted from the first antenna 119879119909
1
and X2is the data transmitted from the second antenna 119879119909
2
simultaneously Let X119890and X
119900be even and odd component
vectors of X that is
X119890= [119883
01198832
sdot sdot sdot 119883119873minus4
119883119873minus2
]119879
X119900= [119883
11198833
sdot sdot sdot 119883119873minus3
119883119873minus1
]119879
(4)
Similarly X1119890 X1119900 X2119890 and X
2119900denote even and odd
component vectors ofX1andX
2 respectively which can then
be expressed in terms of even and odd component vectors as
X1119890
= X119890 X
1119900= minusXlowast
119900
X2119890
= X119900 X
2119900= Xlowast
119890
(5)
Note that since the two corresponding signals transmittedfrom two antennas at the same time slots are orthogonal themaximum likelihood decoding is reduced to simple linearprocessing at the receiver The received signal at the receiveris given by
Y1= H
11X1+H
21X2+ V
1
Y2= H
12X1+H
22X2+ V
2
(6)
where Y1and Y
2are the received signals in the first and
second received antenna H11
and H21
are the channel fre-quency response of the first and second antenna transmittedto the first received antenna and H
12and H
22are the
channel frequency response of the first and second antennatransmitted to the second received antenna The channelfrequency response at all data subcarriers for each transmit-receive antenna pair is defined as
H119901119902
=
[[[
[
1198671199011199020
0 sdot sdot sdot 0
0 1198671199011199021
sdot sdot sdot 0
0 0 119867119901119902119873minus1
]]]
]
for 119901 = 1 119899
119879
119902 = 1 119899119877
(7)
Equivalently (6) can be represented as
Y1119890
= H11119890
X1119890
+H21119890
X2119890
+ V1119890
Y1119900
= H11119900
X1119900
+H21119900
X2119900
+ V1119900
Y2119890
= H12119890
X1119890
+H22119890
X2119890
+ V2119890
Y2119900
= H12119900
X1119900
+H22119900
X2119900
+ V2119900
(8)
International Journal of Antennas and Propagation 3
OFDM
transmitter
OFDM
receiver
Least square estimation
MMSEestimation
Path numberselection mechanism
Zeropadding N-FFT
Correction factordetermination
Linearinterpolation
Fine channel estimation for all pilots tones
Adaptive path number selection mechanism
Channel estimator
H11
HNN
HN1
H1N
X1
XN
Y1
YNV
Figure 1 Block diagram of pilot tone channel estimation aided with adaptive path number selection mechanism for MIMO-OFDM fadingchannel
The received signal at the 119902th receive antenna for the 119896thpilot tone transmitted from 119901th antenna can be written as
119884119902119896
= 119883119901119896
119867119901119902119896
+ 119881119902119896 119896 = 0 1 119873 minus 1
119901 = 1 119899119879
119902 = 1 119899119877
(9)
where 119873 is the frequency tones in each OFDM data block119883119901119896
is the transmitted signal of 119901th transmitted antenna119867119901119902119896
is the channel frequency response form 119901th transmitantenna to 119902th receive antenna and 119881
119902119896is the AWGN noise
Then from (9) the channel estimation at pilot subcarriersbased on the least square (LS) algorithm can be obtained as
119871 be the set of 119871 pilot tones which is one of
the sets 119894 119894 + 119873119871 119894 + (119871 minus 1)119873119871 119894 = 0 1 119873119871 minus 1used for transmitting the training data Collect these channelresponses in a vector H
119901119902119896119901
= [1199011199021198961
119901119902119896119871
]119879 which
is obtained from the FFT matrixThe intermediate processing steps between the LS esti-
mates of the channel gains over the pilot subcarriers andinterpolation processing are added in order to ensure ade-quate estimation accuracy for fast fading channel The blockdiagram of the proposed pilot tone channel estimation aidedwith adaptive path number selection mechanism is shown inFigure 1 Here ℓ is defined as the number of dominant pathsestimated from the adaptive channel path number selectorwhich chooses ℓ paths with larger power from (h
119901119902119896119901
)119871times1
and let 119887
1 1198872 119887
ℓ be a set of the selected pilot index Since
AWGN assumption for each subcarrier is adopted and sinceeach pilot tone carries data of constant modulus radic120576
119909 the
minimum mean square error (MMSE) estimation of h119901119902
isgiven by [10]
h119901119902119896119901
= Qminus1119901119902119896119901
H119901119902119896119901
= h119901119902119896119901
+Qminus1119901119902119896119901
1
radic120576119909
S119896119901
(11)
where S119902119896119901
= [1198781199021198961
119878119902119896119871
]119879 (h
119901119902119896119901
)ℓtimes1
= [ℎ1199011199021198961
ℎ1199011199021198962
sdot sdot sdot ℎ119901119902119896ℓ
]119879 and Q
119901119902119896119901
is a Vandermonde matrix withdistinct 119871 twiddle factor119882119896119894
119873
((Q119901119902119896119901
)ℓtimes119871
)
minus1
=
[[[[[[[
[
(119876119901119902119896119901
)
minus1
(1198871 1) (119876
119901119902119896119901
)
minus1
(1198871 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198871 119871)
(119876119901119902119896119901
)
minus1
(1198872 1) (119876
119901119902119896119901
)
minus1
(1198872 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198872 119871)
(119876119901119902119896119901
)
minus1
(119887ℓ 1) (119876
119901119902119896119901
)
minus1
(119887ℓ 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(119887ℓ 119871)
]]]]]]]
]
(12)
Other notations are represented as follows 119864sdot is theexpectation operator trsdot is the trace operator sdot means2-norm I
119871represents the 119871 times 119871 identity matrix Therefore
the mean square error (MSE) in the channel estimate can bederived as
Equations (17) and (18) show that using less pilot numberin the pilot-aided channel estimation can get smaller MSEin the channel impulse response estimate However in thefrequency selective fast fading channel less pilot numbermaycausemore linear interpolation lossThe case of ℓ = 1will notbe considered for path number selection mechanism becauseit cannot reflect the variation of channel characterizationof the frequency selective fading channel The preliminarychannel frequency response estimate (H
119901119902)119873times1
is obtained bythe 119873-FFT of an 119873 times 1 estimated channel impulse response(hℓ119901119902
)119873times1
= [(h119879119901119902
)ℓtimes1
0119879(119873minusℓ)times1
]119879 It can be written as
ℓ
119901119902119896=
1
radic119873
ℓminus1
sum
119899=0
ℎℓ
119901119902(119899)119882
119896119899
119873 119896 = 0 1 119873 minus 1 (19)
The preliminary channel frequency response estimates atpilot tones for 119896 = 119896
1 1198962 119896
119871are Hℓ
119901119902119871times1= [
ℓ
1199011199021198961
ℓ
119901119902119896119871
]119879 The correction factor for fine channel frequency
response estimate at 119896119901th pilot tone is defined as
119862ℓ
119901119902119896119901
=
119901119902119896119901
ℓ
119901119902119896119901
=
(1radic119873)sum119871minus1
119899=0ℎ119901119902 (119899)119882
119896119901119899
119873
(1radic119873)sumℓminus1
119899=0ℎℓ
119901119902(119899)119882
119896119901119899
119873
(20)
For example the fine correction factor at 1198961th pilot tone
for 119871 = 4 and ℓ = 2 is determined as
1198622
1199011199021198961
=
1199011199021198961
2
1199011199021198961
= 1 +
ℎ119901119902 (2)119882
21198961
119873+ ℎ119901119902 (3)119882
31198961
119873
ℎ119901119902 (0) + ℎ
119901119902 (1)1198821198961
119873
(21)
From (21) it is observed that the fine correction factorcan compensate the power loss caused by less path employedin the preliminary channel estimates When the number ofpaths chosen is ℓ the fine correction factor in a vector for 119871pilot tones is
(Cℓ119901119902
)119871times1
= [119862ℓ
1199011199021198961
119862ℓ
119901119902119896119871
]119879
(22)
The fine correction factors for all data subcarriers can beobtained through linear interpolation [11] Two consecutivefine correction factors in 119871 pilot tones are used to determinethe fine correction factors for other data subcarriers that arelocated between the 119896
119901th and 119896
(119901+1)th subcarriers
119862ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901
+ (
119862ℓ
119901119902119896119901+1
minus 119862ℓ
119901119902119896119901
119880) times 119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(23)
The fine channel estimations for all data subcarriers are
ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901+119906
times ℓ
119901119902119896119901+119906
= (
119901119902119896119901
ℓ
119901119902119896119901
+(
(119901119902119896119901+1
ℓ
119901119902119896119901+1
) minus (119901119902119896119901
ℓ
119901119902119896119901
)
119880) times 119906)
times ℓ
119901119902119896119901+119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(24)
where 119880 is the number of data subcarriers between twoadjacent pilot subcarriers The fine channel estimations atpilot tones are expressed as
ℓ
119901119902119896119901
= 119862ℓ
119901119902119896119901
times ℓ
119901119902119896119901
= ℓ
119901119902119896119901
119901 = 1 sim 119871 (25)
International Journal of Antennas and Propagation 5
The fine channel estimations for those data subcarrierslocated in the intervals of (0 119896
Although MSE in channel frequency response estimatedecreases with the path number under the more seriousfrequency selective fading channel condition less selectedpath numbermay cause larger errorwhen the interpolation offine channel frequency response estimation is conducted forall the data subcarriers Therefore an adaptive path numberselection mechanism is proposed to choose appropriate pathnumber according to the characteristics of time-varyingfading channel The selection procedure of the path numberis described as follows In the first step of the proposedmechanism the pilot signals in the first OFDM data block
Calculations of 119888119901119902ℓ
and 119889119901119902ℓ
for ℓ = 2 3 4
if 1198881199011199022
ge 1198881199011199023
amp 1198881199011199022
ge 1198881199011199024
thenif (119889
1199011199022le 119889
1199011199023|| 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseif (1198891199011199023
le 1198891199011199022
amp 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseℓ = 4
endelseif 119888
1199011199023ge 1198881199011199022
amp 1198881199011199023
ge 1198881199011199024
thenif (119889
1199011199023le 119889
1199011199022|| 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseif (1198891199011199024
le 1198891199011199022
amp 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseℓ = 2
endelse
if (1198891199011199024
le 1198891199011199022
|| 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseif (1198891199011199022
le 1198891199011199023
amp 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseℓ = 3
endend
Algorithm 1 Algorithm of adaptive path number selection mech-anism for 119871 = 4
are used to estimate (h119901119902
)119871times1
In the second step thepreliminary estimates of channel frequency response at pilottones (Hℓ
119901119902)119871times1
for ℓ = 2 3 119871 are obtained from (19)and in the third step the fine correction factors at pilottones (Cℓ
119901119902)119871times1
are obtained from (20) and the fine channelfrequency response estimations (Hℓ
119901119902)119873times1
are determinedby (24) (25) and (26) In the fourth step the estimatedchannel frequency transfer function (Hlong
119901119902 )119873times1
=long119901119902119896
119896 =
0 1 119873 minus 1 obtained from two continuous long trainingsymbols which are defined in [9] is compared with the finechannel estimation for path number selectionThe differencevalues between the fine estimations of channel frequencyresponse (Hℓ)
119873times1and (Hlong
119901119902 )119873times1
= long119901119902119896
119896 = 0 1 119873minus
1 are compared with two times of noise variance of theMIMO-OFDM receiver respectively The total number ofcounts 119888
119901119902ℓwhich satisfy the condition of ℓ
119901119902119896minus
long119901119902119896
lt
21205902
119904is calculated
119888119901119902ℓ
= Num (ℓ
119901119902119896minus
long119901119902119896
lt 21205902
119904(threshold)
for 119896 = 0 1 119873 minus 1)
for ℓ = 2 3 119871
(30)
where 21205902
119904is defined as the threshold of ((Hℓ
119901119902)119873times1
minus
(Hlong119901119902 )
119873times1) With reference to the algorithm of adaptive
path number selection mechanism listed in Algorithm 1
6 International Journal of Antennas and Propagation
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
2 International Journal of Antennas and Propagation
capacity for MIMO-OFDM system operating in frequencyselective fading channel Both perfect interpolation and non-perfect interpolation for pilot-aided channel estimations areconsidered In [7] the sequential decision feedback sequenceestimation with an adaptive threshold equalizer techniqueand pilot tone plus interpolation channel estimation schemeare used to design the Alamouti coded small constellation(BPSK and QPSK) OFDM receiver in fast fading channels
An adaptive path number selection mechanism is pro-posed for channel estimation over MIMO-OFDM fadingchannels to provide the suboptimum system performancewhenever the high order modulation MIMO-OFDM systemis operated either in frequency nonselective fast fading or infrequency selective fast fading channels The 2 times 2 SFBC-OFDM system and a six-path fading channel model areconsidered as an example of the MIMO-OFDM system inthe simulations to prove that the acceptable bit error rate(BER) can be achieved by employing 16-QAM and 64-QAM modulations in time-varying fast fading channelsWe consider the vehicle speed of 200 kmh resulting inthe Doppler frequency of 1093Hz to satisfy the fast fadingcondition for MIMO-OFDM channel [8 9]
The rest of this paper is organized as follows The pro-posed MIMO-OFDM channel estimation algorithm isdescribed in Section 2 where the fine channel estimationfor all data subcarriers is derived The adaptive path numberselection mechanism for the MIMO-OFDM fading channelis presented in Section 3 The BER performance of theMIMO-OFDM system using the proposed suboptimalchannel estimation approach is simulated and discussed inSection 4 Finally concluding remarks are given in Section 5
2 MIMO-OFDM Channel Estimation
We consider a generic downlink multiuser MIMO-OFDMchannel model Let the number of transmit antennas be 119899
119879
and the number of receive antennas 119899119877 One OFDM symbol
of each user is transmitted across 119873 subcarriers To simplifythe formula derivations the data vector X for each user canbe expressed in polyphase representation as
X = [1198830
1198831
sdot sdot sdot 119883119873minus2
119883119873minus1
]119879 (1)
where 119879 denotes the transpose of the vector Thus the demo-dulated signal vector is given by
Y = HX + V (2)
where H is a diagonal matrix whose diagonal elements arethe 119873-DFT of the channel impulse response h and V isthe 119873-DFT of the channel noise With reference to theconventional channel estimation approach of a given OFDMsystem [9] ten short OFDM training signals are used forpacket detection coarse frequency offset estimation andtiming synchronization Two periods of the long trainingsignals are used for improving channel estimation accuracyof the short training symbols A phase-locked loop is adoptedin the receiver for estimating and compensating the carrierfrequency offset Each OFDM data block contains 119871 pilotsubcarriers which are used to track the carrier phase
A typical 2 times 2 SFBC-OFDM model which consists oftwo transmit antennas and two receive antennas is used todescribe the theoretical analysis and the proposed channelestimation scheme User data vector X is first encodedinto two spatial vectors X
1and X
2by the space-frequency
encoder Denote the transmitted signal vector of each user ina space-frequency block as
X1= [119883
0minus 119883
lowast
1sdot sdot sdot 119883
119873minus2minus 119883
lowast
119873minus1]119879
X2= [119883
1119883lowast
0sdot sdot sdot 119883
119873minus1119883lowast
119873minus2]119879
(3)
where X1is the data transmitted from the first antenna 119879119909
1
and X2is the data transmitted from the second antenna 119879119909
2
simultaneously Let X119890and X
119900be even and odd component
vectors of X that is
X119890= [119883
01198832
sdot sdot sdot 119883119873minus4
119883119873minus2
]119879
X119900= [119883
11198833
sdot sdot sdot 119883119873minus3
119883119873minus1
]119879
(4)
Similarly X1119890 X1119900 X2119890 and X
2119900denote even and odd
component vectors ofX1andX
2 respectively which can then
be expressed in terms of even and odd component vectors as
X1119890
= X119890 X
1119900= minusXlowast
119900
X2119890
= X119900 X
2119900= Xlowast
119890
(5)
Note that since the two corresponding signals transmittedfrom two antennas at the same time slots are orthogonal themaximum likelihood decoding is reduced to simple linearprocessing at the receiver The received signal at the receiveris given by
Y1= H
11X1+H
21X2+ V
1
Y2= H
12X1+H
22X2+ V
2
(6)
where Y1and Y
2are the received signals in the first and
second received antenna H11
and H21
are the channel fre-quency response of the first and second antenna transmittedto the first received antenna and H
12and H
22are the
channel frequency response of the first and second antennatransmitted to the second received antenna The channelfrequency response at all data subcarriers for each transmit-receive antenna pair is defined as
H119901119902
=
[[[
[
1198671199011199020
0 sdot sdot sdot 0
0 1198671199011199021
sdot sdot sdot 0
0 0 119867119901119902119873minus1
]]]
]
for 119901 = 1 119899
119879
119902 = 1 119899119877
(7)
Equivalently (6) can be represented as
Y1119890
= H11119890
X1119890
+H21119890
X2119890
+ V1119890
Y1119900
= H11119900
X1119900
+H21119900
X2119900
+ V1119900
Y2119890
= H12119890
X1119890
+H22119890
X2119890
+ V2119890
Y2119900
= H12119900
X1119900
+H22119900
X2119900
+ V2119900
(8)
International Journal of Antennas and Propagation 3
OFDM
transmitter
OFDM
receiver
Least square estimation
MMSEestimation
Path numberselection mechanism
Zeropadding N-FFT
Correction factordetermination
Linearinterpolation
Fine channel estimation for all pilots tones
Adaptive path number selection mechanism
Channel estimator
H11
HNN
HN1
H1N
X1
XN
Y1
YNV
Figure 1 Block diagram of pilot tone channel estimation aided with adaptive path number selection mechanism for MIMO-OFDM fadingchannel
The received signal at the 119902th receive antenna for the 119896thpilot tone transmitted from 119901th antenna can be written as
119884119902119896
= 119883119901119896
119867119901119902119896
+ 119881119902119896 119896 = 0 1 119873 minus 1
119901 = 1 119899119879
119902 = 1 119899119877
(9)
where 119873 is the frequency tones in each OFDM data block119883119901119896
is the transmitted signal of 119901th transmitted antenna119867119901119902119896
is the channel frequency response form 119901th transmitantenna to 119902th receive antenna and 119881
119902119896is the AWGN noise
Then from (9) the channel estimation at pilot subcarriersbased on the least square (LS) algorithm can be obtained as
119871 be the set of 119871 pilot tones which is one of
the sets 119894 119894 + 119873119871 119894 + (119871 minus 1)119873119871 119894 = 0 1 119873119871 minus 1used for transmitting the training data Collect these channelresponses in a vector H
119901119902119896119901
= [1199011199021198961
119901119902119896119871
]119879 which
is obtained from the FFT matrixThe intermediate processing steps between the LS esti-
mates of the channel gains over the pilot subcarriers andinterpolation processing are added in order to ensure ade-quate estimation accuracy for fast fading channel The blockdiagram of the proposed pilot tone channel estimation aidedwith adaptive path number selection mechanism is shown inFigure 1 Here ℓ is defined as the number of dominant pathsestimated from the adaptive channel path number selectorwhich chooses ℓ paths with larger power from (h
119901119902119896119901
)119871times1
and let 119887
1 1198872 119887
ℓ be a set of the selected pilot index Since
AWGN assumption for each subcarrier is adopted and sinceeach pilot tone carries data of constant modulus radic120576
119909 the
minimum mean square error (MMSE) estimation of h119901119902
isgiven by [10]
h119901119902119896119901
= Qminus1119901119902119896119901
H119901119902119896119901
= h119901119902119896119901
+Qminus1119901119902119896119901
1
radic120576119909
S119896119901
(11)
where S119902119896119901
= [1198781199021198961
119878119902119896119871
]119879 (h
119901119902119896119901
)ℓtimes1
= [ℎ1199011199021198961
ℎ1199011199021198962
sdot sdot sdot ℎ119901119902119896ℓ
]119879 and Q
119901119902119896119901
is a Vandermonde matrix withdistinct 119871 twiddle factor119882119896119894
119873
((Q119901119902119896119901
)ℓtimes119871
)
minus1
=
[[[[[[[
[
(119876119901119902119896119901
)
minus1
(1198871 1) (119876
119901119902119896119901
)
minus1
(1198871 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198871 119871)
(119876119901119902119896119901
)
minus1
(1198872 1) (119876
119901119902119896119901
)
minus1
(1198872 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198872 119871)
(119876119901119902119896119901
)
minus1
(119887ℓ 1) (119876
119901119902119896119901
)
minus1
(119887ℓ 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(119887ℓ 119871)
]]]]]]]
]
(12)
Other notations are represented as follows 119864sdot is theexpectation operator trsdot is the trace operator sdot means2-norm I
119871represents the 119871 times 119871 identity matrix Therefore
the mean square error (MSE) in the channel estimate can bederived as
Equations (17) and (18) show that using less pilot numberin the pilot-aided channel estimation can get smaller MSEin the channel impulse response estimate However in thefrequency selective fast fading channel less pilot numbermaycausemore linear interpolation lossThe case of ℓ = 1will notbe considered for path number selection mechanism becauseit cannot reflect the variation of channel characterizationof the frequency selective fading channel The preliminarychannel frequency response estimate (H
119901119902)119873times1
is obtained bythe 119873-FFT of an 119873 times 1 estimated channel impulse response(hℓ119901119902
)119873times1
= [(h119879119901119902
)ℓtimes1
0119879(119873minusℓ)times1
]119879 It can be written as
ℓ
119901119902119896=
1
radic119873
ℓminus1
sum
119899=0
ℎℓ
119901119902(119899)119882
119896119899
119873 119896 = 0 1 119873 minus 1 (19)
The preliminary channel frequency response estimates atpilot tones for 119896 = 119896
1 1198962 119896
119871are Hℓ
119901119902119871times1= [
ℓ
1199011199021198961
ℓ
119901119902119896119871
]119879 The correction factor for fine channel frequency
response estimate at 119896119901th pilot tone is defined as
119862ℓ
119901119902119896119901
=
119901119902119896119901
ℓ
119901119902119896119901
=
(1radic119873)sum119871minus1
119899=0ℎ119901119902 (119899)119882
119896119901119899
119873
(1radic119873)sumℓminus1
119899=0ℎℓ
119901119902(119899)119882
119896119901119899
119873
(20)
For example the fine correction factor at 1198961th pilot tone
for 119871 = 4 and ℓ = 2 is determined as
1198622
1199011199021198961
=
1199011199021198961
2
1199011199021198961
= 1 +
ℎ119901119902 (2)119882
21198961
119873+ ℎ119901119902 (3)119882
31198961
119873
ℎ119901119902 (0) + ℎ
119901119902 (1)1198821198961
119873
(21)
From (21) it is observed that the fine correction factorcan compensate the power loss caused by less path employedin the preliminary channel estimates When the number ofpaths chosen is ℓ the fine correction factor in a vector for 119871pilot tones is
(Cℓ119901119902
)119871times1
= [119862ℓ
1199011199021198961
119862ℓ
119901119902119896119871
]119879
(22)
The fine correction factors for all data subcarriers can beobtained through linear interpolation [11] Two consecutivefine correction factors in 119871 pilot tones are used to determinethe fine correction factors for other data subcarriers that arelocated between the 119896
119901th and 119896
(119901+1)th subcarriers
119862ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901
+ (
119862ℓ
119901119902119896119901+1
minus 119862ℓ
119901119902119896119901
119880) times 119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(23)
The fine channel estimations for all data subcarriers are
ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901+119906
times ℓ
119901119902119896119901+119906
= (
119901119902119896119901
ℓ
119901119902119896119901
+(
(119901119902119896119901+1
ℓ
119901119902119896119901+1
) minus (119901119902119896119901
ℓ
119901119902119896119901
)
119880) times 119906)
times ℓ
119901119902119896119901+119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(24)
where 119880 is the number of data subcarriers between twoadjacent pilot subcarriers The fine channel estimations atpilot tones are expressed as
ℓ
119901119902119896119901
= 119862ℓ
119901119902119896119901
times ℓ
119901119902119896119901
= ℓ
119901119902119896119901
119901 = 1 sim 119871 (25)
International Journal of Antennas and Propagation 5
The fine channel estimations for those data subcarrierslocated in the intervals of (0 119896
Although MSE in channel frequency response estimatedecreases with the path number under the more seriousfrequency selective fading channel condition less selectedpath numbermay cause larger errorwhen the interpolation offine channel frequency response estimation is conducted forall the data subcarriers Therefore an adaptive path numberselection mechanism is proposed to choose appropriate pathnumber according to the characteristics of time-varyingfading channel The selection procedure of the path numberis described as follows In the first step of the proposedmechanism the pilot signals in the first OFDM data block
Calculations of 119888119901119902ℓ
and 119889119901119902ℓ
for ℓ = 2 3 4
if 1198881199011199022
ge 1198881199011199023
amp 1198881199011199022
ge 1198881199011199024
thenif (119889
1199011199022le 119889
1199011199023|| 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseif (1198891199011199023
le 1198891199011199022
amp 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseℓ = 4
endelseif 119888
1199011199023ge 1198881199011199022
amp 1198881199011199023
ge 1198881199011199024
thenif (119889
1199011199023le 119889
1199011199022|| 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseif (1198891199011199024
le 1198891199011199022
amp 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseℓ = 2
endelse
if (1198891199011199024
le 1198891199011199022
|| 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseif (1198891199011199022
le 1198891199011199023
amp 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseℓ = 3
endend
Algorithm 1 Algorithm of adaptive path number selection mech-anism for 119871 = 4
are used to estimate (h119901119902
)119871times1
In the second step thepreliminary estimates of channel frequency response at pilottones (Hℓ
119901119902)119871times1
for ℓ = 2 3 119871 are obtained from (19)and in the third step the fine correction factors at pilottones (Cℓ
119901119902)119871times1
are obtained from (20) and the fine channelfrequency response estimations (Hℓ
119901119902)119873times1
are determinedby (24) (25) and (26) In the fourth step the estimatedchannel frequency transfer function (Hlong
119901119902 )119873times1
=long119901119902119896
119896 =
0 1 119873 minus 1 obtained from two continuous long trainingsymbols which are defined in [9] is compared with the finechannel estimation for path number selectionThe differencevalues between the fine estimations of channel frequencyresponse (Hℓ)
119873times1and (Hlong
119901119902 )119873times1
= long119901119902119896
119896 = 0 1 119873minus
1 are compared with two times of noise variance of theMIMO-OFDM receiver respectively The total number ofcounts 119888
119901119902ℓwhich satisfy the condition of ℓ
119901119902119896minus
long119901119902119896
lt
21205902
119904is calculated
119888119901119902ℓ
= Num (ℓ
119901119902119896minus
long119901119902119896
lt 21205902
119904(threshold)
for 119896 = 0 1 119873 minus 1)
for ℓ = 2 3 119871
(30)
where 21205902
119904is defined as the threshold of ((Hℓ
119901119902)119873times1
minus
(Hlong119901119902 )
119873times1) With reference to the algorithm of adaptive
path number selection mechanism listed in Algorithm 1
6 International Journal of Antennas and Propagation
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
119871 be the set of 119871 pilot tones which is one of
the sets 119894 119894 + 119873119871 119894 + (119871 minus 1)119873119871 119894 = 0 1 119873119871 minus 1used for transmitting the training data Collect these channelresponses in a vector H
119901119902119896119901
= [1199011199021198961
119901119902119896119871
]119879 which
is obtained from the FFT matrixThe intermediate processing steps between the LS esti-
mates of the channel gains over the pilot subcarriers andinterpolation processing are added in order to ensure ade-quate estimation accuracy for fast fading channel The blockdiagram of the proposed pilot tone channel estimation aidedwith adaptive path number selection mechanism is shown inFigure 1 Here ℓ is defined as the number of dominant pathsestimated from the adaptive channel path number selectorwhich chooses ℓ paths with larger power from (h
119901119902119896119901
)119871times1
and let 119887
1 1198872 119887
ℓ be a set of the selected pilot index Since
AWGN assumption for each subcarrier is adopted and sinceeach pilot tone carries data of constant modulus radic120576
119909 the
minimum mean square error (MMSE) estimation of h119901119902
isgiven by [10]
h119901119902119896119901
= Qminus1119901119902119896119901
H119901119902119896119901
= h119901119902119896119901
+Qminus1119901119902119896119901
1
radic120576119909
S119896119901
(11)
where S119902119896119901
= [1198781199021198961
119878119902119896119871
]119879 (h
119901119902119896119901
)ℓtimes1
= [ℎ1199011199021198961
ℎ1199011199021198962
sdot sdot sdot ℎ119901119902119896ℓ
]119879 and Q
119901119902119896119901
is a Vandermonde matrix withdistinct 119871 twiddle factor119882119896119894
119873
((Q119901119902119896119901
)ℓtimes119871
)
minus1
=
[[[[[[[
[
(119876119901119902119896119901
)
minus1
(1198871 1) (119876
119901119902119896119901
)
minus1
(1198871 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198871 119871)
(119876119901119902119896119901
)
minus1
(1198872 1) (119876
119901119902119896119901
)
minus1
(1198872 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(1198872 119871)
(119876119901119902119896119901
)
minus1
(119887ℓ 1) (119876
119901119902119896119901
)
minus1
(119887ℓ 2) sdot sdot sdot (119876
119901119902119896119901
)
minus1
(119887ℓ 119871)
]]]]]]]
]
(12)
Other notations are represented as follows 119864sdot is theexpectation operator trsdot is the trace operator sdot means2-norm I
119871represents the 119871 times 119871 identity matrix Therefore
the mean square error (MSE) in the channel estimate can bederived as
Equations (17) and (18) show that using less pilot numberin the pilot-aided channel estimation can get smaller MSEin the channel impulse response estimate However in thefrequency selective fast fading channel less pilot numbermaycausemore linear interpolation lossThe case of ℓ = 1will notbe considered for path number selection mechanism becauseit cannot reflect the variation of channel characterizationof the frequency selective fading channel The preliminarychannel frequency response estimate (H
119901119902)119873times1
is obtained bythe 119873-FFT of an 119873 times 1 estimated channel impulse response(hℓ119901119902
)119873times1
= [(h119879119901119902
)ℓtimes1
0119879(119873minusℓ)times1
]119879 It can be written as
ℓ
119901119902119896=
1
radic119873
ℓminus1
sum
119899=0
ℎℓ
119901119902(119899)119882
119896119899
119873 119896 = 0 1 119873 minus 1 (19)
The preliminary channel frequency response estimates atpilot tones for 119896 = 119896
1 1198962 119896
119871are Hℓ
119901119902119871times1= [
ℓ
1199011199021198961
ℓ
119901119902119896119871
]119879 The correction factor for fine channel frequency
response estimate at 119896119901th pilot tone is defined as
119862ℓ
119901119902119896119901
=
119901119902119896119901
ℓ
119901119902119896119901
=
(1radic119873)sum119871minus1
119899=0ℎ119901119902 (119899)119882
119896119901119899
119873
(1radic119873)sumℓminus1
119899=0ℎℓ
119901119902(119899)119882
119896119901119899
119873
(20)
For example the fine correction factor at 1198961th pilot tone
for 119871 = 4 and ℓ = 2 is determined as
1198622
1199011199021198961
=
1199011199021198961
2
1199011199021198961
= 1 +
ℎ119901119902 (2)119882
21198961
119873+ ℎ119901119902 (3)119882
31198961
119873
ℎ119901119902 (0) + ℎ
119901119902 (1)1198821198961
119873
(21)
From (21) it is observed that the fine correction factorcan compensate the power loss caused by less path employedin the preliminary channel estimates When the number ofpaths chosen is ℓ the fine correction factor in a vector for 119871pilot tones is
(Cℓ119901119902
)119871times1
= [119862ℓ
1199011199021198961
119862ℓ
119901119902119896119871
]119879
(22)
The fine correction factors for all data subcarriers can beobtained through linear interpolation [11] Two consecutivefine correction factors in 119871 pilot tones are used to determinethe fine correction factors for other data subcarriers that arelocated between the 119896
119901th and 119896
(119901+1)th subcarriers
119862ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901
+ (
119862ℓ
119901119902119896119901+1
minus 119862ℓ
119901119902119896119901
119880) times 119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(23)
The fine channel estimations for all data subcarriers are
ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901+119906
times ℓ
119901119902119896119901+119906
= (
119901119902119896119901
ℓ
119901119902119896119901
+(
(119901119902119896119901+1
ℓ
119901119902119896119901+1
) minus (119901119902119896119901
ℓ
119901119902119896119901
)
119880) times 119906)
times ℓ
119901119902119896119901+119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(24)
where 119880 is the number of data subcarriers between twoadjacent pilot subcarriers The fine channel estimations atpilot tones are expressed as
ℓ
119901119902119896119901
= 119862ℓ
119901119902119896119901
times ℓ
119901119902119896119901
= ℓ
119901119902119896119901
119901 = 1 sim 119871 (25)
International Journal of Antennas and Propagation 5
The fine channel estimations for those data subcarrierslocated in the intervals of (0 119896
Although MSE in channel frequency response estimatedecreases with the path number under the more seriousfrequency selective fading channel condition less selectedpath numbermay cause larger errorwhen the interpolation offine channel frequency response estimation is conducted forall the data subcarriers Therefore an adaptive path numberselection mechanism is proposed to choose appropriate pathnumber according to the characteristics of time-varyingfading channel The selection procedure of the path numberis described as follows In the first step of the proposedmechanism the pilot signals in the first OFDM data block
Calculations of 119888119901119902ℓ
and 119889119901119902ℓ
for ℓ = 2 3 4
if 1198881199011199022
ge 1198881199011199023
amp 1198881199011199022
ge 1198881199011199024
thenif (119889
1199011199022le 119889
1199011199023|| 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseif (1198891199011199023
le 1198891199011199022
amp 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseℓ = 4
endelseif 119888
1199011199023ge 1198881199011199022
amp 1198881199011199023
ge 1198881199011199024
thenif (119889
1199011199023le 119889
1199011199022|| 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseif (1198891199011199024
le 1198891199011199022
amp 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseℓ = 2
endelse
if (1198891199011199024
le 1198891199011199022
|| 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseif (1198891199011199022
le 1198891199011199023
amp 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseℓ = 3
endend
Algorithm 1 Algorithm of adaptive path number selection mech-anism for 119871 = 4
are used to estimate (h119901119902
)119871times1
In the second step thepreliminary estimates of channel frequency response at pilottones (Hℓ
119901119902)119871times1
for ℓ = 2 3 119871 are obtained from (19)and in the third step the fine correction factors at pilottones (Cℓ
119901119902)119871times1
are obtained from (20) and the fine channelfrequency response estimations (Hℓ
119901119902)119873times1
are determinedby (24) (25) and (26) In the fourth step the estimatedchannel frequency transfer function (Hlong
119901119902 )119873times1
=long119901119902119896
119896 =
0 1 119873 minus 1 obtained from two continuous long trainingsymbols which are defined in [9] is compared with the finechannel estimation for path number selectionThe differencevalues between the fine estimations of channel frequencyresponse (Hℓ)
119873times1and (Hlong
119901119902 )119873times1
= long119901119902119896
119896 = 0 1 119873minus
1 are compared with two times of noise variance of theMIMO-OFDM receiver respectively The total number ofcounts 119888
119901119902ℓwhich satisfy the condition of ℓ
119901119902119896minus
long119901119902119896
lt
21205902
119904is calculated
119888119901119902ℓ
= Num (ℓ
119901119902119896minus
long119901119902119896
lt 21205902
119904(threshold)
for 119896 = 0 1 119873 minus 1)
for ℓ = 2 3 119871
(30)
where 21205902
119904is defined as the threshold of ((Hℓ
119901119902)119873times1
minus
(Hlong119901119902 )
119873times1) With reference to the algorithm of adaptive
path number selection mechanism listed in Algorithm 1
6 International Journal of Antennas and Propagation
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
Equations (17) and (18) show that using less pilot numberin the pilot-aided channel estimation can get smaller MSEin the channel impulse response estimate However in thefrequency selective fast fading channel less pilot numbermaycausemore linear interpolation lossThe case of ℓ = 1will notbe considered for path number selection mechanism becauseit cannot reflect the variation of channel characterizationof the frequency selective fading channel The preliminarychannel frequency response estimate (H
119901119902)119873times1
is obtained bythe 119873-FFT of an 119873 times 1 estimated channel impulse response(hℓ119901119902
)119873times1
= [(h119879119901119902
)ℓtimes1
0119879(119873minusℓ)times1
]119879 It can be written as
ℓ
119901119902119896=
1
radic119873
ℓminus1
sum
119899=0
ℎℓ
119901119902(119899)119882
119896119899
119873 119896 = 0 1 119873 minus 1 (19)
The preliminary channel frequency response estimates atpilot tones for 119896 = 119896
1 1198962 119896
119871are Hℓ
119901119902119871times1= [
ℓ
1199011199021198961
ℓ
119901119902119896119871
]119879 The correction factor for fine channel frequency
response estimate at 119896119901th pilot tone is defined as
119862ℓ
119901119902119896119901
=
119901119902119896119901
ℓ
119901119902119896119901
=
(1radic119873)sum119871minus1
119899=0ℎ119901119902 (119899)119882
119896119901119899
119873
(1radic119873)sumℓminus1
119899=0ℎℓ
119901119902(119899)119882
119896119901119899
119873
(20)
For example the fine correction factor at 1198961th pilot tone
for 119871 = 4 and ℓ = 2 is determined as
1198622
1199011199021198961
=
1199011199021198961
2
1199011199021198961
= 1 +
ℎ119901119902 (2)119882
21198961
119873+ ℎ119901119902 (3)119882
31198961
119873
ℎ119901119902 (0) + ℎ
119901119902 (1)1198821198961
119873
(21)
From (21) it is observed that the fine correction factorcan compensate the power loss caused by less path employedin the preliminary channel estimates When the number ofpaths chosen is ℓ the fine correction factor in a vector for 119871pilot tones is
(Cℓ119901119902
)119871times1
= [119862ℓ
1199011199021198961
119862ℓ
119901119902119896119871
]119879
(22)
The fine correction factors for all data subcarriers can beobtained through linear interpolation [11] Two consecutivefine correction factors in 119871 pilot tones are used to determinethe fine correction factors for other data subcarriers that arelocated between the 119896
119901th and 119896
(119901+1)th subcarriers
119862ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901
+ (
119862ℓ
119901119902119896119901+1
minus 119862ℓ
119901119902119896119901
119880) times 119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(23)
The fine channel estimations for all data subcarriers are
ℓ
119901119902119896119901+119906
= 119862ℓ
119901119902119896119901+119906
times ℓ
119901119902119896119901+119906
= (
119901119902119896119901
ℓ
119901119902119896119901
+(
(119901119902119896119901+1
ℓ
119901119902119896119901+1
) minus (119901119902119896119901
ℓ
119901119902119896119901
)
119880) times 119906)
times ℓ
119901119902119896119901+119906
119901 = 1 sim 119871 minus 1 119906 = 1 2 119880 minus 1
(24)
where 119880 is the number of data subcarriers between twoadjacent pilot subcarriers The fine channel estimations atpilot tones are expressed as
ℓ
119901119902119896119901
= 119862ℓ
119901119902119896119901
times ℓ
119901119902119896119901
= ℓ
119901119902119896119901
119901 = 1 sim 119871 (25)
International Journal of Antennas and Propagation 5
The fine channel estimations for those data subcarrierslocated in the intervals of (0 119896
Although MSE in channel frequency response estimatedecreases with the path number under the more seriousfrequency selective fading channel condition less selectedpath numbermay cause larger errorwhen the interpolation offine channel frequency response estimation is conducted forall the data subcarriers Therefore an adaptive path numberselection mechanism is proposed to choose appropriate pathnumber according to the characteristics of time-varyingfading channel The selection procedure of the path numberis described as follows In the first step of the proposedmechanism the pilot signals in the first OFDM data block
Calculations of 119888119901119902ℓ
and 119889119901119902ℓ
for ℓ = 2 3 4
if 1198881199011199022
ge 1198881199011199023
amp 1198881199011199022
ge 1198881199011199024
thenif (119889
1199011199022le 119889
1199011199023|| 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseif (1198891199011199023
le 1198891199011199022
amp 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseℓ = 4
endelseif 119888
1199011199023ge 1198881199011199022
amp 1198881199011199023
ge 1198881199011199024
thenif (119889
1199011199023le 119889
1199011199022|| 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseif (1198891199011199024
le 1198891199011199022
amp 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseℓ = 2
endelse
if (1198891199011199024
le 1198891199011199022
|| 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseif (1198891199011199022
le 1198891199011199023
amp 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseℓ = 3
endend
Algorithm 1 Algorithm of adaptive path number selection mech-anism for 119871 = 4
are used to estimate (h119901119902
)119871times1
In the second step thepreliminary estimates of channel frequency response at pilottones (Hℓ
119901119902)119871times1
for ℓ = 2 3 119871 are obtained from (19)and in the third step the fine correction factors at pilottones (Cℓ
119901119902)119871times1
are obtained from (20) and the fine channelfrequency response estimations (Hℓ
119901119902)119873times1
are determinedby (24) (25) and (26) In the fourth step the estimatedchannel frequency transfer function (Hlong
119901119902 )119873times1
=long119901119902119896
119896 =
0 1 119873 minus 1 obtained from two continuous long trainingsymbols which are defined in [9] is compared with the finechannel estimation for path number selectionThe differencevalues between the fine estimations of channel frequencyresponse (Hℓ)
119873times1and (Hlong
119901119902 )119873times1
= long119901119902119896
119896 = 0 1 119873minus
1 are compared with two times of noise variance of theMIMO-OFDM receiver respectively The total number ofcounts 119888
119901119902ℓwhich satisfy the condition of ℓ
119901119902119896minus
long119901119902119896
lt
21205902
119904is calculated
119888119901119902ℓ
= Num (ℓ
119901119902119896minus
long119901119902119896
lt 21205902
119904(threshold)
for 119896 = 0 1 119873 minus 1)
for ℓ = 2 3 119871
(30)
where 21205902
119904is defined as the threshold of ((Hℓ
119901119902)119873times1
minus
(Hlong119901119902 )
119873times1) With reference to the algorithm of adaptive
path number selection mechanism listed in Algorithm 1
6 International Journal of Antennas and Propagation
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
Although MSE in channel frequency response estimatedecreases with the path number under the more seriousfrequency selective fading channel condition less selectedpath numbermay cause larger errorwhen the interpolation offine channel frequency response estimation is conducted forall the data subcarriers Therefore an adaptive path numberselection mechanism is proposed to choose appropriate pathnumber according to the characteristics of time-varyingfading channel The selection procedure of the path numberis described as follows In the first step of the proposedmechanism the pilot signals in the first OFDM data block
Calculations of 119888119901119902ℓ
and 119889119901119902ℓ
for ℓ = 2 3 4
if 1198881199011199022
ge 1198881199011199023
amp 1198881199011199022
ge 1198881199011199024
thenif (119889
1199011199022le 119889
1199011199023|| 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseif (1198891199011199023
le 1198891199011199022
amp 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseℓ = 4
endelseif 119888
1199011199023ge 1198881199011199022
amp 1198881199011199023
ge 1198881199011199024
thenif (119889
1199011199023le 119889
1199011199022|| 1198891199011199023
le 1198891199011199024
) then ℓ = 3
elseif (1198891199011199024
le 1198891199011199022
amp 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseℓ = 2
endelse
if (1198891199011199024
le 1198891199011199022
|| 1198891199011199024
le 1198891199011199023
) then ℓ = 4
elseif (1198891199011199022
le 1198891199011199023
amp 1198891199011199022
le 1198891199011199024
) then ℓ = 2
elseℓ = 3
endend
Algorithm 1 Algorithm of adaptive path number selection mech-anism for 119871 = 4
are used to estimate (h119901119902
)119871times1
In the second step thepreliminary estimates of channel frequency response at pilottones (Hℓ
119901119902)119871times1
for ℓ = 2 3 119871 are obtained from (19)and in the third step the fine correction factors at pilottones (Cℓ
119901119902)119871times1
are obtained from (20) and the fine channelfrequency response estimations (Hℓ
119901119902)119873times1
are determinedby (24) (25) and (26) In the fourth step the estimatedchannel frequency transfer function (Hlong
119901119902 )119873times1
=long119901119902119896
119896 =
0 1 119873 minus 1 obtained from two continuous long trainingsymbols which are defined in [9] is compared with the finechannel estimation for path number selectionThe differencevalues between the fine estimations of channel frequencyresponse (Hℓ)
119873times1and (Hlong
119901119902 )119873times1
= long119901119902119896
119896 = 0 1 119873minus
1 are compared with two times of noise variance of theMIMO-OFDM receiver respectively The total number ofcounts 119888
119901119902ℓwhich satisfy the condition of ℓ
119901119902119896minus
long119901119902119896
lt
21205902
119904is calculated
119888119901119902ℓ
= Num (ℓ
119901119902119896minus
long119901119902119896
lt 21205902
119904(threshold)
for 119896 = 0 1 119873 minus 1)
for ℓ = 2 3 119871
(30)
where 21205902
119904is defined as the threshold of ((Hℓ
119901119902)119873times1
minus
(Hlong119901119902 )
119873times1) With reference to the algorithm of adaptive
path number selection mechanism listed in Algorithm 1
6 International Journal of Antennas and Propagation
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
The number of paths can be adaptively selected for thelargest 119888
119901119902ℓand the smallest 119889
119901119902ℓin the first OFDM data
block or in each of the OFDM data blocks
4 Simulation Results
The function of the proposed adaptive path number selectionmechanism is simulated in MIMO-OFDM fading channelThe features for a mobile OFDM system include a bandwidthof 10MHz and 64 subcarriers the measured signal interval119879119898
= packet time = 840 120583sec Each transmitted packetcontains 100 OFDM data blocks the path number selectionsare conducted at the first data blocks Four equally spacedpilot subcarriers which are inserted in the positions of 8th24th 40th and 56th subcarriers in an OFDM data block areapplied for each of the transmitted OFDM data blocks Thesix-path channel model listed in Table 1 where the first threepaths have no path delay and the interpath delay time afterpath three is 50 nsec is employed to simulate mobile OFDMperformance so that 119871 = 4
Two-ray Rayleigh fading channel and six-path fadingchannel with 13 nsec delay spread are used to test the biterror rate (BER) performance of the OFDM transceiver InFigure 2 two-ray Rayleigh fading channel is used to validatesix-path fading channel with 13 nsec delay spread Figure 2(a)shows the BER performance of OFDM transceiver using 16-QAM Figure 2(b) shows the BER performance of OFDMtransceiver using 64-QAM For demonstration we have cho-sen 120 kmhr and 200 kmhr performance for high speedthat is 200 kmhr seems to degrade than the performance forsystem with less speed that is 120 kmhr because at higherspeed the channel behaves as a fast fading channel and forslower speed channel behaves as a slow fading channel [8]The test results show that the BER performance of the OFDMtransceiver in the high-speed time-varying fading channelwill be reduced to less than 10minus5 at the minimum SNR of12 dB for 16-QAM and 28 dB for 64-QAM at 120Kmhr For200Kmhr user speed the performance of 64-QAM OFDM
transceiver over six-path fading channel with 13 nsec delayspread degrades to unacceptable levels
For the purpose of the diversity gain a simple 2 times 2 SFBCis combined with the OFDM system where the adaptivepath number selection mechanism is employed for eachtransmit-receive antenna pair Let two frequency-domaindata signals at two consecutive subcarriers be encoded usingAlamouti code and transmitted from two antennas Since thechannel response for that subcarrier within one SFBC blockis stationary then the maximum-likelihood symbol detectoris used to detect the transmitted symbols
The BER performance of the 2 times 2 SFBC-OFDM systemin terms of 16-QAM and 64-QAMmodulations over the six-path fading channel with 13 nsec and 26 nsec delay spreadis shown in Figures 3 and 4 respectively where the userspeed is set as 200 kmh The calculations of 13 nsec and26 nsec root mean square (rms) delay spread are shown inthe appendix For OFDM system the channel is frequencynonselective fading if the delay spread is in the range of(0 20 nsec) and the channel is frequency selective fadingif the delay spread exceeds 20 nsec [8] It is observed thatthe acceptable BER (lt10minus5) for QAM modulated MIMO-OFDM systems operated in fast-varying fading channels canalways be achieved by employing the proposed path numberselection mechanism In Figure 4(a) the BER value of the16-QAM modulated MIMO-OFDM systems employing theproposed path number selection mechanism over frequencynonselective fast fading channels with 13 nsec delay spreadis lower than ℓ = 4 and slightly higher than ℓ = 2 and 3in the region of interest (BER lt 10
minus5) The required 119864
1198871198730
for the acceptable BER is low for all cases It indicates thatthe MIMO mode is not necessary to be used for the 16-QAM OFDM systems when the delay spread is small InFigure 4(b) the gain of the 64-QAM modulated MIMO-OFDM system employed the proposed adaptive path numberselection mechanism in frequency nonselective fast fadingchannel with 13 nsec delay spread exceeds 1 dB comparedwith ℓ = 4 and its BER value is slightly higher than ℓ = 2
and 3 in the region of interest In frequency nonselective fastfading channel choosing smaller number of paths can getthe smaller mean square error in channel impulse responseestimate Figure 4 shows that the BER value of the QAMmodulated MIMO-OFDM systems employing the proposedpath number selection mechanism over frequency selectivefast fading channels with 26 nsec delay spread is lower thanℓ = 2 and 3 and slightly higher than ℓ = 4 in the region
International Journal of Antennas and Propagation 7
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
Figure 2 BER of the OFDM transceiver over two-ray Rayleigh fading channel and six-path fading channel with 13 nsec delay spread for (a)16-QAM and (b) 64-QAM
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10 12EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 3 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
of interest The error floors of the BER performance appearat an 119864
1198871198730of about 8 dB for 16-QAM (curve ℓ = 2) and
about 15 dB for 64-QAM (curves ℓ = 2 and 3) respectivelyThe frequency selectivity of the multipath fading channelincreases with its delay spread In a frequency selective fastfading channel the BER of the MIMO-OFDM decreaseswith an increase of the path number due to more linear
interpolation loss are generated by using less path number infrequency selective fast fading channel By examining Figures3 and 4 it is concluded that the pilot-based channel estimateusing the proposed path number selection mechanism at thefirst data block can satisfy the OFDM system performancerequirements under different operating conditions of time-varying fast fading channels
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
8 International Journal of Antennas and Propagation
EbN0 (dB)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 4 BER performance of 2 times 2 SFBC-OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAMmodulation and (b) 64-QAMmodulation
BER
10minus6
10minus5
10minus4
10minus3
10minus2
10minus1
100
0 2 4 6 8 10EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
5 10 15 20
BER
10minus6
10minus4
10minus2
100
0EbN0 (dB)
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 5 BER performance of OFDM system over the six-path fading channel with 13 nsec delay spread for (a) 16-QAMmodulation and (b)64-QAMmodulation
In Figure 5 the BER value of theQAMmodulatedOFDMsystem employing the proposed path selection mechanismover time-varying fading channels with 13 ns delay spread islower than ℓ = 4 and slightly higher than ℓ = 2 and 3
Figure 6 shows that the BER value of the QAM modu-lated OFDM systems employing the proposed path selectionmechanism over time-varying fading channels with 26 nsdelay spread is lower than ℓ = 2 and 3 and slightly higher
than ℓ = 4 The frequency selectivity of the multipath fadingchannel increases with its delay spread
5 Conclusions
An adaptive path number selection mechanism is proposedto improve the accuracy of the pilot-based channel estima-tion approach for QAM modulated MIMO-OFDM systems
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
International Journal of Antennas and Propagation 9
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(a)
BER
10minus6
10minus7
10minus5
10minus4
10minus3
10minus2
10minus1
100
EbN0 (dB)0 5 10 15 20 25
Path selection985747 = 4
985747 = 3
985747 = 2
(b)
Figure 6 BER performance of OFDM system over the six-path fading channel with 26 nsec delay spread for (a) 16-QAM modulation and(b) 64-QAMmodulation
operating in time-varying fast fading channels The finecorrection factors are derived It is demonstrated that thenumber of paths is scalable and adaptively changed withthe characteristics of time-varying MIMO-OFDM fadingchannels to provide a suboptimum BER performance forQAMmodulated 2times 2 SFBC-OFDM systems operated eitherin frequency nonselective fast fading or in frequency selectivefast fading channels
Appendix
Calculations of Delay Spread 26 nsecand 13 nsec [8]
The fading channel generator at the 119894th path consists of twononline-of-sight (NLOS) branches and a LOS branch InNLOS branch two independent and identically distributed(iid) Gaussian signal sources are connected to identicalDoppler filters The channel weighing factor 119908
119894[1198961015840] is deter-
mined by
119908119894 [119896] = 119875
119894(119904119894 NLOS [119896] + 119904
119894 LOS [119896]) 119896 = 1 2 119873
(A1)
where the output of NLOS branch at the 119894th path in the fadingchannel weighing generator is
119904119894 NLOS [119896] = 119910
119894 [119896] times (1
radic1 + 119896119894
) 119896 = 1 2 119873
(A2)
where
119910119894 [119896] = (
infin
sum
119897=minusinfin
1199091 [119897] ℎ119894 [119896 minus 119897]) + 119895(
infin
sum
119897=minusinfin
1199092 [119897] ℎ119894 [119896 minus 119897])
119896 = 1 2 119873
(A3)
1199091and 119909
2are independent Gaussian functions and ℎ
119894is
impulse response of Doppler filterThe output of LOS branchat 119894th path in the fading channel weighing generator is
119904119894LOS
[119896] = radic119896119894
1 + 119896119894
times exp(1198952120587 (119891119889119894
cos 120579119894+ 119891119900119894
)119896
119891119904dop
)
119896 = 1 2 119873
(A4)
Furthermore 119908119894[119896] is interpolated by factor 119868 to get the
sequence V119894[1198961015840] with sampling rate 119891sig = 119868 times 119891
119904dop
V119894[1198961015840] =
119908119894[1198961015840
119868] 119896
1015840= 119868 2119868 119873119868
0 otherwise(A5)
The image signal of V119894[1198961015840] is removed by an interpolation
low pass filter with unit impulse response ℎ119868[1198961015840]The interpo-
lated fading envelop signal 119903119894[1198961015840] is stored in the register bank
as
119903119894[1198961015840] =
infin
sum
119897=minusinfin
V119894 [119897] ℎ119868 [119896 minus 119897] 119896
1015840= 1 2 119873119868 (A6)
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
10 International Journal of Antennas and Propagation
where the sampling interval of 119903119894[1198961015840] is
Δ119905 =1
119891sig (A7)
The parameters listed in Table 1 represent for rms delayspread 120591rms = 23 nsec As an example steps involved in thecalculation of 120591rms = 23 nsec using the values in Table 1will be shown From Table 1 the Tap powers (119875
119894) are 0 dB
minus65 dBminus144 dB andminus175 dB at Excess delay 0 nsec 50 nsec100 nsec and 150 nsec respectively We first normalize theseTap powers to get values 09751W 02183W 00354Wand 00173W at Excess delay 0 nsec 50 nsec 100 nsec and150 nsec respectively
Normalized tap delay powers are weighed using weighingfactor 119908
119894[1198961015840] As an example if weighing factors were found
to be 07099ndash04263i minus06830ndash03211i minus0393ndash04039i andminus00443ndash00841i for excess delay at 0 ns 50 ns 100 ns and150 ns respectively Taking the absolute values for the tapdelay power and the weighing factor we get final tap powers08074 01648 00200 and 00016 at Excess delay 0 nsec50 nsec 100 nsec and 150 nsec respectively thus calculatingrms delay spread using (A8) [12]
120591drms =radic1205912minus (120591)
2 (A8)
where the mean excess delay 120591 is defined as
120591 =sum1198961198862
119896120591119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 120591119896
sum119896119875 (120591
119896)
(A9)
and 1205912 is defined as
1205912=
sum1198961198862
1198961205912
119896
sum1198961198862
119896
=sum119896119875 (120591
119896) 1205912
119896
sum119896119875 (120591
119896)
(A10)
Similarly tap powers 0 db minus185 dB minus214 dB and minus245 dBfor Excess delay 0 ns 50 ns 100 ns and 150 ns respectivelyfor 120591rms = 13 nsec and tap powers 0 db minus65 dB minus75 dB andminus85 dB for Excess delay 0 ns 50 ns 100 ns and 150 ns respec-tively for 120591rms = 26 nsec
Acknowledgment
This work is supported in part by research grants fromNational ScienceCouncil Taiwan (NSC 102-2218-E-155-001)
References
[1] S R Saunders and A A Zavala Antennas and Propagationfor Wireless Communication Systems John Wiley amp Sons 2ndedition 2007
[2] T D Chiueh and P Y TsaiOFDMBaseband Receiver Design forWireless Communications John Wiley amp Sons 2007
[3] J Chen Y Tang and S Li ldquoAnalysis and optimization ofpilot-symbol-assisted M-OAM for OFDM systemsrdquo WirelessCommunications and Mobile Computing vol 5 no 1 pp 15ndash222005
[4] O Simeone Y Bar-Ness and U Spagnolini ldquoPilot-basedchannel estimation for OFDM systems by tracking the delay-subspacerdquo IEEE Transactions on Wireless Communications vol3 no 1 pp 315ndash325 2004
[5] M Torabi S Aıssa and M R Soleymani ldquoOn the BERperformance of space-frequency block coded OFDM systemsin fading MIMO channelsrdquo IEEE Transactions on WirelessCommunications vol 6 no 4 pp 1366ndash1373 2007
[6] I Cosovic and G Auer ldquoCapacity of MIMO-OFDM withpilot-aided channel estimationrdquo Eurasip Journal on WirelessCommunications and Networking vol 2007 Article ID 324602007
[7] J Kim R W Heath Jr and E J Powers ldquoReceiver designs forAlamouti coded OFDM systems in fast fading channelsrdquo IEEETransactions onWireless Communications vol 4 no 2 pp 550ndash559 2005
[8] J Mar C-C Kuo Y-R Lin and T-H Lung ldquoDesign ofsoftware-defined radio channel simulator for wireless commu-nications case study with DSRC and UWB channelsrdquo IEEETransactions on Instrumentation and Measurement vol 58 no8 pp 2755ndash2766 2009
[9] ldquoStandard Specification for Telecommunications and Infor-mation Exchange Between Roadside and Vehicle Systemmdash5Ghz Band Dedicated Short Range Communications (DSRC)Medium Access Control (MAC) and Physical Layer (PHY)Specificationsrdquo IEEE 802 December 2005
[10] R Negi and J Cioffi ldquoPilot tone selection for channel estimationin a mobile ofdm systemrdquo IEEE Transactions on ConsumerElectronics vol 44 no 3 pp 1122ndash1128 1998
[11] J Rinne and M Renfors ldquoPilot spacing in Orthogonal Fre-quency Division Multiplexing systems on practical channelsrdquoIEEE Transactions on Consumer Electronics vol 42 no 4 pp959ndash962 1996
[12] T S RappaportWireless Communications Principles and Prac-tice Prentice Hall 2nd edition 2002
