2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications Coded Modulation in UWB Communications Yafei Tian and Chenyang Yang School of Electronics and Information Engineering, Beihang University 37 Xueyuan Road, Haidian District, Beijing, P. R. China 100083 Email: {ytian, cyyang}@buaa.edu.cn Abstract- Exploiting the abundant freedom of UWB signals can increase the Euclidean distance among codewords which will lead to an enhancement of the communication quality. In this paper, a coded modulation UWB system combining PPM, PAM and convolutional coding is proposed, which can significantly in- crease the power efficiency without degrading the data rate. The performance of this coded modulation system primarily depends on the free Euclidean distance and the number of corresponding error bits induced by the error paths. The code generator with maximal minimum free distance and minimum error bits is found to optimize the system. In order to avoid the difficulty of channel estimation and accurate time synchronization in rich multipath environments, a joint multiple symbol detector and decoder for the coded modulation system is presented which is able to approximate the performance of uncoded PPM system in AWGN channel under viable computational burden. Simulation results obtained from Nakagami multipath channel agree with our analysis. I. INTRODUCTION UWB communication systems are power-limited, hence spectrum efficiency could be sacrificed to exchange power efficiency. PPM and PAM are popular in IR-UWB schemes due to their feasibility [11 [2] but it is difficult for them to build a power efficient system. Although M-ary PPM itself can achieve the Eb/No limit with infinite bandwidth and asymptotic large number of A1 [3], a more realistic way to improve the power efficiency is to enlarge the Euclidean distance among transmitted codewords. Moreover, data rate and error rate can be traded off more easily with the increasing of the dimension of signal space, since for the same distance more codewords can be selected from the expanded signal space. In this paper, we propose a coded modulation scheme to expand the signal space and increase the codeword distance simultaneously. Coded modulation is first developed in TCM system, instead of designing the encoder and the modulator indepen- dently, it jointly designs them for enlarging the Euclidean distance of transmitted symbols. Therefore, in the bandwidth limited channel it can improve the power efficiency only by increasing the number of signal points in the constellation. Though borrowing its basic idea, our coded modulation is different from TCM that what we increased is signal po- larity by replacing PPM with PPAM, a modulation scheme combining PPM and PAM proposed in [4], while in TCM it is the levels/phases that are increased. Therefore, some of the fully-explored methods in TCM, such as mapping by set partitioning, are not applicable to our system. In this paper, we will look for the optimal coded modulation generators through computer search in terms of the mapping rules we defined. In AWGN channel, the coded modulation signal can be demodulated using Viterbi algorithm, however in the practical UWB channel, which has rich multipath components and each component has extremely low SNR, the channel estimation and precise time synchronization are challenging. It is well known that differential demodulation is often used to avoid channel estimation, but it induces performance degradation compared with coherent demodulation. To improve the per- formance of differential demodulation, [5] introduced a con- cept of multiple symbol differential demodulation. Applying the relative information among multiple successive symbols, MPSK signals corrupted by AWGN can be demodulated with the performance approaching coherent demodulation. Inspired by this idea, [6] presented a multiple symbol detection (MSD) method for PPM signal in rich multipath channels. By exploit- ing the coherence of channel in short block, this method can achieve the performance of known channel without explicit channel estimation and accurate time synchronization. In the MSD, a signal vector is formed with samples starting from the assumed position of the transmitted pulse in each symbol, and a Frobenius norm is calculated according to the sum of these vectors of different symbols. The components of the vectors will mutual enhance if the assumed positions are correct, in the contrast they will mutual eliminate if some of the assumptions are wrong, since the multipath components can be reasonably supposed as independent from each other in UWB channels. Consequently, the norm of sum vector can be used as a metric to pick out the proper position assumptions of the transmitted pulses. To reduce the complexity of MSD algorithm while inherit its merit, we generalize it in this paper to accommodate PPAM signals, and implement the joint detector and decoder with a modified Viterbi algorithm. Since there exists one to one mapping between the uncoded bit sequence and the modulated signal, the received multipath signals can be de- coded into the information bits directly. In the trellis of the joint decoder, every path is an assumption of the transmitted sequence. From the position supposed by current branch we can form a vector from the samples of received signals, and the branch metric is obtained by multiplying a sign on the vector according to the supposed amplitude. Path metric is then calculated as the Frobenius norm of the summation of the branch metrics, and the path which makes the metric maximum will be the survivor. By employing equal gain combining in 978-3-8007-2909-8/05/$20.00 @2005 IEEE 491
Transcript
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
Coded Modulation in UWB CommunicationsYafei Tian and Chenyang Yang
School of Electronics and Information Engineering, Beihang University37 Xueyuan Road, Haidian District, Beijing, P. R. China 100083
Email: {ytian, cyyang}@buaa.edu.cn
Abstract- Exploiting the abundant freedom of UWB signalscan increase the Euclidean distance among codewords which willlead to an enhancement of the communication quality. In thispaper, a coded modulation UWB system combining PPM, PAMand convolutional coding is proposed, which can significantly in-crease the power efficiency without degrading the data rate. Theperformance of this coded modulation system primarily dependson the free Euclidean distance and the number of correspondingerror bits induced by the error paths. The code generator withmaximal minimum free distance and minimum error bits isfound to optimize the system. In order to avoid the difficultyof channel estimation and accurate time synchronization in richmultipath environments, a joint multiple symbol detector anddecoder for the coded modulation system is presented which isable to approximate the performance of uncoded PPM system inAWGN channel under viable computational burden. Simulationresults obtained from Nakagami multipath channel agree withour analysis.
I. INTRODUCTION
UWB communication systems are power-limited, hencespectrum efficiency could be sacrificed to exchange powerefficiency. PPM and PAM are popular in IR-UWB schemesdue to their feasibility [11 [2] but it is difficult for them tobuild a power efficient system. Although M-ary PPM itselfcan achieve the Eb/No limit with infinite bandwidth andasymptotic large number of A1 [3], a more realistic wayto improve the power efficiency is to enlarge the Euclideandistance among transmitted codewords. Moreover, data rateand error rate can be traded off more easily with the increasingof the dimension of signal space, since for the same distancemore codewords can be selected from the expanded signalspace. In this paper, we propose a coded modulation schemeto expand the signal space and increase the codeword distancesimultaneously.
Coded modulation is first developed in TCM system,instead of designing the encoder and the modulator indepen-dently, it jointly designs them for enlarging the Euclideandistance of transmitted symbols. Therefore, in the bandwidthlimited channel it can improve the power efficiency only byincreasing the number of signal points in the constellation.Though borrowing its basic idea, our coded modulation isdifferent from TCM that what we increased is signal po-larity by replacing PPM with PPAM, a modulation schemecombining PPM and PAM proposed in [4], while in TCMit is the levels/phases that are increased. Therefore, some ofthe fully-explored methods in TCM, such as mapping by setpartitioning, are not applicable to our system. In this paper, we
will look for the optimal coded modulation generators throughcomputer search in terms of the mapping rules we defined.
In AWGN channel, the coded modulation signal can bedemodulated using Viterbi algorithm, however in the practicalUWB channel, which has rich multipath components and eachcomponent has extremely low SNR, the channel estimationand precise time synchronization are challenging. It is wellknown that differential demodulation is often used to avoidchannel estimation, but it induces performance degradationcompared with coherent demodulation. To improve the per-formance of differential demodulation, [5] introduced a con-cept of multiple symbol differential demodulation. Applyingthe relative information among multiple successive symbols,MPSK signals corrupted by AWGN can be demodulated withthe performance approaching coherent demodulation. Inspiredby this idea, [6] presented a multiple symbol detection (MSD)method for PPM signal in rich multipath channels. By exploit-ing the coherence of channel in short block, this method canachieve the performance of known channel without explicitchannel estimation and accurate time synchronization. In theMSD, a signal vector is formed with samples starting from theassumed position of the transmitted pulse in each symbol, anda Frobenius norm is calculated according to the sum of thesevectors of different symbols. The components of the vectorswill mutual enhance if the assumed positions are correct, in thecontrast they will mutual eliminate if some of the assumptionsare wrong, since the multipath components can be reasonablysupposed as independent from each other in UWB channels.Consequently, the norm of sum vector can be used as a metricto pick out the proper position assumptions of the transmittedpulses.
To reduce the complexity of MSD algorithm while inheritits merit, we generalize it in this paper to accommodatePPAM signals, and implement the joint detector and decoderwith a modified Viterbi algorithm. Since there exists oneto one mapping between the uncoded bit sequence and themodulated signal, the received multipath signals can be de-coded into the information bits directly. In the trellis of thejoint decoder, every path is an assumption of the transmittedsequence. From the position supposed by current branch wecan form a vector from the samples of received signals, andthe branch metric is obtained by multiplying a sign on thevector according to the supposed amplitude. Path metric isthen calculated as the Frobenius norm of the summation of thebranch metrics, and the path which makes the metric maximumwill be the survivor. By employing equal gain combining in
978-3-8007-2909-8/05/$20.00 @2005 IEEE 491
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
among adjacent symbols we suppose T, > MTp + Td. whereAl - 29-1 and Td is the maximal multipath delay. Theexpression of the transmitted signal is then
x(t) = Z an E8(t - nT, -dTp),n
PPM
Fig. 1. Coded modulation system diagram
the procedure of path metric calculation, the fertile diversityinformation embedded in UWB channel is exploited, and sincethe distances among codewords has been enlarged by codedmodulation, the scheme proposed in this paper can achievesuperior performance without the needs of channel estimationand fine timing.
The remainder of this paper is organized as follows. Insection II, coded modulation scheme and the search procedureof optimal code generator is described. In section III, a jointdetection and decoder for the signal received in multipathchannel is provided. The simulation results and comparisonsare presented in section IV and the conclusions are given inthe last section.
II. CODED MODULATION
A. System DescriptionA natural way to modulate ultra-short impulse is to
modulate its position and polarity. That means only one bitis needed to modulate the amplitude, and the others are usedto modulate the position. To keep the same data rate withuncoded PPM system, we choose the rate of convolutionalcoding as (m-1)/m. A system diagram of 2/3 rate is depictedin figure 1, in which the encoder is introduced from [7]. Theconstraint length is K = 2 and each time 2 bits are shiftedinto the registers, the generators are
gl = [1011], g2 = [1101], g3 [1010].
The octal form of which are (13,15,12).Define the m - 1 uncoded bits of the nth symbol as
bn = [bo. bm-2]
After coding the m bits are
Cn = [Co * * * Cm-I]
Then after modulation, the amplitude of the pulse is
an = 1 -2co
and the position is
dn = bi2de( [cl Cm,]),where function bi2de(.) changes the binary number to decimalnumber.
Define the duration of a symbol as T8, the duration of a
transmitted pulse as Tp. To avoid the multipath interference
where 0(t) denotes transmitted pulse and its energy has beennormalized.
In this section only AWGN channel is considered and themultipath channel will be tackled in next section, so with thisassumption the received signal is
r(t) =, an E8,(t-nT. - dnTp) + z(t), (2)
n
where z(t) indicates additive white Gaussian noise with zero
mean and variance a2 =NAfter matched filter and A/D convertor, the jth sample
of the nth symbol can be expressed as
r,=ann Es(j - dn) + -i 1 (3)
where 6(j) is the Dirac function.We know that if the transmitted signal is modulated by
BPSK, the soft decision Viterbi decoder is actually the jointdemodulator and decoder. Even though our modulation methodis different from BPS K, we only need few modifications on thecalculation of branch metric to accommodate PPAM signals.In the decoder trellis, suppose the transmitted coded sequence
on the nth branch of the ith path is cn(), and the amrlitudeand position of the modulated signal are a.i and d(i), thenthe branch metric is changed to be
(I) = a rd( ) (4)
From (3) we know that, when the assumed amplitude andposition are both correct, i.e., d(') dn and a(') = an, thenAn -= /E + a) zj. Otherwise, if the amplitude is wrong,then ,u(i) -VEg + an)zj, or if the position is wrong, thenM= a(i)zj. Define the metric of the whole path as
(5)PM (i) =(),n
then only both correct assumptions of position and amplitudecan fortify the path metric successively. Therefore, when allthe signal is arrived, the uncoded bit sequence correspondingto the path with highest metric should be the estimate of thetransmitted information bits.
B. Code GeneratorIt is shown from figure 1 that all the characteristics of
convolutional coding depend on the polynomial generators,and it is the polynomials which determine the system perfor-mance. Usually, the performance of convolutional coding isstudied through the minimum free distance dfree, which isdefined as the minimum distance between two paths divergedfrom one state and merged to the same state again. Because ofthe linearity, we only count the minimum distance between theall zero path and any other possible paths from zero state to
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
TABLE ICODE GIENELRATORS
Code Generators in Octal
05 13 0761 27 37305 154 177
Fig. 2. Illustration of adversary paths
zero state. This kind of paths are illustrated in figure 2 and areshown as i- 01, 2. It is clear that error decision will occur inthe decoding procedure if the metric of path 1 exceeds path 0,suppose all zero bits are transmitted. Further more, the closerthe distance between them, the higher probability that errorwill happen. Hence, in order to achieve better performance,the code with as large df,ee as possible should be lookedfor. If a group of codes have the same df ee, the total errorbits caused by the error paths corresponding to the graduallyincreased df ee should be served as the criterion instead.
The definition of the path distance differs in different re-ceiving schemes. If the decoder and demodulator are separated,the input of decoder is the demodulated signal. In this case,no matter hard decision or soft decision, Hamming distanceshould be used to measure the distance between paths. Inthe contrast, Euclidean distance between transmitted signalsshould be used when decoder and demodulator are combinedand the input of decoder is the received raw signal. Then from(4) and (5) the contribution of the positions and amplitudes ofthe transmitted pulses corresponding to path 0 and I to thepath distance e can be calculated as,
0
122Es
d(°) = d(l) and a(=)= a(l)dn _dnd(°) = d(l) and a(°) a(')
Daut etc. studied the searching problem for short con-straint length convolutional code and his searching procedurestill applies for us after considering the difference of thedefinition of path distance. What should be obviated here is thecatastrophic codes. A code is catastrophic if there exists a zero-distance path in the trellis which starts from some nonzerostate and goes back to itself. In this case a closed-loop of zero-distance branches will appear and some finite errors in channelwill lead to infinite errors in the decoded bits. According to thismethod, the generators for codes with 2/3 rate and constraintlength K = 2,3,4 is found and listed in table I.
III. MULTIPATH SIGNAL JOINT DETECTION ANDDECODING
In this section we will develop the joint detection al-gorithm for practical UWB channel which has abundant ofmultipath components. We will firstly give an expression ofthe sampled signal received in multipath channel, then we willpresent the multiple symbol detection method with unknown
channel information according to ML criteria and the codedmodulation scheme. The formula of branch metric and pathmetric in the Viterbi algorithm will be provided in the end.
Define the impulse response of multipath channel as
L-i
h(t) = E a1(t -Up)1=0
where L = LTTI + 1 denotes the multipath number, a, has aNakagami m-distribution [9], its probability density functionis
|~~~~1 m Rm-e-mle IQ g> 0
Fr(rni) (Qct)m (-m1a 1-le-m/Q al < 0
(6)where ml and Q, is the fading figure and mean square of a1,respectively.
After matched filter, the sampled signal received fromthis channel is
L-1
E ancl E -1(j-dn-) + Zj1=0
Define J = J + 1 and rn = [ro,T,- ,rJ,njTIn the trellis of Viterbi algorithm, consider the ith pathas the transmitted path. Then define the transmitted signalafter channel as s(i) = [0,O, a(')hT,... ,03], where h[tlo- ,aLl]T,IIhi2 - 1, the beginning position of h ins(i) is d(i). When the Ith path is the true transmitted path, thereceived sample vector will be
rn = VEsS(I) + Zn,
where Zn is Gaussian noise vector with zero mean andcovariance matrix R. = E[ZnZ] - N)2
According to ML criteria, the joint detector must thor-oughly search the trellis to find the most possible transmittedsignal, which will render the conditional probability of thereceived signal maximal,
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
Since zn is a Gaussian vector, with known transmitted between P(co, y; z) and e7z a further approximation can besignal s(i) and channel gain h, r has a multi-variant Gaussian made as followsdistribution, i.e., (I) = arg max p(r s(i))
p(rls(i), h) = 7r-NJIRz -NN-1T
.exp{-E (rn- VEsf(i)71=0
*RI1 ( n- lEssn) } (9)
It can be simplified in terms of our model of receivedsignal as,
L-1i
p(rls(L, h) =Al 171l exp { IEs(. al1-0
(10)
whereA1 = 7rNJIR -N exp{-+Ao},
N-1 J-1
Ao-ZZrIn+ NE,,n=O j=O
N-1
() = E () rn=O
Because of the independency of each multipath, p(h) =H1I0=1 p(alc). After some manipulation, the conditional proba-bility with unknown channel information can be derived as,
p(rls(')) - J p(rjs('), h)p(h)dh-oo
L-1
1=0
(lE;oVI}2Orl(i)2(l 21 4E821yl
where 4D(a, y; z) is the confluent hypergeometric function,which is defined as
Ay(-y+1)(?+2 3(When a = sy, we have 4(a, -y;z) = eZ. This means whenmi = 2 , we have
p(rls(')) = A1 exp 4EQjy } (13)
Equation (11) is sufficient to measure the path, but itscalculation is rather involved, thus more simplification is stillexpected. Depending on (13) and the intimate connection
s(i)
L- 4sY(i)2ci argmax 4E,Qlyls(i) __l N2m J
(14)
In most practical systems, the statistic information ofchannel such as ml and Q1 are not known a priori. To removethese two parameters, we assume they are invariant along withI and a quite simple expression is obtained,
sM I argmax{y(i)2 } (15)
Supporting by Viterbi algorithm, (15) can be realized withlow complexity. In the searching procedure, define the vectorof sampled receiving signal as
rd(,) n [rd ,n rd+ln' ' d()+L-I,n]7
branch metric as-= a(i)rdw (16)
and path metric as
(17)PA,l- ( = IIE p(t) 171
The rest of the operations in Viterbi algorithm are widelyknown and the transmitted uncoded bits can be reaped directly.From this procedure we can see that, since only relativeposition and polarity are taken into consideration, the jointdetection algorithm is not vulnerable to the absolute valuesand does not require the channel gains. With the correctassumption of the searching path, the multipath signals in allthe symbols will enhance collectively, otherwise the samplesin different symbols will eliminate mutually because of theinconsistency of the position and polarity of the sampledmultipath.
IV. SIMULATION RESULTSIn the subsequent part simulation results are provided to
compare the performance between the uncoded PPM schemeand the coded modulation scheme proposed in this paper. Theencoder listed in table I with K = 4 is used and the codingrate is 2/3. In each symbol, two bits input the encoder andthree bits output, the first of which modulates the polarity ofthe pulse and the other two modulate the position. Considerthe pulse width Tp = lns, maximal multipath delay Td =20ns, then 20 multipath components are produced and eachcomponent has an independent Nakagami m-distribution withfading figure m = 2.0 and exponential power delay profile.Packet transmission is simulated with each packet comprising1000 bits. The channel is invariant during one packet, butwill vary randomly in different packets. Since the experimentdepends on the channel realization remarkably, the results willbe fully averaged. In our simulations, 100-1000 packets aretransmitted based on the error rate in different SNR.
2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications
>,.. ....................
.X
..s .::
::.:... ::::. ..::::... :::X,N........:
:: :: ::
N::::
4
AWGN, NC, 4PPM.-AWGN, CC, 4PPAM
4:- MP, CC, 4PPAM
I... ..
............. .......
... ...
2 3 4 5 6 7 8 9 10
Eb/No
Fig. 3. Performance comparison with uncodedmodulation scheme. MSD is used in the MP case.
PPM scheme and coded
Figure 3 depicts the numerical results, in the figure MPdenotes multipath channel, NC indicates no coding and CCrepresents convolutional coding. The generator polynomial ofCC is (305,154,177), which is the searching result in sectionII. It is shown that the coded modulation system offers 5dBimprovement under 10-5 bit error rate compared with theuncoded 4PPM system in AWGN channel. In the multipathchannel, although 20 multipath components are deployed, theperformance of coded modulation scheme can still approach tothat of the uncoded PPM scheme worked in AWGN channel.
V. CONCLUSION
A coded modulation scheme is proposed for UWB com-
munications in this paper. By efficient combining the convo-
lutional coding and pulse position and amplitude modulation,
signal space is expanded and the Euclidean distance amongthe codewords is enlarged thus the performance is significantlyimproved accordingly. In order to jointly design the encoderand modulator, a new measure of distance between paths isexplored. Optimal generator polynomials of 2/3 rate convolu-tional code with constraint length 2, 3 and 4 are provided.A multiple symbol detection scheme to jointly detect anddecode the coded modulation signal after multipath channelis also developed, with the help of Viterbi algorithm it canachieve a superior performance with low complexity andunknown channel information. Notwithstanding, the amountof operations will still increase linearly with the multipathnumber. Therefore, selected combining or partial combiningin the computation of the path metric is deserved to beinvestigated in future works.
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