Mobile WiMAX Impact of Channel Estimation Error on the Performance of Limited Feedback Linear...

8/8/2019 Mobile WiMAX Impact of Channel Estimation Error on the Performance of Limited Feedback Linear Precoding

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Abstract — The mobile WiMAX standard (802.16e) uses

multiple-input multiple-output (MIMO) limited feedback linear

precoding to exploit the channel state information at the

transmitter. Although the performance of limited feedback

linear precoding in relation to traditional open-loop MIMO-

OFDM has been extensively studied in the literature, these

studies commonly assume perfect channel estimation at the

receiver. In a practical OFDM-based system, the estimated

channel matrix often differs from the actual channel matrix due

to errors incurred in the channel estimation process. This

results in degraded performance relative to the case with

perfect channel estimation. To date, few researchers have

studied the impact of channel estimation error on the

performance of an OFDM limited feedback linear precoding

system. This paper investigates the channel estimation errorusing 1) an MMSE channel estimator that takes into account

the subcarrier correlation when estimating the channel, 2) a

Low Rank (LR) channel estimator that relaxes the requirement

for a perfect channel covariance matrix in the MMSE receiver,

and 3) a ZF estimator where this correlation information is

ignored. Simulation results show that with the MMSE

estimator the system suffers very little array gain loss with a

performance degradation of 0.2dB SNR. Compared to the

MMSE estimator, the LR estimator incurs a small performance

loss of around 0.5dB. Finally, when the ZF estimator is

implemented, a significant performance degradation is

observed with approximately 4-5dB loss in array gain loss.

Index Terms —802.16e, WiMAX, MIMO, linear precoding,

limited feedback.

I. I NTRODUCTION

The first WiMAX systems were based on the IEEE

802.16-2004 standard [1]. This targeted fixed broadband

wireless applications via the installation of Customer

Premises Equipment (CPE). In December 2005 the IEEE

completed the 802.16e-2005 [2] amendment, which added

new features to support mobile applications.

Mobile WiMAX now supports both open-loop and

closed-loop multiple-input multiple-output (MIMO)

techniques. Open-loop techniques, such as space time block

coding (STBC) and spatial multiplexing (SM), can be used

to increase diversity gain or system throughput without the

need for channel state information (CSI) at the transmitter.However, recent work [3, 4] has reported further increases in

system performance (both diversity and array gain) and

throughput by applying linear precoding closed-loop

techniques at the transmitter that exploit knowledge of the

CSI.

The key idea behind linear precoding is to customize the

transmit signal by pre-multiplication with a precoding

matrix. It is well-known that singular value decomposition

(SVD) linear precoding provides the highest achievable

performance [4]. However, the SVD approach requires

perfect CSI at the transmitter, which cannot be achieved in a

MIMO Mobile WiMAX system with numerous antennas,

subcarriers, and a rapidly changing channel. The need to

reduce the amount of CSI feedback information motivates

the use of a codebook based linear precoding technique [5,

6]. Here, the mobile station (MS) calculates the optimal

precoding matrix for each subcarrier and feeds back the

matrix, rather than the CSI, to the base station (BS).

Specifically, the optimal precoding matrix is constrained to

one of N distinct matrices, which are referred to as codebook

entries, designed offline and known to both the MS and BS.

The MS identifies the optimal precoding matrix based on the

current CSI. Since the codebook is known at the BS, the MS

only needs to feedback a binary index of the optimal precoding matrix, rather than the entire precoding matrix

itself. For each combination of the number of transmit ( T N )

and receive ( R N ) antennas, the 802.16e standard defines

two codebooks: one with 8 entries and the other with 64

entries [7]. These correspond to 3-bit and 6-bit codebook

indices for each precoding matrix respectively.

The performance improvement of codebook based linear

precoding MIMO-OFDM systems has been previously

reported in the literature [8]. However, results are often

based on the assumption that the channel is perfectly

estimated at the receiver. In practice, the OFDM channel

estimator at the receiver always leads to imperfect channel

estimation. If the channel is not perfectly known at the

receiver, the performance of the linear precoding technique

will degrade due to two reasons: 1) the receiver will select

the optimal precoding matrix based on the errored channel

estimation H , and not the true channel H, and 2) the use of

errored channel information at the receiver (e.g., H is used

instead of H in the MMSE receiver of the SM system). This

paper investigates the impact of channel estimation error on

the performance of a linear precoding mobile WiMAX

system using the distributed PUSC subcarrier permutation

scheme.

The paper is organized as follows: Section II describes

important parameters used in the mobile WiMAX simulator.

An overview of precoded spatial multiplexing and dominant

eigenbeamforming for mobile WiMAX systems is described

in Section III. Training-based channel estimation techniques

supported in the mobile WiMAX standard are described in

Section IV. Section V investigates the impact of channel

estimation error on the performance of a precoded mobile

WiMAX system. Finally, conclusions are presented in

Section VI.

II. LINK LEVEL MOBILE WIMAX SIMULATOR

A detailed downlink Mobile WiMAX link-level simulator

Mobile WiMAX: Impact of channel estimation error on

the Performance of Limited Feedback Linear PrecodingMai Tran, Andrew Nix, and Angela Doufexi

Centre for Communications Research, Merchant Venturers Building,

University of Bristol, Bristol BS8 1UB, UK



2

[9] using the PUSC subcarrier permutation and

convolutional coding with soft Viterbi decoding has been

implemented by the authors based on the 802.16e-2005

standard [2]. The simulator models a cell with an omni-

directional basestation (BS) and three mobile stations (MS)

randomly situated in the cell. In the downlink, each MS is

randomly allocated 5 out of a total of 15 subchannels. The

BS transmits data simultaneously to 3 MS, with each sharing

a common OFDMA symbol. Table I summarises the

OFDMA parameters used in the Mobile WiMAX simulator.

A detailed description of the simulator can be found in [9].

TABLE I: OFDMA PARAMETERS

Parameter Value

Carrier frequency (GHz) 2.3

FFT size 512

Channel bandwidth (MHz) 5

Sampling frequency F s (MHz) 5.6

Sampling period 1/ F s ( s) 0.18

Subcarrier frequency spacing ∆ f =F s /N FFT (kHz) 10.94

Useful symbol period T b = 1/ ∆ f (µs) 91.4

Guard Time T g = T b/8 (µs) 11.4

OFDMA symbol duration T s =T g +T b (µs) 102.9

Number of used subcarriers ( N used ) 421

Number of pilot subcarriers 60

Number of data subcarriers 360

Number of data subcarriers in each subchannel 24

Number of subchannels 15

Number of users ( N users) 3

Number of subchannels allocated to each user ( N ALSU ) 5

Based on the ETSI 3GPP2 spatial channel model (SCM)

[10, 11], urban micro and urban macro tapped delay line

(TDL) channels were generated for use in this analysis. The

TDL comprises 6 taps with non-uniform delays. Each tap

experiences Rayleigh fading based on an MS velocity andthe traditional Jake’s Power Doppler Spectrum [12]. The

antenna element separation is 10 λ at the BS and 0.5 λ at

the MS, where λ represents the carrier wavelength.

III. LINEAR PRECODING

This section summarizes two different linear precoding

systems, namely linear precoding spatial multiplexing (SM

PRE) and dominant eigenbeamforming (DE), both of which

are implemented in the mobile WiMAX simulator.

A. Linear precoding spatial multiplexing (SM PRE)

For purposes of simplicity, a generic linear precoding

spatial multiplexing system for a single subcarrier is

illustrated in Fig. 1.In the case of an OFDM mobile WiMAX system, the k -th

subcarrier is allocated a precoding matrix k F , and the

1 R N × receive symbol vector k y is given by

sk k k k k

E

M = +y H F s n (1)

where k is the subcarrier index, s E is the total transmit

power for the k -th subcarrier, M is the number of spatial

streams ( T M N < ), k H is the R T N N × normalised channel

matrix, k s is an 1M × transmit data symbol vector (which is

spread over T N transmit antennas by multiplying by an

T N M × precoding matrix k F ), and k n is an 1 R N × noise

vector whose entries are complex, independent and

identically distributed (i.i.d) additive white Gaussian noise

(AWGN) samples with zero mean and variance 2σ .

T N x

R N y

1 x

1 y

Fig. 1: Linear precoding spatial multiplexing system block diagram

In this paper the received symbol vector k y is decoded

using an MMSE linear decoder k G , given by

-12* * * *n

k k k k k M k k

s

M

E

σ

G = F H H F + I F H . (2)

The optimal precoding matrix opt F is determined for each

subcarrier using the minimum mean square error (MSE)

criterion [5] as

( )1

* * * *

2

s sk M k k k k

n

E E MSE

M M σ

−

= +

F I F H H F (3)

where

( )( )argminik

i

opt k Q

trace MSE ∈

=F

F F (4)

and Q is the codebook (which is known to both the BS and

MS). Q is constructed using the methods described in

section 8.4.5.4.10.15 of [2].

B. Dominant Eigenbeamforming (DE)

The second linear precoding system considered in this

paper is dominant eigenbeamforming (DE), as illustrated in

Fig. 2 for the k -th subcarrier. Here the BS transmits a single

spatial stream across the T N transmit antennas.

T N x

R N

1 x

1 y

Fig. 2: Dominant eigenbeamforming system block diagram

In a precoded mobile WiMAX system, the k -th subcarrier

is assigned a 1T N × precoding vector k f . The receive



3

symbol vector k y for a DE system can be expressed as

k s k k k k E s= +y H f n . (5)

In this paper k y is decoded using a traditional maximum

ratio combiner g [6].

2/k k k k k =g H f H f (6)

The optimal precoding vector opt f is determined from (7)

using the criterion defined in [6]. 2

2argmax

ik

i

opt k k Q∈

=f

f H f (7)

IV. CHANNEL ESTIMATION IN MOBILE WIMAX

In order to perform channel estimation, the mobile

WiMAX standard supports a training-based technique [2,

13] where known symbols are transmitted to aid the

receiver’s channel estimation algorithm. There are two ways

to transmit training symbols: 1) transmitting preamble-based

symbols in which known preambles are sent at the beginning

of each frame, and 2) transmitting pilot-based symbols

where several known pilots are inserted into each OFDM

symbol within a frame in order to track the changing channel

between OFDM symbols.Our mobile WiMAX simulator assumes a block fading

channel where the channel remains constant over a WiMAX

transmission frame, but changes between frames. Therefore

only the preamble is needed in our simulator to estimate the

channel. With a frame duration of 5ms, as defined in the

standard, this block fading assumption is valid for mobile

applications with velocities up to 80 km/h (i.e., a coherence

time of 6 ms). A preamble-based OFDM channel estimation

system with N subcarriers is often modelled as

=y Xh + n (8)

where X is an N N × diagonal matrix whose diagonal

elements are the pilot symbols in the frequency domain, h is

an 1 N ×

complex channel vector whose entries are thefrequency response of N subcarriers, and n is an 1 N × noise

vector of independent and identically distributed complex,

zero-mean Gaussian noise variables with variance 2σ .

Without loss of generality, we assume that the channel is

normalised such that { }21k E h = and { }2

, 1k k E X = . The

channel estimate h can be obtained using the zero forcing

(ZF) or the minimum mean-square error (MMSE) channel

estimator [14-16]. For example, by using the ZF channel

estimator, the channel estimate vector h is given by1ˆ

ZF −=h X y . (9)

The ZF channel estimator is implemented with very low

complexity but fails to consider the potentially significantcorrelation between subcarriers, and therefore suffers from a

high mean-square error [14]. In order to improve the quality

of the channel estimate, an MMSE based channel estimator

[14, 16] that minimizes the mean-square error by leveraging

the subcarrier correlation, can be used. The MMSE channel

estimate ˆMMSE h in the frequency domain is given by [14]

( )1

2ˆ ˆMSE hh hh ZF σ

−= +h R R I h (10)

where R hh= E {hh*} denotes the auto-covariance matrix of

the channel vector h and I denotes the N N × identity

matrix.

The main drawback of the MMSE estimator is that it

requires a perfect channel covariance matrix at the receiver.

In practice the receiver does not often have this information

in advance, and hence this too needs to be estimated. The

work in [17] proposes a low-rank MMSE estimator (LR)

that uses the channel covariance matrix estimated from a

uniform power-delay profile (pdf). The estimated correlation between the m-th and the n-th subcarrier in this case is given

by

2

,

1, if

, if 1

m n j L

N m n

m n

r m ne

m n j L

N

π

π

−−

=

= ≠− −

2

(11)

where L is the number of samples in the guard interval, and

N is the number of subcarriers within an OFDM symbol. It

can be seen that this estimator only requires knowledge of

the guard interval length and the number of subcarriers in

the system. Results in [17] also show that the wrong channel

statistics (due to the use of a uniform pdf) only incurs asmall performance loss relative to the case with perfect

knowledge of the covariance matrix.

In a MIMO-OFDM system the received signal at each

receive antenna is the superposition of transmit signals from

T N transmit antennas. Therefore, in order to differentiate

the preamble signals transmitted from each antenna, an

independent pattern for transmitting preamble signals [18] is

implemented as illustrated in Fig. 3. The independent pattern

transmits preamble signals from each antenna at a time when

the other antennas keep silent. By doing this all the

preambles are received at the receiver without interfering

with one another.

Fig. 3: Independent pattern for transmitting preambles [18] for a MIMO

system with 2 transmit antennas

0 50 100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

1.2

1.4

Subcarrier index

C h a n n e l a m p l i t u d e

Perfect channel

Estimation at 0dB SNR



Fig. 4: MMSE channel estimation at various SNRs



4

Fig. 4 and Fig. 5 compare the actual channel with the

channels estimated using the MMSE and ZF estimators,

correspondingly, for various SNR values. It can be seen that

the MMSE estimator achieves a very accurate channel

estimate. It can maintain a reasonable channel estimate

accuracy even at 0dB SNR. However when the ZF estimator

is used the channel estimate performance becomes very poor

at low SNRs. At an SNR of 0dB the ZF channel estimate is

unusable.

0 50 100 150 200 250 300 350 4000

0.5

1

1.5

2

2.5

3

Subcarrier index

C h a n n e l a m p l i t u d e

Perfect channel




Fig. 5: ZF channel estimation at various SNRs

Fig. 6 compares the mean-squared error (MSE) between

the MMSE, LR and ZF estimators. As expected, the MSE of

the MMSE and LR estimators are much smaller than that of

the ZF estimator.

0 5 10 15 20 25 30 35 4010-6

10-4

10-2

100

SNR (dB)

M S E

LR uniform estimator

MMSE estimator

ZF estimator

Fig. 6: MSE of MMSE, LR and ZF estimators

V. SYSTEM PERFORMANCE ANALYSIS

This section studies the packet error rate (PER)

performance of the precoded MIMO mobile WiMAX

system with MMSE, LR and ZF channel estimation. Linear

precoding with channel estimation errors can be simulated

by assuming that the receiver selects the optimal precoder

matrix ( )ˆ f =F H using knowledge of the channel estimate

matrix H , and not the true channel H.

The ideal case with perfect channel knowledge at thereceiver (denoted as Perf H) is demonstrated as a benchmark

for PER comparison.

A. Dominant Eigenbeamforming

Fig. 7 shows the PER performance of the 2 2× QPSK

and 16QAM 3/4 rate DE systems using MMSE, LR and ZF

channel estimators. It can be seen that the performance for

the MMSE channel estimate is quite close to that of the ideal

channel system (degraded by approximately 0.2dB). The LR

estimator, although using inaccurate channel statistics, only

suffers an approximate 0.5dB loss relative to the MMSE

approach. This result agrees with the performance of the LR

estimator demonstrated in [17]. Finally, the ZF channel

estimation scheme suffers significant performance

degradation with a 4dB loss in array gain.

Fig. 8 illustrates the impact of MMSE, LR and ZF channel

estimations on the PER performance of a 2 2× QPSK and

16QAM 3/4 rate Alamouti system [19]. Comparing Fig. 7

with Fig. 8 it can be seen that different channel estimation

algorithms have a similar impact on the performance of

closed-loop and open-loop MIMO diversity systems. This

similar performance degradation initially seems counter-intuitive because the channel estimation in a closed-loop

MIMO system causes both an incorrect precoding matrix

ôpt f at the transmitter and an errored channel H at the

receiver. This is expected to result in a higher performance

degradation than the open-loop MIMO system, where only

an errored channel H is experienced at the receiver. In fact,

a closed-loop MIMO system in this case is equivalent to an

open-loop MIMO system operating over a channel ôpt Hf

with an errored channel estimate ˆôpt Hf at the receiver. This

results in a similar performance loss to the open-loop

system.

-4 -2 0 2 4 6 8 10 12 14 16 1810

-3

10-2

10-1

100

SNR (dB)

P E R

QPSK 3/4 DE PRE 2x2 Perf H

16QAM 3/4 DE PRE 2x2 Perf H

QPSK 3/4 DE PRE 2x2 MMSE H

16QAM 3/4 DE PRE 2x2 MMSE H

QPSK 3/4 DE PRE 2x2 LR uni

16QAM 3/4 DE PRE 2x2 LR uni

QPSK 3/4 DE PRE 2x2 ZF H

16QAM 3/4 DE PRE 2x2 ZF H

Fig. 7: PER performance of 2x2 DE QPSK and 16QAM 3/4 rate systems

with MMSE, LR and ZF channel estimation

-2 0 2 4 6 8 10 12 14 16 18 2010

-3

10-2

10-1

100

SNR (dB)

P E R

QPSK 3/4 ST22 Perf H

16QAM 3/4 ST22 Perf H

QPSK 3/4 ST22 MMSE H

16QAM 3/4 ST22 MMSEH

QPSK 3/4 ST22 LR uni

16QAM 3/4 ST22 LR uni

QPSK 3/4 ST22 ZF H

16QAM 3/4 ST22 ZF H

Fig. 8: PER performance of 2x2 Alamouti QPSK and 16QAM 3/4 rate

systems with MMSE, LR and ZF channel estimation

-6 -4 -2 0 2 4 6 8 10 12 14 1610

-3

10-2

10-1

100

SNR (dB)

P E R

QPSK 3/4 DE PRE 4x2 Perf H

16QAM 3/4 DE PRE 4x2 Perf H

QPSK 3/4 DE PRE 4x2 MMSE H

16QA M 3/4 DEPRE 4x2 MMSE H

QPSK 3/4 DE PRE 4x2 LR uni

16QAM 3/4 DE PRE 4x2 LR uni

QPSK 3/4 DE PRE 4x2 ZF H

16QAM 3/4 DE PRE 4x2 ZF H

Fig. 9: PER performance of 4x2 DE QPSK and 16QAM 3/4 rate systems




5

Fig. 9 illustrates the PER performance of a 4 2× QPSK

and a 16QAM 3/4 rate DE system using MMSE, LR and ZF

channel estimators. It demonstrates a performance

degradation of 0.2dB, 1dB, and 5dB for MMSE, LR and ZF

systems respectively.

B. Linear precoding spatial multiplexing

Fig. 10 studies the impact of MMSE, LR and ZF

estimators on the PER performance of 4 2× SM PRE QPSK

and 16QAM 3/4 rate systems. It presents the same performance degradation as observed for the DE system.

Compared to the ideal system with perfect channel

knowledge, the use of an MMSE estimator only incurs a

small array gain loss of 0.2dB. The LR estimator suffers

very little loss relative to the MMSE estimator, and the ZF

estimator degrades by approximately 4dB in array gain.

0 5 10 15 20 2510

-3

10-2

10-1

100

SNR (dB)

P E R

QPSK 3/4 SM PRE 4x2 Perf H

16QAM 3/4 SM PRE 4x2 Perf H

QPSK 3/4 SM PRE 4x2 MMSE H

16QAM 3/4 SM PRE 4x2 MMSE H

QPSK 3/4 SM PRE 4x2 LR uni

16QAM 3/4 SM PRE 4x2 LR uni

QPSK 3/4 SM PRE 4x2 ZF H

16QAM 3/4 SM PRE 4x2 ZF H

Fig. 10: PER performance of 4x2 SM PRE QPSK and 16QAM 3/4 rate

systems with MMSE, LR, and ZF channel estimation

Fig. 11 demonstrates the PER performance of a 2 2×

open-loop SM system using different channel estimators. As

expected, a similar performance loss to the SM PRE system

(Fig. 10) is observed.

4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 3810

-3

10-2

10-1

100

SNR (dB)

P E R

QPSK 3/4 SM 2x2 Perf H

16QAM 3/4 SM 2x2 Perf H

QPSK 3/4 SM 2x2 MMSE H

16QAM 3/4 SM 2x2 MMSE H

QPSK 3/4 SM 2x2 LR uni

16QAM 3/4 SM 2x2 LR uni

QPSK 3/4 SM 2x2 ZF H

16QAM 3/4 SM 2x2 ZF H

Fig. 11: PER performance of 2x2 SM QPSK and 16QAM 3/4 rate systems


VI. CONCLUSIONS

This paper has studied the impact of channel estimationerror on the performance of a linear precoding Mobile

WiMAX system. Three different channel estimators were

implemented: 1) an MMSE estimator with a perfect channel

covariance matrix, 2) an LR estimator with an estimated

channel covariance matrix, and 3) a ZF estimator where the

correlation factor is ignored. Spatial Multiplexing and

Dominant Eigenbeamforming systems with 2 2× and 4 2×

antenna configurations were studied. Results have shown

that a linear precoding Mobile WiMAX system using

MMSE channel estimation maintains a very good

performance with only a 0.2dB array gain degradation

compared to the ideal system with perfect channel

knowledge. The LR channel estimator, based on a uniform

channel correlation, only incurred a small loss of

performance (i.e., 0.5dB) relative to the MMSE, even

though it used incorrect channel statistics. Finally, a ZF

estimator with no channel statistic information degraded

system performance by 4-5dB.

VII. ACKNOWLEDGEMENTS

The authors would like to thank the Centre for Communications Research for providing a range of high-

performance computing facilities.

VIII. R EFERENCES

[1] "IEEE Std 802.16-2004 (Revision of IEEE Std 802.16-2001)," pp.

0_1-857, 2004.

[2] "IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor 1-2005,"

pp. 0_1-822, 2006.

[3] A. Scaglione, P. Stoica, S. Barbarossa, G. B. Giannakis, and H.

Sampath, "Optimal Designs for Space-Time Linear Precoders and

Decoders," IEEE Transactions on Signal Processing , vol. 50, pp.

1051-1064, 2002.

[4] E. Sengul, E. Akay, and E. Ayanoglu, "Diversity Analysis of Single

and Multiple Beamforming," IEEE Transactions on

Communications , vol. 54, pp. 990-993, 2006.

[5] D. J. Love and R. W. Heath, "Limited Feedback Unitary Precoding

for Spatial Multiplexing Systems," IEEE Transactions on

Information Theory, vol. 51, pp. 2967-2975, 2005.

[6] D. J. Love, R. W. Heath, Jr., and T. Strohmer, "Grassmannian

beamforming for multiple-input multiple-output wireless systems,"

IEEE Transactions on Information Theory, vol. 49, pp. 2735-2747,

2003.

[7] Q. Li, X. E. Lin, and J. Zhang, "MIMO Precoding in 802.16e

WiMAX," Journal of Communications and Networks, vol. 9, 2007.

[8] E. Akay, E. Sengul, and E. Ayanoglu, "Performance Analysis of

Beamforming for MIMO OFDM with BICM," IEEE International

Conference on Communications, vol. 1, pp. 613-617, 2005.

[9] D. H. Mai Tran, Andrew Nix, Angela Doufexi, Mark Beach, "Mobile

WiMAX: Downlink Performance Analysis with Adaptive MIMO

Switching," presented at IEEE Mobile WiMAX Symposium 2009,

California, USA, 2009.

[10] 3GPP, "Spatial channel model for multiple input multiple output

(MIMO) simulations (TR 25.996 Rel. 6)," 2003.

[11] G. Calcev, D. Chizhik, B. Goransson, S. Howard, H. Huang, A.Kogiantis, A. F. Molisch, A. L. Moustakas, D. Reed, and H. Xu, "A

Wideband Spatial Channel Model for System-Wide Simulations,"

Vehicular Technology, IEEE Transactions on, vol. 56, pp. 389-403,

2007.

[12] M. J. Gans, "A power-spectral theory of propagation in the mobile-

radio environment," Vehicular Technology, IEEE Transactions on,

vol. 21, pp. 27-38, 1972.

[13] WiMAX Forum, "Mobile WiMAX - Part 1: A Technical Overview

and Performance Evaluation," August, 2006.

[14] J.-J. Van de Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O.

Borjesson, "On channel estimation in OFDM systems," presented at

Vehicular Technology Conference, 1995 IEEE 45th, 1995.

[15] Y. Shen and E. Martinez, "Channel Estimation in OFDM Systems,"

Freescale Semiconductor AN3059, Rev. 0, 1/2006, 2006.

[16] D. Lowe and X. Huang, "Adaptive Low-Complexity MMSE Channel

Estimation for OFDM," presented at Communications and

Information Technologies, 2006. ISCIT '06. International Symposiumon, 2006.

[17] O. Edfors, M. Sandell, J.-J. Van de Beek, S. K. Wilson, and P. O.

Borjesson, "OFDM channel estimation by singular value

decomposition," Communications, IEEE Transactions on, vol. 46,

pp. 931-939, 1998.

[18] J. G. Andrews, A. Ghosh, and R. Muhamed, Fundamentals of

WiMAX: Understanding broadband wireless networking , 1 ed:

Prentice Hall, 2007.

[19] S. M. Alamouti, "A Simple Transmit Diversity Technique for

Wireless Communications," IEEE Journal on Selected Areas in

Communications Sac, vol. 16, pp. 1451-1458, 1998.

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