119303-7474 IJECS-IJENS

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International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: 03 64

119303-7474 IJECS-IJENS June 2011 IJENSI J E N S

Performance Evaluation of Linear Channel Estimation

Algorithms for MIMO-OFDM in LTE-Advanced

Saqib Saleem1, Qamar-ul-Islam, Waqar Aziz, Abdul Basit

Department of Communication System Engineering

Institute of Space Technology

Islamabad, [email protected]

Abstract In this paper two linear channel

estimation techniques, Least Square Error (LSE) andLinear Minimum Mean Square Error (LMMSE)

along with their modified versions, for reduced

complexity, are discussed for LTE-Advanced which

is based on MIMO-OFDM technology. LMMSE

demonstrates better performance but with more

complexity than LSE because it requires channel and

noise statistics. The performance and complexity can

be optimized by modifying LSE and LMMSE

techniques. These algorithms are evaluated based on

CIR samples and multi-path channel taps. MATLAB

Monte Carlo Simulations are used to optimize their

performance in terms of Mean Square Error (MSE),

Bit Error Rate (BER) and Frame Error Rate (FER)

for MIMO System. Simulation parameters aretaken according to the physical layer of LTE-Advanced as given in Release-10 by 3

rdGeneration

Partnership Project (3GPP).

Keywords: LTE-Advanced, LSE, LMMSE, MIMO-

OFDM, 3GPP, ITU, DFT

I. INTRODUCTIONFor machine-to-machine communication requiring

increased capacity, reduced edge-cell starvation and

energy efficient network, migration from 2G cellular

systems, through 3G systems which were not able to

meet ITUs 2Mbps peak data rate requirement,

towards 4G high data rate networks which include

3GPP LTE-Advanced and IEEE 802.16m have been

specified in TR36.912 and TR36.913 [1]. According

to ITU Working Party 5D (WP 5D), radio interface

recommendations proposed for 4G systems focus on

the following technologies: Co-ordinated multipoint

transmission and reception, heterogeneous networks

relaying, SON enhancements etc [2]. According to

World Radio Communication Conference (WRC 07),

the peak data rates of 100 Mbps for high mobility and1Gbps for low mobility can be achieved by the

following system requirements: 4 x 4 MU-MIMO, 70

MHz transmission bandwidth, spectral efficiency of

30b/s/Hz for DL and 15b/s/Hz for UL [3].

To avoid inter-symbol interference (ISI),

occurring due to multipath fading effects, a variety of

adaptive equalizers are implemented which are based

on the channel impulse response, for which a channel

estimator is required. Channel can be estimated by

any one of the following approaches: In semi-blind

approach [4], estimation of both pilots and data

symbols is used. Pilots are only considered in

training-based channel estimation and for blind

estimation, any one of the following channel

constraints can be used: frequency correlation,

cyclostationarity of cyclic prefix etc [5].

In [6], [7] different channel estimation

algorithms and their variants for optimizing both

performance and complexity are discussed for

OFDM System. LMMSE shows better performance

but with high implementation cost. Performance

efficiency of LSE can be improved by increasing CIR

samples. If we use a multipath channel of larger

length, then the performance can be improved even

without having a priori knowledge of the channel

statistics [7].

Two frequency-domain channel estimationalgorithms for MIMO-OFDM system are evaluated

in this paper based on two channel parameters: CIR

samples and number of multipaths. LSE has less

complexity but show poor performance because it

does not make use of the channel statistics, which are

required for other approach, called LMMSE. To

reduce the complexity of LMMSE, many algorithms

are proposed in [7].

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In the rest of the paper, system model of

MIMO-OFDM is given in section-II. LSE and

LMMSE Channel estimation techniques with some

modified algorithms are discussed in section-III with

their simulation results given in section-IV. Finally

the conclusions are drawn in last section.

II. SYSTEM MODELConsider a system having transmitted antennasand receive antennas and OFDM with N sub-carriers with cyclic prefix of length , which islonger than the channel delay spread.

Let [, ] be the transmitted MIMO-OFDM data-block

[, ] = [, ] [, ] [, ] (1)Where

[

, ] is the

transmitted OFDM

symbol on

carrier transmitted by

antenna.

After passing through a Rayleigh fading channel, the

received signal

[, ] = [[, ] [, ] [,]] (2)Where [, ] is the received OFDM symbolon carrier received by antenna and is given by

[, ] = [, ][, ] + [, ] (3)Where

[, ] = [[, ] [, ] [,]] (4)shows a white complex Gaussian noise vector havingcovariance matrix .The matrix [,] is MIMO Channelmatrix given as

[, ] = ,[, ] ,[,] ,[, ] ,[,]Where ,[,] is (,) element of the channelmatrix and is written in terms of complex channel-tap

gain and multipath delays, given as [8]

[, ] = []

(5)

Where is number of channel taps.The impulse response of the Rayleigh fading channel

is [8]

(, ) = () ( ())

(6)where () is channel-tap gain and () is themultipath delay of

channel tap.

III. CHANNEL ESTIMATIONA. LMMSE Channel Estimation

If we assume that the channel statistics

remains same across all receive antennas, then

LMMSE estimation of the channel at receiveantenna is given by [6]

, = , (7)Where , = [ ,] is cross co-variancematrix of the channel vector , and the receivedsignal

.

= [ ]is auto co-variance

matrix of. is DFT matrix used for conversion tofrequency domain channel estimation.So the above Equation can be written in compact

form as [9]

, = ,,( ,, + ) (8)

At receiver the matrix inversion is required which

increases the complexity. The pilot sequences used as

Reference signals are shifted version of each other

for all users.

B. Modified LMMSE Channel EstimationFor large value of N, the complexity of

LMMSE increases due to matrix inversion. If we

consider only first L taps, with significant energy,

then the complexity can be optimized and modified

channel estimation becomes [6]

,,= ,,( ,,

+

)

(9)

Where T is containing first L columns of DFT matrix

F and ,, is upper left corner matrix of,,.C. Low Complex LMMSE Channel Estimation

If we assume that the channel remains

constant over all frequencies and the transmitting

follow same modulation constellation over one

OFDM symbol, then the matrix inversion can be

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simplified, which results in the following channel

estimation [6]

, , = ,,(,,

+

)

(10)

Where is modulation constant and depends uponthe constellation diagram.D. LSE Channel Estimation

In addition to matrix inversion, the limit of

LMMSE is that it also requires a priori knowledge of

the channel statistics which is not possible to have,

especially in real-time wireless communication. To

avoid this probabilistic knowledge, LSE estimation is

preferred which has degraded performance than

LMMSE but has reduced complexity. LSE estimation

is given by [6]

, = (11)where = () (12), can also be written as [6]

, = (13)E. Down-Sampled Impulse Response LSE

Channel EstimationThe complexity of matrix inversion can be

further decreased by discarding some channel taps

and setting their values equal to zeros. For example

the channel vector can be [6] = ( 0 0 ) (14)Here 1/3 of the channel taps are discarded.

IV. SIMULATION RESULTSThe above discussed channel estimation techniques

in this paper are evaluated and optimized in this

section in terms of Mean Square Error (MSE) by

using MATLAB simulations for MIMO-OFDM

system whose parameters are given in Table 1.

Table 1: System Parameters

ParameterNumber of Packets 100

Frame Length 130 Symbols

Modulation BPSK, QPSK,

8-PSK,16-PSK

Channel Type Rayleigh Fading

MIMO 2 x 2

FFT Size 512

CP Length 16

A. Performance Comparison of LSE EstimatorFigure.1 shows the MSE comparison

between LSE and LMMSE from which it is clear that

LMMSE is better technique than LSE which does not

utilize the channel statistics. At high SNR values, the

performance gap is more than at low SNR. But for

improved performance in LMMSE we have to pay

for more complexity which results in increased

computational time and high implementation cost of

hardware to have a priori knowledge of channel

behavior.

Figure.1. Comparison of LSE and LMMSE

The effect of discarding certain CIR samples on

performance for LSE is given in Figure.2. The

performance is better for limited transmitting power

communication systems. For low SNR values, as CIR

samples are increased the performance goes on

degrading. CIR samples less than 20 shows almostsame performance while for value greater than 20,

not only performance is degraded but also has more

complexity. For high SNR values, the value of CIR

samples does not have significant effect on

performance.

Figure.2. Comparison of MSE for different CIR Samples at variousSNR Values

5 10 15 20 25 30 35 4010

1

102

SNR

MSE

MSE vs SNR of LSE and LMMSE Estimator for 2 x 2 System

LSE

LMMSE

0 10 20 30 40 50 60 700.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6x 10

6 MSE v/s CIR Samples for LS Estimat or for 2 x 2 System

CIR Samples

MS

E

SNR =5 dB

SNR =10 dB

SNR =15 dB

SNR =20 dB

SNR =25 dB

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From Figure.3, we observe that less CIR samples

operating at low SNR are preferred for less MSE. As

we increase SNR and CIR Samples, the MSE

increases but after certain values, further increment in

any parameter does not have affect on the

performance and behavior remains almost same.

Figure.3. MSE vs SNR vs CIR samples for LSE

Figure.4. shows the comparison of different

modulations for 2 x 2 system. As expected, BPSK

outperforms all other modulations techniques. At low

SNR, the performance os same for all modulations

but the increasing effect in SNR has clear

demonstration of the difference of performance. So

for high SNR, we choose modulation according to the

system requirement but for low SNR we can choose

any one.

Figure.4. BER of different Modulation for 2 x 2 System

The same observation is also concluded for SER as

shown in Figure.5. But here a performance gap is

found even for low SNR values. So from Figure.5 we

can have a better view for modulation choice.

Figure.5. SER vs SNR of LSE for different Modulations

Figure.6. FER of LSE for different modulations

FER for LSE for different modulations is

shown in Figure.6. Here again we observe that the

performance is almost same for low SNR but by

increasing SNR the high-point modulation degrades

greatly than the low-point modulation. From

Figure.4, 5, 6, we can choose the best one modulation

for any wireless communication system for better

performance optimization. The comparison of the

modified LSE estimators at different SNR values is

demonstrated in Figure.7. For better performance low

SNR operating condition is preferred having less

number of channel taps. For more channel taps the

performance is also lost in terms of more MSE at the

cost of more complexity.

The combined effect of Channel Taps and

SNR of performance of LS is shown in Figure.8 from

which it is clear that for better performance, low SNR

for more number of channel taps are proposed.

020

4060

80

510

1520

250.5

1

1.5

2

2.5

3

x 106

CIR Samples

MSE v/s SNR v/s CIR Samples for LS EStimator

SNR

MSE

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

10

0

SNR

BER

BER vs SNR for LS Estimator for 2 x 2 System

BPSK

QPSK

8-PSK

16-PSK

0 5 10 15 2010

-2

10-1

100

101

102

SNR

SER

SER vs SNR for LS Estimator for 2 x 2 System

BPSK

QPSK

8-PSK

16-PSK

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

100

SNR

FER

FER vs SNR for LS Estimator for 2 x 2 System

BPSK

QPSK

8-PSK

16-PSK

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Figure.7. MSE for Modified LSE Estimator

Figure.8 MSE vs Channel Taps vs SNR for LS

B. Performance Comparison of LMMSEEstimator

For different CIR samples, the performance

of LMMSE estimator is given in Figure.9. Similar to

LSE, low SNR is also preferred for LMMSE. But for

low SNR, the performance is same almost for initial

35 CIR samples and further increment in value, not

only results in degraded performance but also more

complexity. For high SNR, CIR samples have not

impact on performance, only we have to consider the

complexity issue.

The modified LMMSE estimators are

optimized according to their performance in

Figure.10. We observe the for low SNR, theperformance is better for less than 10 Channel taps

but further increment in channel taps degrades the

performance not too much only affect is on

complexity. As the SNR value is increased, the range

of channel taps for better performance also increases,

for example, for SNR value of 10, the performance is

ideal for up to 30 channel taps and similarly for 25

dB SNR, channel taps can be 60 for accepted

performance.

Figure.9 MSE vs CIR Samples for LMMSE

Figure.10 Effect of Channel Taps on LMMSE

Figure.11. MSE vs SNR vs Channel taps for Modified LMMSE

Figure.11 shows that for better performance, in case

of LMMSE, small values of SNR and channel taps

are preferred. For specific values of channel taps, the

performance lowers down significantly by increasing

the SNR value.

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18x 10

40 MSE v/s Channel Taps for Modified LS Estimator for 2 x 2 System

Channel Taps

M

SE

SNR =5 dB

SNR =15 dB

SNR =25 dB

020

4060

80

510

1520

25

0

0.5

1

1.5

2

x 1041

SNR

MSE v/s SNR v/s Channel Taps for Modified LS EStimator for 2 x 2 System

Channel Taps

MSE

0 10 20 30 40 50 60 702

4

6

8

10

12

14x 10

15 MSE v/s CIR Samples for LMMSE Est imator for 2 x 2 Syst em

CIR Samples

MSE

SNR =5 dB

SNR =10 dB

SNR =15 dB

SNR =20 dB

SNR =25 dB

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7

8

9x 10

35 MSE v/s Channel Taps for Modified MMSE Estimators for 2 x 2 System

Channel Taps

MSE

SNR =5 dB

SNR =10 dB

SNR =15 dB

SNR =20 dB

SNR =25 dB

0 2040 60

80

51015

20250

0.5

1

1.5

2

2.5

x 1035

Channel Taps

MSE v/s SNR v/s Channel Taps for Modified MMSE EStimators for 2 x 2 Sys tem

SNR

MSE

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In Figure.12 MSE variation according the

varying values of SNR and CIR Samples is

demonstrated. Less values of SNR and CIR samples

are proposed for better system performance.

Figure.12. Effect of SNR and CIR Samples for LMMSE

V. CONCLUSIONIn this paper, two channel parameters, CIR samples

and Channel Taps are used to evaluate the

performance comparison of two linear channel

estimation techniques, LSE and LMMSE. The

performance of LMMSE is better than LSE because

it depends on the channel and noise statistics, which

is not possible to have in wireless communication

and further it also increases the complexity of the

transceiver. For LSE, small number of CIR samples

and channel taps are preferred for low SNR

conditions. And same system parameters are also

proposed for LMMSE approach. For LSE, generallyCIR samples less than 30 and channel taps

approximately 40 are used and for LMMSE, only 10

channel taps are used for better performance.

Performance can be further improved by using

adaptive channel estimation techniques like RLS,

LMS and Kalman Filtering.

REFERENCES

[1] Krystian Safjan, Valeria DAmico, DanielBultmann, David Martin, Ahmed Saadani,

Hendrik, Assesing 3GPP LTE-Advanced as

IMT-Advanced Technology: The WINNER +Evaluation Group Approach, IEEE

Communications Magazine, February 2011.

[2] Panayiotis Kolios, Vasilis Friderikos, KaterinaPapadaki, Future Wireless Mobile Networks:

Energy Consumption and Resource Utilization in

Mechnical Relaying, IEEE Vehicular

Technology Magazine, March 2011.

[3] Agilient Technologiess Report on IntroducingLTE-Advanced:Application Note,

www.agilent.com/find/4glte

[4] S.M. Riazul Islam and Kyung Sup Kwak,Winner-Hopf Interpolation Aided Kalman

Filter-Based Channel Estimation for MB-OFDM

UWB Systems in Time Varying Dispersive

Fading Channel, ICACT, Feb.7-10,2011

[5] Tareq Y.AL-Naffouri, An EM-Based Froward-Backward Kalman Filter for the Estimation of

Time-Variant Channels in OFDM, IEEE

Transactions on Signal Processing, Vol.55,No.7,

July 2007.

[6] Saqib Saleem, Qamar-ul-Islam, Optimization ofLSE and LMMSE Channel Estimation

Algorithms based on CIR Samples and Channel

Taps, IJCSI International Journal of Computer

Science Issues, Vol.8, Issue.2, pp.437-443,

January 2011.

[7] Saqib Saleem, Qamar-ul-Islam, Performance

and Complexity Comparison of ChannelEstimation Algorithms for OFDM System,

International Journal of Electrical and Computer

Sciences IJECS-IJENS, Vol.11, No.2, pp.6-12,

April 2011.

[8] Eric Pierre Simon, Hussain Hijazi, Laurent Ros,Joint Carrier Frequency Offset and Fast Time-

Varying Channel Estimation for MIMO-OFDM

Systems, CSNDSP 2010.

[9] Hussain Hijazi, Eric Pierre Simon, MartineLienard, Laurent Ros, Channel Estimation for

MIMO-OFDM Systems in Fast Time-Varying

Environments, 4th

ISCCSP 2010, Limassol,

Cyprus, 3-5 March 2010

0

20

40

60

80

5

10

15

20

250

5

10

15

x 1015

CIR Samples

MSE v/s SNR v/s CIR Samples for LMMSE EStimator

SNR

MSE

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119303-7474 IJECS-IJENS