Enhanced Channel Estimation Technique in MIMO-OFDM System

M. A. Ahmed, S. A. Jimaa, and I.Y. Abualhaol

ECE Department, College of Engineering Khalifa University of Science, Technology and Research

Sharjah,UAE Email :{20059,saj}@kustar.ac.ae, ibrahimee@ieee.org

Abstract- Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM), MIMO-OFDM, is considered as a spectrally efficient approach to achieve high throughput communications. This paper investigates the performance of MIMO-OFDM system using the proposed NLMS adaptive equalizer and the developed Singular Value Decomposition (SVD) technique in estimating the channel. The performances of using various values of the NLMS algorithms step-size were also investigated and an optimum value, based on a trade-off between the convergence speed and the steady state noise floor, was chosen. Then, the bit error rate (BER) performance of the NLMS adaptive receiver is compared with that of the SVD algorithm. It is clear that the SVD gives better performance over the NLMS adaptive filter.

Keywords- MIMO-OFDM; Adaptive Filter; NLMS; Step-Size; SVD

I. INTRODUCTION In a multi-channel system, frequency selective fading or narrowband interference affects a small percentage of sub-channels whereas in a single channel system, a single fade or interference might cause the entire channel to fail. To realize OFDM, we have to maintain orthogonality between sub-channels (i.e., reducing crosstalk between them). Orthogonality can be maintained using a cyclic prefix which is the copy of the last part of an OFDM symbol. Cyclic prefix will be appended to the transmitted symbol [1]. This introduces a loss in the signal to noise ratio (SNR). However, the zero inter channel interference (ICI) mitigates the loss. Inter Symbol Interference (ISI) can be avoided using pulse shaping. Raised cosine windowing of the transmitted pulses will result into a sinc shaped frequency response of each sub-channel where the roll off region acts as a guard interval. Thus, the frequency spectrum of each sub-channel falls much more quickly and therefore reduces the interference to the adjacent frequency bands. In a discrete time model of an

OFDM system, the modulation and the demodulation are substituted with inverse FFT and FFT, thereby achieving frequency division multiplexing by a baseband filtering process. Furthermore, it will eliminate the banks of sub-channels oscillators and coherent demodulators required by frequency division multiplexing [2]. One of the simplest, yet robust adaptive filter algorithms is the normalized least mean square (NLMS). The weight vector of NLMS can be changed automatically, while that of LMS cannot [3]. If the rate of convergence is fast, the filter will be adapted quickly to a stationary environment of unknown statistics. The most important parameter that dominates the NLMS algorithm is the step-size. If the step-size is set to a large value, the convergence rate of NLMS algorithm will be fast. However, the steady state MSE will increase. On the other hand, if the step-size is set to a small value, the convergence rate will be slow but the steady state MSE will decrease [4]. Recent related work is given in [5] and [6]. In [5], only the MMSE performances of using the NLMS adaptive algorithm for different MIMO systems have been investigated. While in [6], there is a new channel estimation method for OFDM by combining LS and MMSE using Evolutionary Programming was proposed. The realization of SVD algorithm has been investigated in OFDM system [7], [8]. In this work we evaluated the performance of the NLMS algorithm for MIMO-OFDM system using various step-sizes and an optimum step-size was chosen, based on a trade-off between the convergence speed and the steady state MSE. Then, the BER performance of the proposed NLMS adaptive receiver with optimum step-size is compared with that of the conventional receiver. In addition to that, the SVD algorithm was studied and compared to the NLMS adaptive filter. The remainder of this paper is organized as follows. Section II introduces the system overview. Sections III, and IV describe the system model and simulation results. Finally, Section V concludes the paper.

2012 Third International Workshop on the Performance Enhancements in MIMO OFDM Systems978-1-4673-1430-5/12/$31.00 2012 IEEE 545

II. SYSTEM OVERVIEW

The MIMO OFDM system was implemented with the aid of MATLAB/SIMULINK. The execution process is binary data that is modulated using BPSK and mapped into the constellation points. The digital modulation scheme will transmit the data in parallel by assigning symbols to each sub-channel and the modulation scheme will determine the phase mapping of sub-channels by a complex I-Q mapping vector [7]. The complex parallel data stream has to be converted into an analogue signal that is suited to the transmission channel. This is performed by the Inverse Fast Fourier Transform (IFFT). IFFT converts the signal to the time domain since OFDM treats the transmitted symbols as they are in the frequency domain. Assuming that the sub-channels number is N, the transmitted symbol X(k) is transformed to x(n) by IFFF as following:

= = !! = , . . , (1)

Each OFDM symbol is appended by a copy of 0.25% of IFFT size to the original OFDM symbol resulting in making the transmitted signal periodic, which plays a major role in avoiding ISI and ICI. The transmitted symbol after adding the cyclic prefix:

The symbols will follow into the fading channel with impulse response h(n) that has additive noise n. The MIMO OFDM system with At transmit and Ar receive antennas can be described as:

()() = () () () () ()()+

(3)

The wireless fading channel consists of many parallel Gaussian sub-channels; hence it can be expressed as following: = !! = , . . ,

(4)

Z is the number of paths for the signal propagation, hq is the amplitude response of path q, fDq is the Doppler shift of path q, q is the delay of path q. Single path fading will omit the

summation operator from the previous expression. At the receiver side, the received symbol yt(n) will be transformed back to the frequency domain Y(k) by FFT after omitting the cyclic prefix.

= = ()!! ! = , , (5) A. NLMS Algorithm The weight vector of an adaptive filter should be changed in a minimal mechanism, subject to a constraint imposed on the updated filters output. The NLMS algorithm is based on the principal of minimal disturbance from one iteration to the heading iteration [1]. Let the received symbol vector at time

associating to the vth OFDM symbol be = [ , , ,! ] (6)

The weight vector for the ith sub-channels, i = 0,1,...,N - 1 is = [, ,, , ,,! ] (7)

The desired response is = ( + )() (8)

According to the NLMS algorithm, the update procedure for the weight vector wi(v) is characterized as

Where ei(v) is the error for the ith sub-channels, i = 0,1,...,N-1 is the step-size parameter = () (10)

The optimal value of the incremental change is obtained by = () ()() (11) + () = ()() (12)

A constant value is appended to the denominator to avoid that w(v+1) cannot be bounded when the tap-input vector y(v) is too small, and then the final expression of NLMS can be + () = () + () (13)

B. Step-Size The stability of the NLMS filter depends on the step-size

parameter. Therefore, we have to find the optimum step-size for the adaptive filter. The desired response is set as follows

!() = = 1,2 + = ! ,! + 1, . .1 (2) + = + () (9) 546

= + + () (14)

Where u(v) is an unknown disturbance. An estimate of the unknown parameter w is calculated from the tap-weight vector w(v). The weight error vector is = () (15)

By substituting (15) into (13), we obtain + = () + () (16) The stability of the adaptive filter can be studied by identifying the mean square deviation, denoting E as the expected value

= (17)

By substituting (16) into (17), we obtain + = ()()

(18)

Where () is the undisturbed error signal that can be written as follows

The bounded range for the normalized step-size can be obtained from (18) as follows

< < ()()/ [ / ] (20) For real valued data input, we can use the following equation = (21)

By substituting (21) into (20)

< < [ ] (22)

where E[|e(v)|2] is the estimation of the error signal power. E[|y(v)|2] is the estimation of the input signal power, is the estimation of the mean-square deviation, is the stable parameter and optimum is the optimum step-size parameter [8], [9].

C. SVD Algorithm We can simplify (3) as follows = + (24) Where x represents ! dimensional transmitted symbol, n is ! noise vector, and H is the !! matrix of channel gains. Channel gain matrix can be obtained at the receiver using SVD decomposition.

xVx~

= nHxy += yU Hy=~

xx~

y~y

Figure 1: General MIMO-OFDM system model with adaptive filter

based on NLMS algorithm The transformation shown in Figure 1, transforms the MIMO channel into ! parallel SISO channels with an input and an output . From singular value decomposition and using (24), we can have transmitter precoding and receiver shaping as follows

= ! = ! + = ! ! +

= ! + !

(25)

Hence, the expression can be written as = + (26) For 2x2 MIMO-OFDM system, we channel will be = ! 00 ! (27)

The result of the channel estimation is the

= () (19)

< < (23) 547

decomposition of the channel as we multiply the transmitter and receiver with a gain equal to the summation of ! and !.

III. SYSTEM MODEL The simulation model of the MIMO-OFDM used in the tests is shown in Fig. 2

Bas

eban

d M

odul

atio

n

IFFT +

AppendingCP

RayleighFlat Fading

Channel+

AWGN

FFT+

RemovingCP

Bas

eban

d D

emod

ulat

ion

Ada

ptiv

e R

ecei

ver

FFT+

RemovingCP

ChannelEstimation

Splitter Adder

Figure 1: General MIMO-OFDM system model with adaptive filter based

on NLMS algorithm The generated sub-channels will be modulated using BPSK, the number of sub-channels is 64, and the number of the cyclic prefix is 16 sub-channels. The transmitted symbols will be sent by two antennas on the transmitter side and received by two antennas on the receiver side. The symbols will pass through a Rayleigh fading channel. The power will be divided evenly among the two antennas at the transmitter. The NLMS adaptive filter at the receiver will compensate the effect of the communication channel on the transmitted symbols. The adaptive NLMS receiver subsystem is shown in Fig. 2. It comprises the OFDM demodulation, the NLMS adaptive filter, and then the received symbols were demodulated and I-Q de- mapped to obtain the original transmitted symbols.

FFT+

RemovingCP

Adaptive NLMS Filter

Baseband DemodulationAdder

FFT+

RemovingCP

Figure 2: Adaptive filtering with NLMS algorithm

This subsystem has been used to investigate the effect of varying the step-size of the NLMS adaptive filter algorithm on the BER performance of the MIMO-OFDM system and also to test the impact of utilizing the NLMS adaptive filter on the BER performance.

IV. SIMULATION RESULTS The error performance of the aforementioned NLMS algorithm is explored by performing extensive computer simulations. In these simulations, we considered 2 by 2 MIMO-OFDM system. The data symbol is based on a BPSK modulation. Various values of the algorithms step-size have been used and the signal to noise ratio is 15 dB. The BER performance of using different NLMS algorithm step-sizes on the MIMO-OFDM has been investigated and the result is shown in Fig. 3. It is clear that the step-sizes with values 0.3 - 0.5 give fewer errors. Also the MSE performances, shown in Fig. 4, for various step-sizes have been investigated to measure the convergence speed of the NLMS algorithm. It is clear that the step-size of 0.4 gives fast convergence and the step-size of 0.3 gives lowest MSE level. Hence the step-size of 0.3 was chosen as the best step-size since it provides a trade off between the convergence speed and the steady state noise floor. Finally, the BER performance versus Eb/No for step-sizes 0.3, 0.4, 0.5, and 0.6 have been investigated and compared with that of the conventional MIMO-OFDM receiver. It is clear that using the conventional receiver (i.e., without using the NLMS adaptive filter) the BER is almost 50% because the channel state information is not known at the receiver. However, utilizing the NLMS adaptive receiver structure greatly enhanced the BER performance [10]. The BER performances of the optimized NLMS adaptive equalizer against the SVD channel estimation technique is shown in Fig. 6. The SVD curve with full knowledge of the channel shows an identical result to the theoretical result of the 2x2 MIMO-OFDM over Rayleigh fading channel. The previous data shows a high skew and can be comparable to the optimized NLMS adaptive equalizer. Therefore, the current and the previous data can be added to achieve a more realistic estimation of the channel. The averaging of the current and the previous data proves a better performance than a mere previous data. The SVD will decompose the channel into parallel channels and the channel will be multiplied by !and ! to achieve a performance close to the theoretical one.

V. CONCLUSION

The MSE and BER performances of the proposed NLMS algorithm for MIMO-OFDM system over fading channels were studied and extensive simulations results presented. The BER performance of using different step-sizes for the NLMS algorithm has been investigated and the results showed that the step-sizes with the values of 0.3 - 0.5 give a minimum BER. Also the developed SVD technique has been compared with that of the proposed optimum step-size NLMS adaptive algorithm and the results show that SVD outperforms the NLMS adaptive algorithm.

Optimized NLMS adaptive receiver 548

0 10 20 30 40 50 60 70 80 90 1000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of Iterations

MS

E

Step Size = 0.3Step Size = 0.4Step Size = 0.5Step Size = 0.6

0 1 2 3 4 5 6 7 8 9 1010-3

10-2

10-1

100

Eb/No

BER

data1Averaging of SVDCurrent and Previous SVDSVDOutdated SVDNLMS with step-size = 0.3

Figure 3: BER versus different step-size

Figure 4: Convergence Speed performances for various step-sizes

VI. REFERENCES [1] L. Garcia, Adaptive filtering.Rijeka:Croatia, 2011, pp. 3-18 [2] A. L. Intini, Orthogonal Frequency Division Multiplexing for Wireless

Networks,Dept. Elect. and Comp. Eng.,Uni of California,CA, LA,2000

[3] Ahmedul Kabir, Khandaker Abir Rahman, and Ishtiaque Hussain, Performance study of LMS and NLMS adaptive algorithms in interference cancellation of speech signals.Journal of State University of Bangladesh, Vol. 1,No. 1, pp. 57-65, 2007.

[4] Ling Qin, and Maurice G.Bellanger Convergence analysis of a variable step-size normalized adaptive filter algorithmProc. EUSIPCO, Adaptive Systems, PAS.4, 1996.

[5] Md. M. Rana and Md. K. Hosain. Adaptive Channel Estimation Techniques for MIMO-OFDM Systems. International Journal of Advanced Computer Science and Applications, Vol. 1, pp. 134-138, Dec. 2010 [6] K. Vidhya and K. R. S. Kumar. Enhanced Channel Estimation Technique for MIMO-OFDM Systems with the Aid of EP

Techniques. European Journal of Scientific Research, Vol. 67, pp. 140-156, Dec. 2011

FIGURE 5: BER PERFORMANCE VERSUS EB/N0

Figure 6: BER performance versus Eb/N0 for SVD and NLMS [7] H. Liu and G. Li, OFDM-Based Broadband Wireless Networks,

Hoboken,New Jersey: J. Wiley and Sons INC, 2005, pp. 13-29 [8] Q.Feng and H. Li. The Research and Realization of SVD Algorithm in

OFDM System. in Proc. CISP,2010, pp. 4467-4471 [9] T. Arnantapunpong, T. Shimamura and S. A. Jimaa. A new variable

step size normalized LMSalgorithm.in Proc.NCSP, 2010 [10] A. Goldsmith, Wireless Communications, 3rd edition, New York: Cambridge University Press, 2009, (see pp 321-324)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110-2

10-1

100

Step Size

BER

BER versus different step size for NLMS adaptive filter

0 5 10 15 20 2510-2

10-1

100

Eb/No

BER

data1BER without NLMS adaptive filterStep Size = 0.3Step Size = 0.4Step Size = 0.5Step Size = 0.6549