BER Performance Comparison of STBC-MIMO with different Equalizers

BER Performance Comparison of STBC-MIMO with different Equalizers

Isha Hadke1, Ajay Boyat 2, Brijendra Kumar Joshi3

1,2Electronics & Communication Department

1,2Medi-Caps Institute of Technology & Management Indore, India

3Military College of Telecommunication and Engineering

Mhow, Indore, India

Abstract

Multiple-Input Multiple-Output (MIMO) wireless technology has been acknowledged as one of the most potential techniques to sustain high data rate and high performance in distinct channel conditions. Alamoutis space time block coding (STBC) technique for MIMO system has brought tremendous breakthroughs in wireless technologies just because of its simplicity in decoding. Equalization known for mitigating Inter- symbol Interference (ISI) results in interference between successive transmission created by multipath propagation is also been discussed with BPSK modulation over Rayleigh fading channel. In this paper we present performance comparison of space time block coding with different equalizer techniques such as zero forcing (ZF) Equalizer, minimum mean square error (MMSE), maximum likelihood sequence estimation (MLSE). It is observed that the ML equalizer render minimum SNR value for the related BER value. The lower SNR for the same BER implies that it consumes much less power than the other two equalization techniques. This entail that MLSE outperforms ZF and MMSE equalizer.

Keywords- MIMO, MMSE, MLSE, STBC, ZF

1. Introduction

   Multiple-Input Multiple-Output (MIMO) systems boost modern communication to a great extent. MIMO systems are simply defined as the system comprising multiple transmitter antennas and multiple receiver antennas. Communication researches show that MIMO system can provide a potentially tremendous capacity, which grows approximately linear with the number of antennas. Implementation of MIMO in wireless communication

   systems increased instantaneously, especially in wireless LANs (Local Area Networks). The MIMO system expands our focus to turn multi-path propagation, which is an existing obstacle in conventional wireless communication, into an advantage for users [1], [2].

   The most important characteristic of MIMO systems is space-time processing. Space-Time Codes (STCs) are the codes intended for the use in MIMO systems. In STCs, signals are coded in both spatial and temporal dimensions which render improved bit error rate (BER) performance. Space time coding also aids in enhancing information rate. Along with dissimilar types of STCs, the one which seize various benefit over other kind of STCs is orthogonal Space-Time Block Codes (OSTBCs). OSTBC is one of the algorithms recognized for MIMO systems, which render high diversity when the channel is unknown at the transmitter. As these codes work independent of receiver antenna thus is form of transmitter diversity. This code comprises the capability of transmitting each symbol per time instant, hence also recognized as full rate code [2]. To combat from the effects of Inter-symbol interference (ISI), various equalization techniques is discussed and simulation study shows BER performance comparison between them.

2. System Model

   Considering a MIMO system having two transmit antenna and two receive antenna as shown in Fig.1. At the transmitter end, the data stream are first converted using serial to parallel convertor and then mapped using BPSK modulation technique, after that data stream enters into a Space Time Encoder which is capable of increasing data

   rate by transmitting various data stream parallel. The encoder outputs are then conveyed to transmit antennas from where the the signal is passed through a wireless propagation channel, which is assumed to be Rayleigh

   y1=px1+px2+z1 (4) y2=p 2 z2 (5)

   having uniformly distributed phase and Rayleigh

   distributed magnitude.

   Fig.1. Proposed MIMO Model

   The 2 x 2 channel matrix is represented as H =

   represents the channel coefficient among ith receive and jth transmit antenna.

   At the receiver end, receiver performs equalization (this can be ZF/MMSE/MLSE) to reduce or eliminate ISI created by a multipath channel. The data stream can now be decoded and demodulated using space time decoder and then serially converted using parallel to serial convertor.

   1. Space Time Block Code

      Alamouti has recommended a complex orthogonal space- time block code designed for two transmit antennas. In the Alamouti encoder, two consecutive symbols x1 and x2 are encoded with the following space-time coded matrix described by [4]

      X = (1)

      It is obvious that the encoding is done in both the space and time domains. Alamouti encoded signal is transmitted from the two transmit antennas over two symbol instances. At t+T, i.e. during the first symbol instant two symbols x1 and x2 are simultaneously transmitted from the two transmit antennas. At t= 2T, i.e. during the second symbol instant these symbols are transmitted again, where

      is transmitted from the first transmit antenna and

      transmitted from the second transmit antenna. For

      where z1 and z2 signify the additive noise at time t and t+Ts respectively. In this paper we have proposed Alamoutis space time block code for two transmit antenna and two receive antenna case [4].

3. Equalizer

   Equalizer is a digital filter that grants an estimated inverse of channel frequency response. Equalization is used to alleviate the effects of Inter-symbol Interference (ISI) to minimize the likelihood of error that occurs without elimination of ISI, but this dropping of ISI effects has to be balanced with prevention of noise power enhancement [1].

   1. ZF Equalizer

      Zero Forcing Equalizer (ZF) is a linear equalization algorithm exploit in communication assumption, which reverses the frequency response of the channel. This equalizer was first recommended by Robert Lucky. The ZF Equalizer employs the inverse of the channel to the received signal, to recover the signal before the channel. The name Zero Forcing corresponds to pulling down the ISI to zero in a noise free case. This will be advantageous when ISI is significant compared to noise. Considering a channel containing frequency response F(f) the zero forcing equalizer C(f) is designed such that C(f) = 1 / F(f). Thus the collective effect of channel and equalizer provide a flat frequency response and linear phase F(f)*C(f) = 1. For a certain channel containing frequency response H(s) then the input signal is multiplied by the reciprocal of this [10]. This is expected to remove the effect of channel from the received signal, in precisely the ISI [5]. For minimal complexity let us assume a 2×2 MIMO channel, the channel is designed as,

      The signal received on the first receive antenna is,

      1 1,1 1 1,2 2 1 1,1 1,2

      1 1,1 1 1,2 2 1 1,1 1,2

      y =h x +h x +n =[h h ] + (6)

      The signal received on the Second receive antenna is,

      y =h x +h x +n =[h h ] + (7)

      Maximum Likelihood signal detection of Alamoutis space-time coding scheme, we assume that two channels

      2 2,1 1 2,2 2 2 2,1 2,2

      gains p(t) and p(t) remain constant over two consecutive symbol periods such that

      p(t)=p(t+T)=p=|p| (2)

      p(t)=p(t+T)=p=|p| (3)

      Where |p| and symbolize the amplitude gain and phase rotation over the two symbol periods. At the receiver the received signals y1 and y2 at time t and t+Ts can be given as

      Where y1, y2 are the received symbol on the first and second antenna respectively,

      p,1 s the channel from 1st transmit antenna to 1st receive antenna,

      p,2 is the channel from 2nd transmit antenna to 1st receive antenna,

      p,1 is the channel from 1st transmit antenna to 2nd receive antenna,

      p,2 is the channel from 2nd transmit antenna to 2nd receive antenna,

      x1, x2 are the transmitted symbols and

      n1, n2 are the noise on 1st and 2nd receive antennas.

      The equation can be described in matrix notation as follows:

      = (8)

      Equivalently,

      method minimizing the MSE within a specific class, as like as the class of linear estimators. The linear MMSE estimator is a kind of estimator achieving minimum MSE among all estimators of the form AY + b. If the measurement Y is a random vector, A is a matrix and b is a vector [11]. Let us now make an effort to understand the math for extracting the two symbols which interfered with each other. In the first fraction of time, the signal received on the first receive antenna is,

      y = H.x + n (9)

      To solve for x, we need to find a matrix W which satisfies

      y1=p,1×1+h

      1,2×2+n1=[h

      1,1

      h ] +n

      (14)

      1,2 1

      1,2 1

      WH = I. The Zero Forcing (ZF) detector for meeting this constraint is given by,

      The signal received on the second receive antenna is

      W = (HHH)-1 HH (10)

      Where W – Equalization Matrix and H – Channel Matrix,

      y2=h

      Where

      2,1×1+h

      2,2×2+n2=[h

      2,1

      h ] +n

      2,2 2

      2,2 2

      (15)

      This matrix is known as the Pseudo inverse for a general m x n matrix where

      y1, y2 are the received symbol on the first and second antenna respectively,

      y1, y2 are the received symbol on the first and second

      HHH=

      (11)

      antenna respectively,

      p,1 is the channel from 1st transmit antenna to 1st receive antenna,

      p,2 is the channel from 2nd transmit antenna to 1st

      receive antenna,

      (12)

      p,1 is the channel from 1st transmit antenna to 2nd

      receive antenna,

      p,2 is the channel from 2nd transmit antenna to 2nd

      It is seen that the off diagonal elements in the matrix HHH are not equal to zero, for the reason that the off diagonal elements are non zero in values. Zero forcing equalizer efforts to null out the interfering terms at the moment of acquiring the equalization, i.e. the interference from x2 is tried to be null out when solving for x1 and vice versa. But implementation of this causes amplification of noise. Hence Zero forcing equalizer is not the best developed equalizer. However, it is simple and evident to implement [5].

      receive antenna,

      x1, x2 are the transmitted symbols and

      n1, n2 are the noise on 1st and 2nd receive antennas.

      Equivalently,

      y = H.x + n (16)

      The Minimum Mean Square Error (MMSE) approach tries to find a coefficient W which

      Minimizes the

   2. MMSE Equalizer

      A minimum mean square error (MMSE) estimator

      Criterion,

      E{[Wy-x][Wy-x]H} (17)

      illustrates the approach which minimizes the mean square error (MSE), which is a general method of computing the estimator quality [11]. The important feature of MMSE equalizer is that it does not usually eliminate ISI completely but, suppresses the total power of the noise and ISI components in the output [5]. Let x be an unknown random variable, and let y be a known random variable. In [7], an estimator (y) is any function of the measurement y, and its mean square error is given by.

      MSE = E {( )}, (13)

      where the expectation is held over both x and y.

      The MMSE estimator is then characterized as the estimator attaining least MSE. In a lot of cases, it is

      Where W – Equalization Matrix H – Channel Matrix and

      n – Channel noise y- Received signal.

      To solve for x, we need to find a matrix W which satisfies W*H =I. The Minimum Mean Square Error (MMSE) detector for meeting this constraint is given by, [5]

      W = [HHH+ NoI]-1 HH (18)

   3. MLSE Equalizer

      A maximum likelihood sequence estimator (MLSE) for a single carrier communication systems transmitting N complex symbols s = {s1, s2, , sN}T, chosen from an alphabet D, having impulse response h = {h0, p,, hL-1} of length L through a multipath channel, the symbol received on the kth instant is described by [8]

      impossible to determine a closed form for the MMSE estimator. In these cases, one possibility is to look for the

      = s

      = s

      r

      r

      k j k-j

      + nk,

      (19)

      where nk is the kth zero-mean, 2 variance, Gaussian noise sample. To find the most likely transmitted sequence s, the cost function

      the above following observations are made. The ML equalizer is the best of the three equalizers, as it provide minimum SNR value for corresponding BER value. The lower SNR for the same BER implies that it consumes much less power than the other two techniques. Hence we

      L =

      L =

      rk jsk-j (20)

      can conclude that BER performance of ML Equalizer is superior to zero forcing Equalizer and Minimum Mean

      needs to be minimized. The MLSE equalizer based on the Viterbi Algorithm (VA) minimizes equation (20) optimally by exploiting a trellis, with computational complexity linear in N and exponential in L. In our future work we will propose that the combination of MIMO with OFDM will make the system more spectrally efficient, here we will also recommend combination of different equalization which will bring more robustness to the system [6].

4. Simulation Model and Result

The simulation test bench has been prepared for the MIMO technique. The parameters used in this are listed below,

Parameter	Values
Modulation technique	BPSK
Channel	Rayleigh
SNR level	0-25 dB
MIMO tech.	STBC
Equalizer	ZF,MMSE,MLSE

The result is given in comparative manner below

Performance of different Equalizer for 2×2 MIMO System

ZF

-1 MMSE

10 MLSE

-2

Bit Error Rate

Bit Error Rate

10

-3

10

Square Equalizers.

6. References

[1] M. Gupta, R. Nema, R. S. Mishra, P. Gour, Bit Error Rate Performance in OFDM System Using MMSE & MLSE Equalizer Over Rayleigh Fading Channel through the BPSK, QPSK, 4QAM & 16 QAM Modulation Technique, IJERA, vol. 1, Issue 3, pp.1005-1011. [2]http://www.springer.com/cda/content/document/cda_downloa ddocument/9780387292915c2.pdf?SGWID=0045369518p10424 2088.

1. I. Khan, S. A. Khan Tanoli, and N. Rajatheva, Capacity and performance analysis of space-time block coded MIMO-OFDM systems over Rician fading channel, International Journal of Electrical and Computer Engineering 4:15, 2009.

2. Md. M. Haque, M. S. Rahman and K. D. Kim, Performance Analysis of MIMO- OFDM for 4G Wireless Systems under Rayleigh Fading Channel, International Journal of Multimedia and Ubiquitous Engineering vol. 8, No.1, January, 2013.

3. M. Kumar & J. Kaur, Performance analysis of BPSK system with ZF & MMSE equalization, International Journal of Latest Trends in Engineering and Technology (IJLTET) vol. 1 Issue 3 September 2012.

4. H.C. Myburgh, Student Member, IEEE, and J.C. Olivier, A Low Complexity Recurrent Neural Network MLSE Equalizer: Applications and Results.

5. N. S. Kumar, Dr.K. R. Shankar Kumar, Performance Analysis of M*N Equalizer based Minimum Mean Square Error (MMSE) Receiver for MIMO Wireless Channel, International Journal of Computer Applications (0975 8887)vol. 16 No.7, February 2011.

6. H.C. Myburgh and J.C. Olivier. Near-Optimal Low Complexity MLSE Equalization, Proceedings of Wireless Communications and Networking Conference, WCNC 2008:226 230, 2008.

[9]A. F. Molisch, Wireless Communications, by Wiley India

(p) Ltd 2005.

1. http://en.wikipedia.org/wiki/Zero_Forcing_Equalizer

2. http://en.wikipedia.org/wiki/Minimum_meansquare_error

-4

10

-5

10

0 5 10 15 20 25

Average Eb/No,dB

Fig.2. BER performance of MIMO system

5. Conclusion

This paper is a simulation study on the performance comparison of STBC-MIMO with different Equalizer using BPSK modulation technique. The test bench has been developed successfully for simulation and the BER

0.001 has been targeted by different equalizer on 2×2 MIMO System. The SNR levels for BER 0.001 are 10, 14 and 17 dB for MLSE, MMSE and ZF respectively. From