IJECT Vol. 4, IssuE spl - 4, AprIl - JunE 2013 ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

w w w . i j e c t . o r g 84 InternatIonal Journal of electronIcs & communIcatIon technology

Analysis of MIMO System Through ZF & MMSE Detection Scheme1Swetamadhab Mahanta, 2Ankit Rajauria1,2Dept. of ECE, RIET, Jaipur, Rajasthan, India

AbstractThis paper proposes an improved vertical Bell Labs Layered Space-Time (V-BLAST) with spatial multiplexing technique used in MIMO systems. The MIMO technology exploits the use of multiple signals transmitted into the wireless medium to improve the wireless channel performance. The MIMO Technique is under significant consideration for development of 4G wireless system. SIC technique is used for a errorless output. This Simulation results shows that the proposed V-BLAST, which employs SIC scheme, offers the performance very close to the optimal turbo-MIMO approach, while providing stupendous improvements in computational complexity.

KeywordsMIMO Systems, V-BLAST, MRC, SIC, ZF, MMSE, MATLAB.

I. IntroductionThe evolution of MIMO system started from the work of Winters [1], Foschini and Gans [2], and Telatar [3-4]. Their work depicted the advantages of using multiple antennas by exploiting signal diversity offered by multipath effect. MIMO system offers a very high spectral efficiency. Multiplexing can also be achieved by using multiple antennas in parallel both in the transmitter and in the receiner such that multiple data streams are able to be transmitted at the same time, resulting in an increased data rate. Now to achieve such spectral efficiency improvements, we need the knowledge of the channel condition, which is represented by the channel matrix. Although, lots of technical problems remains in the design of robust and fast wireless systems that gives better performance necessary to support many develop applications, due to the frequency selective, power-limited and susceptible to noise nature of the channel. The reliable transmission requires symbols to be effectively recovered at the receiving end. For a particular channel coded MIMO system, the superlative soft decoder for the minimization of the BER is generally the maximum-likelihood (ML) detector [5-6]. But, the major drawback of this detection process is that, it sometimes becomes excessive complex because of its complexity that increases exponentially with the increase no of transmitting antennas at the transmitter and also directly proportional to its order. By balancing the error of previously detected symbols, [7] and [8] a new detection scheme has been introduced which surpasses the previous MMSE V –BLAST detector for a particular channel coded MIMO architecture. In [9] and [10], the detection scheme is improved through some hinder data probability estimation. In [11], many reduced-complexity actualizations of the detector schemes are derived so that by using only one matrix inverse, we can able to detect each transmitted symbol vector. Therefore, this detection scheme can act as a promising candidate in practical case. The rest of the paper is organized in the following way. In Section II, the MIMO system model is explained. The V-BLAST detection scheme which is based on MIMO systems under appropriate channel estimation is explained in Section III. In Section IV, we have the functionality of the proposed detection scheme, i.e. Zero Forcing and Minimum Mean Square Error channel. Finally the simulation results and

conclusion are given in Section V and Section VI, respectively.

II. System Model and FunctioningThe MIMO system considered for this proposed scheme isshown in fig. 1.

Fig. 1: Block Diagram of MIMO System Here, we consider tT no of transmit antennas and rR no of receive antennas. Here the overall estimated channel can be shown as a

tr × complex matrix H with the entries of where trh × are the flat fading coefficients of the estimated channel from the tth transmitting antenna to the rth receiving antenna. Now we can write the MIMO system model as,

=

⋅⋅

ry

yy

2

1

+

⋅⋅

rtrtrr

t

t

n

nn

x

xx

hhh

hhhhhh

.

...

............

.. 2

1

2

1

21

22221

11211

Now we can rewrite the above system model as,

y xH= + n (1) Where,

y is r dimensional receive antenna.

H is tr × dimensional channel matrix.hrt is flat fading channel coefficients.

x is t dimensional transmit antenna.

n is r dimensional noise.

III. Related WorkV-BLAST stands for Vertical Bell Lab Layered Space Time Architecture. It is a non linear detection which involves Successive Interference Canceller and that also involves some linear and combinatorial nulling techniques (For example MRC, ZF or MMSE). Generally the MIMO system architecture requires multiple no. of antennas both at transmitter part as well as at the receiver part. It just increases the data rate by transmitting different independent information bits on different antennas in

IJECT Vol. 4, IssuE spl - 4, AprIl - JunE 2013

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ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

parallel (Spatial Multiplexing). For V-BLAST, there is no need of channel knowledge is required at the transmitter part. Generally, the detection process consists of two main parts:1. Interference and noise suppression.2. Interference and noise cancellation.V BLAST employs SIC, where the impact of each estimated symbol is cancel from the receive signal vector.Now from equation (1), we know that,

y xH= + n

i.e. [ ]thhhy .21=

tx

xx

.2

1

+ n (2)

nxhxhxhy tt ++++= ....2211 (3)Now considering the Pseudo Inverse or the left inverse of Hi.e. Q

i.e. tHQ = (4)So,

=

Ht

H

H

q

qq

Q.2

1

(5)

Now,

(6)Where tI is the identity matrix.i.e.

=

tHt

Ht

HHt

HHH

t

hqhq

hqhqhqhqhq

I

.............

..

1

2222

12111

=

100000.000001000001000001

ie, 1.......2211 === hqhq HH

and 0........1221 === hqhq HH

This can be essentiality be summarised as,

(7)Now, multiplying Hq1 in both side of equation (3), we have,

{ } nqxhxhxhqyqy Htt

HH1221111 ...~ ++++== (8)

Finally we get,

nxy ~~11 += (9)

now,this can be employed to decode 1xWhere,

nqn H ~~1= (10)

Finally, by cancelling the interference from 1x , we have efficiently reduced this to an ( )1−× tr MIMO system.

IV. Detection Scheme

A. Maximal-Ratio CombinerIn telecommunication system, Maximal-Ratio Combining (MRC) is a process of diversity enhancement where:

Symbols from individual transmitting antenna are grouped • together.Here the gain of each channel is directly proportional to the • root mean square of the estimated symbols.Also the gain of each channel is inversely proportional to the • mean square noise value of that particular channel.

It may also term as ratio-squared combining. It can also be known as Match Filter .This can also be used as optimum combiner used in AWGN channels. To restore a signal to its original shape and size, this scheme can be employed.

B. Zero Forcing (ZF)Zero Forcing refers to a technique of linear equalization algorithm used in the world of telecommunications that involves inverse of the frequency response of a particular channel. This scheme was firstly proposed by Robert Lucky.The ZF scheme applies the inverse of the frequency response of channel to the symbol received, so that the original signal can be detected to an optimum level. ZF is the one of the best linear receiver detection method having low computational complexity, but it suffers from sudden noise enhancement. At high SNR, it gives optimum result. Now, the estimated result is given by:

( ) yHHHX #1#ˆ −= (11)

Where, #H represents the pseudo-inverse of H .

C. Minimum Mean Square Error (MMSE)In telecommunication, a Minimum Mean Square Error (MMSE) estimator is a estimator which follows an estimation method, through which it minimizes the mean square error for the fitted values of various dependent variables.The method MMSE more closely refers to the estimation in a quadratic cost function in Bayesian setting. The thinking procedure behind this Bayesian approach is to estimate stems from various practical conditions where we sometimes have some major information about the parameters which are required to be estimated.

IJECT Vol. 4, IssuE spl - 4, AprIl - JunE 2013 ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

w w w . i j e c t . o r g 86 InternatIonal Journal of electronIcs & communIcatIon technology

MMSE receiver holds back both interference as well as noise components, but as far as the ZF receiver is concern, it only eliminates the interference or the noise. From this we can conclude that the Mean Square Error (MSE) is minimized. To overcome the drawback of noise enhancement of ZF, the concept of MMSE is introduced. So, we can say that, MMSE is pretentious to ZF in the presence of noise and interference. Now the Linear Minimum Mean Square Estimator for the MIMO System is.

yHHHPX nd12## )(ˆ −+= s (12)

Where,

=dP Power of each diagonal element.

Power of noise component.

Fig. 2: MIMO Estimator

V. Simulation ResultsIn this section, we illustrate the performance of the proposed V-BLAST scheme in MIMO-OFDM systems. The simulations are done for a Rayleigh fading channel using BPSK symbol method. From the comparison plot shown in Figure 3, we observe the performance of BER with Eb/No in the MIMO system. From Figure 4 we compare MMSE with Simulated BER and ZF and MRC. In terms of complexity, the proposed algorithm has much less complexity than not only the full search algorithm but also the sub-region based algorithm. From the results, we observe that similarly to the spatial correlation case, channel estimation error results in a certain amount of degradation in performance for all the detection schemes. However, contrary to the spatial correlation case, the estimation error has an almost equal impact on all schemes.

Fig. 3: Simulated Bit Error Rate Result

Fig. 4: Comparison of Simulated BER Output With MRC and ZF Output

VI. ConclusionThrough this paper, we provide a special multiple antenna system (MIMO) with the V-BLAST technique using several detectors (MRC,ZF). We came to a conclusion that the performance is limited by error propagation. A comparative study of detectors is made by comparing their outputs with reference to the plots of BER and their corresponding SNR. We show the benefits of ordering strategy over other MIMO cancellation methods. MIMO is an important technology for enabling the wireless industry to deliver a vast potential and promise of wireless broadband. However, the drawback of V-BLAST algorithms is propagation of decision errors. Further, due to the interference suppression, early detected symbols at the receiver benefit from lower diversity than later ones. Thus, the algorithm results in unequal diversity advantage for each symbol.

VII. AcknowledgementThe authors would like to thank Club First Techno Edusolutions PVT LTD. and also the Management, Principal, Director and HOD of Electronics and Communication department of Suresh Gyan Vihar University, Jaipur, Rajasthan, India, and Rajasthan Institute of Engineering & technology, Jaipur, Rajasthan, India for encouraging us for this research work.

References[1] V-BLAST architecture from Bell Labs, wikipedia.[2] P. W. Wolniansky, G. J. Foschini, G. D. Golden, R. A.

Valenzuela,"V-BLAST: An architecture for realizing very high data rates over the rich scattering", Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733.

[3] Kyungchun Lee, Joohwan Chun,"Symbol Detection in VBLAST Architectures under Channel Estimation Errors", IEEE Transactions on Wireless Communications, Vol. 6, No. 2, February 2007.

[4] Shreedhar. A. Joshi, Dr. Rukmini T S, Dr. Mahesh H M., "Performance analysis of MIMO Technology using V-BLAST Technique for different linear Detectors in a slow fading channel", IEEE International Conference on Computational conference on Computational Intelligence and Computing

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Research (ICCIC’2010), pp. 453-456.[5] G.J. Foschini et al,"Analysis and Performance of Some Basic

Space-Time Architectures", IEEE Journal Selected Areas Comm. 21, No. 3, pp. 281-320, April 2003.

[6] G.J Foschini,"Layered space-time architecture for wireless communication in a fading environment when using multiple antennas", Bell Lab. Tech. J., Vol. 1, No. 2, pp. 41-59, 1996.

[7] G.J Foschini et al,"Simplified Processing for High Spectral Efficiency Wireless Communication Employing Multielment Arrays", IEEE Journal on Selected Areas in Communications, Vol. 17, No. 11, pp. 1841-1852, Nov. 1999.

[8] J. Winters,“On the capacity of radio communications systems with diversity”, IEEE Journals on Selected Areas of Communication, pp. 871878, June 1987

[9] G. J. Foschini, M. Gans,“On limits of wireless communications in a fading environment when using multiple antennas”, Wireless Personal Comm., pp. 311-335, March 1998.

[10] E. Telatar,“Capacity of multi-antenna gaussian channels”, AT & T Bell Labs Internal Technical Memo, June 1995.

[11] E.Telatar,“Capacity of multi-antenna gaussian channels”, European Transaction on Telecommunication, pp. 585-596, November 1999.