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International Journal of Engineering & Technology IJET-IJENS Vol:13 No:02

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Performance Comparison of MIMO Systems over AWGN and Rayleigh Channels using OSTBC4 with Zero Forcing Receivers Navjot Kaur and Lavish Kansal Electronics and Communication Engineering Department Lovely Professional University, Phagwara, India [email protected] [email protected] Abstract – MIMO (Multiple-input multiple-output) is an antenna technology for wireless communications in which multiple antennas are used at both the transmitter and the receiver. The antennas used at each end of the communications circuit are combined to optimize data speed within the limited radio frequency spectrum. The performance analysis of MIMO system over AWGN and Rayleigh fading channels using OS TBC4 as space time block coding with Zero Forcing (ZF) receiver is presented. The performance can be improved by using different antenna selection at transmitter and receiver sides. In this paper, OS TBC4 is used as space time coding in which the number of transmitting antennas is 4 whereas the receiving antennas are being varied from 1 to 4. S o in this way, MIMO systems take advantage of spatial diversity. The Bit Error Rate (BER) analysis for M-PS K modulation using OS TBC4 over AWGN and Rayleigh channels is presented.

Index Term–

MIMO, AWGN, Rayleigh, OS TBC4, spatial diversity, Zero Forcing, BER, M-PS K.

I. INTRODUCTION Multiple-Input Multiple-Output (MIMO) technology is a wireless technology that uses multiple transmitters and receivers to transfer more data at the same time spatial multiplexing [1]. A MIMO system utilizes the spatial diversity by means of spatially separated antennas in a dense multipath scattering environment. MIMO technology takes advantage of a radio-wave phenomenon called multipath where transmitted information bounces off walls, ceilings, and other objects, reaching the receiving antenna multiple times via different angles and at slightly different times. MIMO takes advantage of multipath to combine the information from multiple signals improving both speed and data integrity [2]. A MIMO system increases the system capacity by introducing additional spatial channels and spectral efficiency for a given total transmitted power by using space-time coding [2]. The high data rates can be achieved by using space-time coding (STC) such as OSTBC4 used as STC over here [3]. The two main functions of STC: diversity & multiplexing. The maximum performance needs tradeoffs between diversity and multiplexing. MIMO systems are meant to improve BER or

data rate by using multiple transmitting and receiving antennas. MIMO makes antennas work smarter by enabling them to combine data streams arriving from different paths and at different times to effectively increase receiver signal-capturing power. Smart antennas use spatial diversity technology, which puts surplus antennas to good use. If there are more antennas than spatial streams, the additional antennas can add receiver diversity and increase range [4]. An efficient implementation of space-time block coding (STBC) for broadband wireless communications improves the performance and diversity gains of a space time (ST) coding system through a number of parameters including type of trellis codes and channel fading [5] [6].

Fig. 1.1. Block Diagram of 2 X 2 MIMO System

The block diagram of 2 X 2 MIMO system is represented in Fig. 1.1. In this paper, the effects of antenna selection on the performance of MIMO systems using OSTBC4 over AWGN and Rayleigh channels using Zero Forcing receivers are considered [7]. The data experiences much impairment during transmission, especially due to noise in the channel.

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International Journal of Engineering & Technology IJET-IJENS Vol:13 No:02 II. LITERATURE REVIEW MIMO technology influences multipath behavior by using multiple, “smart” transmitters and receivers with an added “spatial” dimension to increase the system performance and range. A simple two-branch transmit diversity scheme was presented by S. Alamouti [8]. The scheme uses two transmit antennas and one receive antenna. It provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. The scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. The approach to increase the capacity of MIMO systems by employing the spatial multiplexing where independent information streams are transmitted from the antennas was explained by C. Wang [9]. These information streams are then separated at the receiver by means of appropriate signal processing techniques such as maximum likelihood (ML) which achieves optimal performance or linear receivers like Zero-Forcing (ZF) which provide sub-optimal performance but it also offers significant computational complexity reduction with tolerable performance degradation. S. G. Kim et.al [10] discussed that the MIMO system not only improve spectral efficiency, but also enhance link throughput or capacity of the system by comparing MIMO with SISO technology. The authors presented a tight closed form BER approximation of MPSK for MIMO ZF receiver over continuous flat fading channels. The larger the difference between the number of transmit antennas and receive antennas is, the better performance is.

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simple spatial multiplexing at the transmitter and zero-forcing processing at the receiver in multiuser MIMO scheduling systems. N. S. Kumar et. al [14], investigated about the three types of equalizer for MIMO wireless receivers. The authors discussed about a fixed antenna MIMO antenna configuration and compare the performance with all the three types of equalizer based receiver namely ZF, ML, and MMSE. BER performance of ML Equalizer is superior than zero forcing Equalizer and Minimum Mean Square Equalizers. Based on the mathematical modeling and the simulation result it is inferred that the ML equalizer is the best of the three equalizers. III. M ODULATION TECHNIQUE Modulation is a very general term for superimposing information (whether analog or digital bits) on some form of carrier signal. There are many forms of modulation each with different bandwidth (spectral) efficiency. Modulation is the process of varying the characteristics of carrier signal in accordance to the modulating signal. Modulation is the process of converting analog carrier signals into digital information (modulate) and demodulation is the process of decoding the transmitted information (demodulate). Modulation can be analog and digital type. A modulator performs modulation and a demodulator performs demodulation, the inverse operation of modulation. Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). Phase-shift keying (M-PSK) for which the signal set is:

The impact of antenna selection on the performance of multiple input-multiple output (MIMO) systems over nonlinear communication channels was presented by A. I. Sulyman [11]. The author have derived exact analytical expressions for evaluating the PWEP performance of spacetime trellis codes over nonlinear MIMO channel, case of Rayleigh fading, when antenna selection is employed at the receiver side. Performance degradation due to nonlinearity in the channel reduces as less numbers of antennas are s elected at the receiver, representing some savings in SNR penalty due to nonlinearity for the reduced-complexity system.

(1.1) where Es the signal energy per symbol Ts is the symbol duration and fcτ is the carrier frequency. This phase of the carrier takes on one of the M possible values. (1.2)

V. Tarokh et.al [12] design a channel codes for improving the high data rate and the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into multiple streams that are simultaneously transmitted using multiple transmit antennas. The received signal at each receive antenna is a linear superposition of the multiple transmitted signals perturbed by noise. C. Chen [13] discussed the performance analysis of the lowcost and effective transmission strategy that employs the 138402-9292-IJET-IJENS © April 2013 IJENS

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(1.3) where n(t) is the additive white Gaussian noise.

Fig. 1.2. Constellation Diagram for 8-PSK Signal

(B) RAYLEIGH CHANNEL Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, like that used by wireless devices. Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and receiver. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission medium will vary randomly, or fade, according to a Rayleigh distribution. The Rayleigh distribution is basically the magnitude of the sum of two equal independent orthogonal Gaussian random variables and the probability density function (pdf) is given by:

The circular constellation diagram for M-ary PSK modulation is as shown in Fig. 1.2. The main constraint was to keep the amplitude of the transmitted signals be constant. In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. IV. CHANNELS In telecommunications, communication channel refers to either a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel. A channel is used to convey an information signal, for example a digital bit stream, from one or several transmitters to one or several receivers. A channel has a certain capacity for transmitting information, often measured by its bandwidth in Hz or its data rate in bits per second. In this paper, the focus will be on performance analysis of MIMO system over AWGN channel and Rayleigh channels using OSTBC4 code structure.

(1.4) V. M IM O CHANNEL The 2X2 MIMO channel with an antenna array with 2 elements at the transmitter and an antenna array with 2 elements at the receiver is presented in Fig. 1.3. The inputoutput notation of the MIMO system can now be expressed by the equation: (1.5) where ⊗ denotes convolution, s(t) is a n t X 1 vector corresponding to the n t transmitted signals, y(t) is a n r X 1 vector corresponding to the n r and u(t) is the additive white noise.

(A) AWGN CHANNEL Additive white Gaussian noise (AWGN) is a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density and a Gaussian distribution of amplitude. The model does not account for fading, frequency selectivity, interference, nonlinearity or dispersion. It is a universal channel model for analyzing modulation schemes. AWGN adds a white Gaussian noise to the signal passing through it. This implies that the channel’s amplitude frequency response is flat (thus with unlimited or infinite bandwidth) and phase frequency response is linear for all frequencies so that modulated signals pass through it without any amplitude loss and phase distortion of frequency components. Fading does not exist but the only distortion is introduced by the AWGN. The received signal is simplified to

Fig. 1.3. MIMO Channel

The impulse response of the channel between the jth transmitter element and the ith receiver element is denoted as h ij (τ,t). The MIMO channel can then be described by the n r X n t H(τ,t) matrix:


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case. This will be useful when ISI is significant compared to noise.

(1.6) The matrix elements are complex numbers that correspond to the attenuation and phase shift that the wireless channel introduces to the signal reaching the receiver with delay τ. Space–time block coding is a technique used in wireless communications to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of datatransfer. Space–time coding combines all the copies of the received signal in an optimal way to extract as much information from each of them as possible. Here we have used OSTBC4 as space-time block coding. These codes achieve rate-1/2. The given matrix gives the only way to achieve orthogonality. STBC is designed such that the vectors represents any pair of columns taken from the coding matrix is orthogonal. The result of this is simple, linear, optimal decoding at the receiver. Tarokh et.al [12] discovered a set of STBCs that are particularly straightforward, and coined the scheme's name. They also proved that no code for more than 2 transmit antennas could achieve full-rate. They also demonstrated the simple, linear decoding scheme that goes with their codes under perfect channel state information assumption.

For a channel with frequency response F(f) the zero forcing equalizer C(f) is constructed by C(f) = 1 / F(f). Thus the combination of channel and equalizer gives a flat frequency response and linear phase F(f) C(f) = 1. If the channel response (or channel transfer function) for a particular channel is H(s) then the input signal is multiplied by the reciprocal of it. This is intended to remove the effect of channel from the received signal, in particular the inter symbol interference (ISI). By using the linear model, the received vector can be represented as: y

(1.8)

The received signal on the first receive antenna is,

(1.9) The received signal on the second receive antenna is,

(1.10) where y 1 ,y 2 are the received symbol on the first and second antenna respectively, h 1,1 is the channel from 1st transmit antenna to the 1st receive antenna, h 1,2 is the channel from 2nd transmit antenna to the 1st receive antenna, h 2,1 is the channel from 1st transmit antenna to the 2nd receive antenna, h 2,2 is the channel from 2nd transmit antenna to the 2nd receive antenna, x1 , x2 are the transmitted symbols and n 1 , n 2 are the noise on 1st and 2nd receive antennas. The equation can be represented in matrix notation as follows:

(1.7) VI. ZERO FORCING EQUALIZER Zero Forcing Equalizer refers to a form of linear equalization algorithm used in communication systems which applies the inverse of the frequency response of the channel. This form of equalizer was first proposed by Robert Lucky. It has many useful applications such as IEEE 802.11n (MIMO) where knowing the channel allows recovery of the two or more streams which will be received on top of each other on each antenna. The name Zero Forcing corresponds to bringing down the inter symbol interference (ISI) to zero in a noise free

(1.11) Therefore, y= Hx + n

(1.12)

VII. SIM ULATED RESULTS In this section, the Bit Error Rate analysis of MIMO system over AWGN and Rayleigh channels using OSTBC4 code structure with zero forcing receivers is done for M-PSK


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International Journal of Engineering & Technology IJET-IJENS Vol:13 No:02 Modulation. The BER analysis of MIMO system is done for M-PSK over AWGN and Rayleigh fading channels where M can be 32, 64, 128, 256, 512 and 1024 for different antenna configurations. Here we have used receiving antennas ranging from NR = 1 to NR = 4.

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SNR vs BER Plot of 256-PSK in AWGN Channel

0

10

No. No. No. No.

of Rx of Rx of Rx of Rx

= = = =

1 2 3 4

-1

10

bit error rate

(A) M-PSK over AWGN Channel SNR vs BER Plot of 32-PSK in AWGN Channel

0

10

No. No. No. No.


= = = =

1 2 3 4

-2

10

-1

bit error rate

10

-3

10

0

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30 40 signal to noise ratio

50

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(d) 256-PSK

-2

10


0

10

No. No. No. No.

-3

0

5

10

(a)


25

30

1 2 3 4

-1

10

32-PSK


0

= = = =

bit error rate

10


10

No. No. No. No.


= = = =

1 2 3 4

-2

10

-1

bit error rate

10

-3

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0

10

-2

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(e) 512-PSK SNR vs BER Plot of 1024-PSK in AWGN Channel

0

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No. No. No. No.

-3

10

0

5

10


25

30

= = = =

1 2 3 4

-1

10

bit error rate

(b) 64-PSK SNR vs BER Plot of 128-PSK in AWGN Channel

0


10

No. No. No. No.


= = = =

1 2 3 4

-2

10

-1

bit error rate

10

-3

10

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-2

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(f) 1024-PSK Fig. 1.4. SNR vs BER plots for M-PSK over AWGN channel

-3

10

0

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(c) 128-PSK

50

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SNR vs. BER plots for M-PSK over AWGN channel for MIMO system with different antenna configurations using OSTBC4 with zero forcing receivers are presented in Fig. 1.4 (a) – (f). From the graphs, it can be depicted that in MIMO


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T ABLE I SNR VALUES FOR HIGHER ORDER M-PSK OVER AN AWGN CHANNEL

Number of Receiving Antennas

SNR for different M values of MPSK Modulati on Scheme (in dB) 32

64

128

256

512

1024

1 2 3 4

12 9 9 6

18 15 13 12

23 21 19 15

30 27 23 22

32 30 30 28

39 36 35 32

SNR vs BER Plot of 128-PSK in Rayleigh Channel

0

10

No. No. No. No.


= = = =

1 2 3 4

-1

10

bit error rate

system, the BER keeps on decreasing as we goes on increasing the number of receiving antennas due to space diversity and thus the proposed system provide better BER performance as compared to the other antenna configurations. With the variation in number of receiving antennas from NR = 1 to NR = 4, the SNR varies from 4 dB to 8 dB as presented in table I.

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-2

10

-3

10

0

10

20


50

60

(c) 128-PSK SNR vs BER Plot of 256-PSK in Rayleigh Channel

0

10

No. No. No. No.

(B) M-PSK over Rayleigh Channel SNR vs BER Plot of 32-PSK in Rayleigh Channel

0

10


= = = =

1 2 3 4

= = = =

1 2 3 4

-1

10

bit error rate

No. No. No. No.


-1

bit error rate

10

-2

10

-2

10

-3

10

0

10

20


50

60

-3

10

0

5

10


25

(d) 256-PSK

30


0

10

(a) 32-PSK

No. No. No. No.


0

10


= = = =

1 2 3 4

Rx Rx Rx Rx

= = = =

1 2 3 4

-1

10

bit error rate

No. No. No. No.

of of of of

-1

bit error rate

10

-2

10

-2

10

-3

10

0

20


50

(e) 512-PSK

-3

10

10

0

5

10


25

30

(b) 64-PSK


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and receiving antennas are used to combat multipath fading and enhance SNR. Thus the spatial diversity techniques are used so as to improve signal quality and coverage.


0

10

No. No. No. No.


= = = =

1 2 3 4

REFERENCES

[1]

-1

bit error rate

10

[2] -2

10

[3] -3

10

0

10

20


50

75

60

(f) 1024-PSK Fig. 1.5. SNR vs BER plots for M-PSK over Rayleigh channel

In Fig. 1.5 (a) – (f), the SNR vs. BER plots for M-PSK over Rayleigh fading channel for MIMO system with different antenna configurations using OSTBC4 with zero forcing receivers are presented. Here from the graphs, it can be concluded that as we goes on increasing the number of receiving antennas in the MIMO system, the BER keeps on decreasing due to the space diversity. Thus the system provides better BER performance. With the variation in number of receiving antennas from NR = 1 to NR = 4, the SNR varies from 2 dB to 4 dB as shown in table II. T able II SNR values for higher order M-PSK over a Rayleigh channel

Number of Receiving Antennas

SNR for different M values of MPSK Modulati on Scheme (in dB) 32

64

128

256

512

1024

1 2 3 4

18 17 17 16

24 23 23 22

30 29 29 28

38 37 36 35

42 40 39 38

45 44 42 41

[4] [5]

[6]

[7]

[8] [9]

[10]

[11]

VIII. CONCLUSION In this paper, the performance analysis of MIMO system over AWGN and Rayleigh fading channels employing different antenna configurations using OSTBC4 is presented. The graphs depicts that the BER keeps on decreasing in MIMO system due to space diversity as we goes on increasing the number of receiving antennas. It can be concluded that the BER is improved but it is higher in case of Rayleigh channel in comparison to AWGN channel. The multiple transmitting

[12]

[13]

[14]

N.Kaur & L. Kansal, “ Performance Comparison of MIMO Systems over AWGN and Rayleigh Channels with Zero Forcing Receivers”, Global Journal of Researches in Engineering, Vol. 13, Issue 1, pp. 17-23, 2013. P. Sanghoi & L. Kansal, “ Analysis of WIMAX Physical layer Using Spatial Diversity under different Fading Channels”, International Journal of Computer Application, Vol. 44, no. 20, May 2012. L. Kansal, A. Kansal & K. Singh, “ Performance Analysis of MIMO-OFDM System using QOST BC Code Structure for MPSK”, Signal Processing: An International Journal(SPIJ), vol. 5, Issue 2, 2011. P. Sanghoi & L. Kansal, “Analysis of WIMAX Physical layer Using Spatial Diversity”, International Journal of Computer Application, Vol. 44, no. 5, April 2012. N.Kaur & L. Kansal, “ Performance Comparison of MIMO Systems over AWGN and Rayleigh Channels using OST BC3 with Zero Forcing Receivers”, International Journal of Electrical, Electronics and Computer Systems, Vol. 12, Issue 2, pp. 686-693, 2013. L. Kansal, A. Kansal & K. Singh, “BER Analysis of MIMOOFDM Sytem Using OST BC Code Structure for M-PSK under Different fading Channels”, International Journal of Scientific & Engineering Research, Vol. 2, Issue 11, Nov. 2011. X. Zhang, Z. Lv & W. Wang, “Performance Analysis of Multiuser Diversity in MIMO Systems with Antenna Selection ”, IEEE T ransactions on Wireless Communications, Vol. 7, Issue 1, pp. 1521, 2008. S. Alamouti, “A simple transmit diversity technique for wireless communications”, IEEE Journal on Selected Areas of Communication, Vol. 16, Issue 8, pp. 1451–1458, 1998. C. Wang, “ On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error”, IEEE T ransactions on Wireless Communications, Vol. 6, Issue 3, pp. 805 – 810, 2007. S. G. Kim, D. Yoon, Z. Xu & S. K. Park, “Performance Analysis of the MIMO Zero-Forcing Receiver over Continuous Flat Fading Channels”, IEEE Journal of Selected Areas in Communications, Vol. 20, Issue 7, pp. 324 – 327, 2009. A. I. Sulyman, “Performance of MIMO Systems With Antenna Selection Over Nonlinear Fading Channels”, IEEE Journal of Selected T opics in Signal Processing, Vol. 2, Issue 2, pp. 159-170, 2008. V. T arokh, N. Seshadri & A. R. Calderbank, “Space–T ime Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction”, IEEE T ransactions on Information T heory, Vol. 44, Issue 2, pp. 7 44-765, 1998. C. Chen, “Performance Analysis of Scheduling in Multiuser MIMO Systems with Zero-Forcing Receivers”, IEEE Journal of Selected Areas in Communications, Vol. 25, Issue 7, pp. 1435 – 1445, 2007. N. S. Kumar, G. J. Foschini, G. D. Golden & R. A. Valenzuela, “ Bit Error Rate Performance Analysis of ZF, ML and MMSE Equalizers for MIMO Wireless Communication Receiver”, European Journal of Scientific Research, Vol. 59, Issue 4, pp. 522– 532, 2011.


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Authors Navjot Kaur was born in Jalandhar. She received her B.T ech degree in Electronics and Communication Engineering from Lovely Institute of T echnology, Phagwara, Punjab T echnical University, Jalandhar, in 2008, and presently pursuing M.T ech degree in Electronics and communication engineering from Lovely Professional University, Phagwara, India. Her research interests include MIMO systems and wireless systems. Lavish Kansal was born in Bathinda. He received his B.T ech degree in Electronics and Communication Engineering from PT U, Jalandhar in 2009 and M.E. degree in Electronics and Communication Engineering from T hapar University, Patiala in 2011.He is working as Assistant Professor in the department of Electronics and communication Engineering, Lovely Professional University, Phagwara, India. He has published 15 papers in International journals. His research area includes Digital Signal Processing, Digital Communication & Wireless Communication.


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Performance Comparison of MIMO Systems over ... - Semantic Scholar

Performance Comparison of MIMO Systems over ... - Semantic Scholar

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