Performance Analysis of Single user Spatial Multiplexing Open-loop MIMO Systems with different Receiver Structures and Modulation Schemes

Performance Analysis of Single user Spatial Multiplexing Open-loop MIMO Systems with different Receiver Structures and Modulation Schemes

*Joyatri Bora

Electronics and Comm. Engg. Dept.

North Eastern Regional Institute of Science and Technology

Nirjuli, Itanagar, India

Md. Anwar Hussain

Electronics and Comm. Engg. Dept.

North Eastern Regional Institute of Science and Technology

Nirjuli, Itanagar, India

Abstract In wireless communication, MIMO has gained much attention due to large capacity and diversity gain provided by it. Capacity increases linearly as the number of antenna increases. At the same time complexity of detection of signal also increases exponentially with the number of transmit antenna. We study in this chapter the trade-off between MIMO antenna configuration, data rate, modulation order and type of receivers. For specific values of spectral efficiency, we considered different uncoded modulation formats and different MIMO antenna configurations and analysed bit error rate (BER) performance of three receivers for a range of Eb/N0 values. The rich scattered Rayleigh channel is considered between transmitter and receiver of the MIMO system.

KeywordsMIMO; diversity gain; detection; spectral efficiency; modulation.

1. INTRODUCTION

   The spatial multiplexing (SM) gain or the spectral efficiency can be increased in a wireless communication system by adding multiple antennas both at the transmitter and receiver known as MIMO technology. MIMO increases the multiplexing gain by splitting a high rate signal into many low rate signals and transmitting through different antenna with independent fading path. Reliability in transmission is increased in MIMO by exploiting the diversity gain where several replicas of a signal are transmitted through different fading channel. A well known scheme of exploiting spatial multiplexing (SM) gain is the vertical Bell Labs Layered Space-time (VBLAST) [1], [2] architecture where multiple independent coded streams (layers) are transmitted simultaneously without channel state information (CSI) at the transmitter. Employing spatial multiplexing in MIMO, capacity is increased by min (NT, NR) [3], [4] where NT is the number of transmit antenna and NR is the number of receive antenna in a rich scattering environment. Although gain grows with increased antenna number, detection of signal becomes complex which increases with the number of transmit antenna. The essential part of MIMO system is the detector which separates the spatially multiplexed signals. In open loop MIMO, where only the receiver has information of

   the channel condition, decoding of signal is done by estimating the received signals using linear and non linear detectors. Maximum likelihood (ML) detector is an optimum non linear detector that decodes the signals through exhaustive search of the most likely transmitted signal. So, error probability is minimized but its complexity increases with MIMO antenna configuration and modulation order [5]. Minimum Mean Square Error (MMSE) and Zero-forcing (ZF) are two linear suboptimal detectors with less complex receiver architecture [6]. However ZF suffers from sudden enhancement of noise. MMSE detector maximizes the SINR output minimizing the mean square error in estimating the transmitted signals for all range of SNR.

   We consider an open loop MIMO with no feedback to the transmitter. For spectral efficiency values of 1, 2, and 4 bps/Hz, modulation formats of BPSK, QPSK, and 16 QAM, we considered appropriate transmit and receive antenna orders of the MIMO system and studied BER versus Eb/N0 (Eb is the bit energy and N0 is the noise spectral density) performance of ZF-SIC, MMSE-SIC and ML receivers. For example, for the target spectral efficiency of 4 bps/Hz, signal constellation mapping may be (i) BPSK with transmit antenna, MT = 8 and receive antenna, MR = 8, or (ii) QPSK with transmit antenna, MT = 4 and receive antenna, MR = 4, or

   (iii) 16 QAM with transmit antenna, MT = 2 and receive antenna, MR = 2. We also consider a Single input single output (SISO) system with transmit antenna, MT = 1 and receive antenna, MR = 1 for the above said spectral efficiencies of 1, and 2 bps/Hz with appropriate modulation formats and different receiver structures for comparison. For the same SM gain we also compare the performances of different MIMO systems.

2. SYSTEM MODEL

   We consider a MIMO system with transmitter having MT number of antennas and receiver equipped with MR antennas where MT=MR=M for spatial data multiplexing. The channel between transmitter and receiver is assumed to be rich scattered Rayleigh block fading channel. We assume perfect

   channel knowledge at the receiver end with no feedback to the transmitter i.e. MIMO system is an open loop SU-MIMO.

   The channel can be written as

   (1)

   T

   R T

   Where transmitted signal vector is, x M x1, received signal vector is, y MRx1 and n MRx1 is vector of AWGN with zero mean and each element having 2variance. The channel matrix, H M xM is assumed to be constant within a block and is assumed to be known to the receiver. The channel coefficients hij are the complex path gain from transmit antenna j to receive antenna i.

   (4)

   For better performance, successive interference cancellation is done. The effect of kth symbol is subtracted before the estimation of (k+1)th symbol.

   C. ML receiver

   Maximum likelihood detection calculates the Euclidean distance between received signal vector and the product of all possible transmitted signal vectors with the given channel H, and finds the one with minimum distance. ML receiver tries to detect the transmitted vector x for system model of Equation (1) as

   (5)

   Fig. 1. Block diagram of MIMO system model.

3. DETECTION FOR SM

   At the receiving end of the system, three detection schemes are applied ZF-SIC, MMSE-SIC and ML.

   1. ZF-SIC receiver

      The Zero Forcing detection scheme is linear in nature but noise enhancement takes place. At some high value of SNR, it gives optimum result. The estimated result is given by

      (2)

      Where WZF = (HHH)-1HH and HH is Hermitian of H. With ZF receiver, the interference can be suppressed but because background noise is multiplied with equalization matrix WZF, so strong noise amplification is occurred leading to low SNRs. Here, again SIC is done by nulling the effect of kth symbol before estimating the (k+1)th symbol.

4. RESULTS AND DISCUSSIONS

   SM gain of 1 bps/Hz, the basic 2×2 MIMO Rayleigh channel system employing two transmit (MT=2) and two receive antennas (MR=2) is simulated in MATLAB environment. For an uncoded BPSK modulated system it employs flat Rayleigh fading over independent transmit- receive links. At the receiver end, we assume perfect channel knowledge with no feedback to the transmitter, i.e. an open- loop spatial multiplexing system. A block of BPSK modulated 10,000 random binary bits are transmitted after subdivided into two independent sub-streams from the two transmit antennas, thus providing SM gain of 1 bps/Hz spectral efficiency by the MIMO system. The BER performance of ZF-SIC, MMSE-SIC and ML receivers are shown in Fig. 2 for a range of Eb/N0 values. Similar plot has been drawn in Fig. 3 considering QPSK and employing a SISO system with MT=MR=1 for the same 1 bps/Hz spectral efficiency. From the Fig. 2 and 3, it is observed that 2×2 MIMO system provides better performance with ZF-SIC, MMSE-SIC and ML receivers compared to the SISO system with QPSK modulation and the same receivers, randm binary data blocks, and Eb/N0 values.

   0 2×2 Uncoded BPSK System

   				ZF-SIC MMSE-SIC ML

   10

   -1

   10

   1. MMSE-SIC receiver

   -2

   BER

   To overcome the drawback of sudden noise enhancement 10

   of ZF, the concept of MMSE is introduced for detection.

   MMSE receiver minimizes the mean square error between the output of the receiver and the true data vector minimizing the average squared Euclidean distance between the estimate of the data vector and the true data vector. MMSE receiver is described by a weighting matrix WMMSE given as

   (3)

   So, estimated output of the receiver is

   -3

   10

   -4

   10

   0 5 10 15 20 25

   Eb/No (dB)

   Fig. 2. BER performance of ZF-SIC, MMSE-SIC and ML receiver with BPSK modulation and MT=MR=2 for spectral efficiency of 1 bps/Hz.

   0 1×1 Uncoded QPSK System

   10

   0 1×1 Uncoded 16 QAM System

   10

   				ZF-SIC MMSE-SIC ML

   				ZF-SIC MMSE-SIC ML

   -1 -1

   10 10

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   BER

   BER

   10 10

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   10 10

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   10 10

   0 5 10 15 20 25

   Eb/No (dB)

   Fig. 3. BER performance of ZF-SIC, MMSE-SIC and ML receiver with QPSK modulation and MT=MR=1 for spectral efficiency of 1 bps/Hz.

   0 4×4 Uncoded BPSK System

   				ZF-SIC MMSE-SIC ML

   10

   -1

   10

   -2

   BER

   10

   -3

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   10

   0 5 10 15 20

   Eb/No (dB)

   Fig. 4. BER performance of ZF-SIC, MMSE-SIC and ML receiver with BPSK modulation and MT=MR=4 for spectral efficiency of 2 bps/Hz.

   0 5 10 15 20 25

   Eb/No (dB)

   Fig. 6. BER performance of ZF-SIC, MMSE-SIC and ML receiver with 16QAM modulation and MT=MR=1 for spectral efficiency of 2 bps/Hz.

   Hence, a 2×2 MIMO with BPSK modulation is the choice for SM gain of 1 bps/Hz. Also in the SISO system all the receivers have the same performance for obvious reason. Fig.4, 5 and 6 show the results for spectral efficiency of 2 bps/Hz with BPSK, QPSK and 16 QAM modulation of random binary data block, and 4×4 MIMO, 2×2 MIMO, and 1×1 SISO systems, respectively. We notice that BER performance of the three receivers degrades with order of ZF- SIC >MMSE-SIC > ML. In all the three cases of BPSK, QPSK and 16 QAM modulations, the ML receiver shows better performance. It is observed that, at BER=9×10-4 the ML receiver of 4×4 MIMO with BPSK signaling, gives about 11 dB gain in Eb/N0 over the 2×2 MIMO ML receiver with QPSK signaling. As is observed from Fig. 4, 5, and 6 the SISO system with 16 QAM, shows almost equal performance as 2×2 MIMO with QPSK, and 4×4 MIMO with BPSK, at 25 dB Eb/N0. Also 4×4 MIMO shows better performance than 2×2 MIMO for the entire range of Eb/N0 values.

   0 2×2 Uncoded QPSK System

   10

   -1

   10

   -2

   BER

   10

   -3

   10

   -4

   10

   ZF-SIC MMSE-SIC ML

   0 8×8 Uncoded BPSK System

   				ZF-SIC MMSE-SIC ML

   10

   -1

   10

   -2

   BER

   10

   -3

   10

   -4

   10

   0 5 10 15 20 25

   Eb/No (dB)

   0 5 10 15 20

   Eb/No (dB)

   Fig. 5. BER performance of ZF-SIC, MMSE-SIC and ML receiver with QPSK modulation and MT=MR=2 for spectral efficiency of 2 bps/Hz.

   Fig. 7. BER performance of ZF-SIC, MMSE-SIC and ML receiver with BPSK modulation and MT=MR=2 for spectral efficiency of 4 bps/Hz.

   0 4×4 Uncoded QPSK System

   				ZF-SIC MMSE-SIC ML

   10

   -1

   10

   -2

   BER

   10

   -3

   10

   -4

   10

   0 5 10 15 20 25

   Eb/No (dB)

   Fig. 8. BER performance of ZF-SIC, MMSE-SIC and ML receiver with QPSK modulation and MT=MR=4 for spectral efficiency of 4 bps/Hz.

   In Fig. 7, 8 and 9, we show the bit error rate performance for case of 4 bps/Hz with BPSK and 8×8 MIMO, QPSK and 4×4 MIMO, and 16QAM 1×1 SISO systems, respectively. Here also ML receiver shows better performance compared to ZF- SIC and MMSE-SIC, in BPSK and 8×8 MIMO, QPSK and 4×4 MIMO, and 16QAM SISO system. At bit error rate of 10-4 , ML receiver with BPSK has Eb/N0 gain about 6 dB over QPSK and 13 dB over 16QAM. For MMSE-SIC the Eb/N0 gain is about 2 dB over QPSK and about 8 dB over 16QAM, for ZF-SIC gain is about 5 dB over QPSK and 2 dB over 16 QAM. Also the 8×8 MIMO performs better than the 4×4 and

   2×2 MIMO systems for E /N values from 3-25 dB. It is

5. CONCLUSION

Simulation results of open-loop MIMO systems for uncoded transmission of random binary data blocks at 1 bps/Hz, 2 bps/Hz and 4 bps/Hz, considering appropriate modulation schemes like BPSK, QPSK and 16QAM, and different receiver structures using different appropriate number of transmit and receive antennas for the case of spatial multiplexing of independent data sub-streams are shown and analysed in this chapter. The bit error rate (BER) performance for a range of Eb/N0 values using ZF-SIC, MMSE-SIC and ML receiver are analyzed for the given spectral efficiency. The ML receiver has shown to achieve better performance in all the cases, and the higher order MIMO performs better than a lower MIMO in all the considered spectral efficiencies.

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-1

10

-2

BER

10

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10

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10

0 5 10 15 20

Eb/No (dB)

Fig. 9. BER performance of ZF-SIC, MMSE-SIC and ML receiver with 16QAM modulation and MT=MR=2 for spectral efficiency of 4 bps/Hz.