Study of multiple-input multiple-output systems over fading channels

Abstract

Recently, transmitters and receivers with multiple antennas, i.e., multiple-input multiple-output (MIMO) systems, have been proposed for use in wireless communications. The main advantage of MIMO systems over traditional single-input single-output (SISO) systems is that MIMO systems can provide much higher capacities than SISO systems, thus improving the spectral efficiency of the wireless channels. Alternatively, diversity gain can be obtained with the use of MIMO systems and appropriate transmission strategies. In this thesis, we aim to evaluate the analytical performance of MIMO systems over correlated-Rayleigh and Rician channel conditions. We also perform simulations to verify the analytical results. Multiple-input multiple-output systems can be broadly classified into two types, namely, spatial-multiplexing based and diversity based. For the spatial-multiplexing-based (SM-based) MIMO systems, we will study both the zero-forcing (ZF) detector and the vertical-BLAST (V-BLAST) detecting algorithm. Based on the distribution of the post-detection SNR of the ZF detector, we will derive the bit error rate (BER) expressions for the MIMO systems over correlated-Rayleigh and Rician fading channels. Using the results, the performance degradation due to correlation in a Rayleigh fading channel is expressed in terms of the correlation coefficient. Moreover, we derive a closed-form expression, in terms of the Rician factor and the number of transmit antennas, for the SNR degradation of the Rician channel compared to the independent and identically distributed (i.i.d.) Rayleigh channel. Further, based on the work done related to ZF detector, the performance of V-BLAST algorithms for the MIMO systems with two transmit antennas is analyzed over correlated-Rayleigh and Rician channels. We will derive the analytical BERs of the first and second detection steps for both optimal- and fixed-detection-ordering schemes. The effect of optimal ordering on the SNR and diversity order will then be discussed. Afterwards, we will investigate the SNR degradation of the detection steps for correlated-Rayleigh and Rician channels over an i.i.d. Rayleigh channel. We will also evaluate the capacity of the MIMO Rician channel. We will show that the capacity of a MIMO Rician channel can be well-approximated by that of a MIMO correlated-Rayleigh channel and we will derive a close-form expression for the channel capacity. Based on the analytical results, we will study the asymptotic capacities of the Rician channel at low and high SNR regions, and the asymptotic capacity loss of the channel relative to an i.i.d. Rayleigh channel. Finally, we will investigate thoroughly the performance of diversity-based MIMO systems with antenna selection over an intra-class correlated Rayleigh channel. We will derive the exact BERs of the MIMO systems with three different selection schemes, namely transmit-antenna selection, receive-antenna selection and the full complexity schemes. Then, the asymptotic SNR degradations due to correlation are expressed in terms of the correlation coefficient and the number of antennas. Finally, we evaluate the diversity orders and compare the SNR requirements of different selection schemes at low BER regions.