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Analysis of MIMO Systems in the Presence of Co-channel Interference and Spatial Correlation
[chapter]

Dian-Wu Yue, Qian Wang

2011
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MIMO Systems, Theory and Applications
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BS the number of scatterers is usually smaller than around mobile terminals, thus leading to the fact that the correlation at the BS is stronger than at the MS. Another typical example of this is a downlink transmission from a BS to a MS, where the antennas at the BS can be spaced sufficiently far to achieve uncorrelation among them. On the other hand, it is more difficult to space the antennas far apart at the mobile terminals due to physical size constraints, and consequently correlation
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... s among the antenna elements in such scenarios. The above factors have given us an impetus for studying the capacity of MIMO channels with interference and receive correlation [Wang & Yue (2009) ]. In Section 3, we will investigate the capacity issue in the case where the MIMO channels of the desired user and co-channel interferers are all subject to Rayleigh type of fading. A MIMO system can be configured differently. One configuration is transmit/receive diversity (TRD) which has been widely used due to its simplicity and good performance. The performance of MIMO systems with optimal TRD depends on their operational environments. Their performance in a Rayleigh fading environment without co-channel interference was investigated by Dighe et al. [Dighe et al. (2001) ] by assuming that the MIMO channels follow independent and identical (i.i.d.) Rayleigh distribution. The resulting outage probability is expressible in the form of a determinant. This result was subsequently extended by Kang and Alouini [Kang & Alouini (2003b)] to a general case of independent, but not necessarily identically distributed, Rician fading channels. The results, again, takes the form of determinants. For the case using dual antennas at the transmitter or receiver end, they obtained [Kang & Alouini (2004a)] an explicit expression for outage probability complementing the result of Dighe [Dighe et al. (2001) ]. The performance of MIMO systems with optimal TRD in the presence of co-channel interference was tackled in [Dighe et al. (2003) ] and [Kang & Alouini (2004b)] under various fading environments allowing for the MIMO fading channels of the intended user and interferers to be non-i.i.d. Rician/Rayleigh, i.i.d. Rician/Rayleigh, and Rayleigh/Rayleigh. All these studies focus on MIMO systems with uncorrelated or semi-correlated antennas. By semi-correlation, we mean that the spatial correlation exists only at one side, transmitter or receiver end, of the MIMO systems. Even for the case with semi-correlation, it is usually assumed that the intended user and interferers have the same correlation structure to simplify the mathematical analysis. In fact, the use of this assumption leads to the same mathematical treatment as the one with i.i.d. channels. The i.i.d. or uncorrelated assumption is often invalid in many practical applications. Significant correlation among the antennas exists in realistic environments due to, for example, limited spacing between antennas. Furthermore, the spatial structure (and even the fading distribution) of the interference usually differ from its counterpart for the intended user since their signals propagate over different multi-paths, suffer from different fading, and arrive at the receive antenna array with different incident angles. To handle these general fading situations, we must take different methodology [Yue & Zhang (2010) ]. In Section 4, we will investigate the performance issue of MIMO systems with optimal TRD mainly over general Rayleigh/Rayleigh fading channels in a unified framework. Throughout the paper, we use extensively relevant notations and results from multivariate statistical theory, in particular, various matrix-variate distributions. Although relevant results are available in the statistical literature [Muirhead (1982) ], [Gupta & Nagar (2000) ] and [Mathai et al. (1995) ], they are given only for real variables. The extension of these results to their complex counterparts, as required in this paper, is straightforward. Such results, though useful for wireless communications, are not found in the open references. We therefore first 156

doi:10.5772/15660
fatcat:cpd7pcet3fgohcmmqndqdrkv5q