Symbol Error Rate Analysis of Spatially Correlated Keyhole MIMO Channels with Space-Time Block Coding and Linear Precoding

This paper derives exact expressions for the symbol error rate (SER) of orthogonal space-time block codes over a spatially correlated multiple-input multiple-output (MIMO) channel, in which the signal propagation suffers from a keyhole effect. A correlated double Rayleigh fading keyhole channel is assumed and easy to evaluate expressions are presented for multi- level phase shift keying (M-PSK), pulse amplitude modulation (M-PAM), and quadrature amplitude modulation (M-QAM). These expressions are verified by estimating the SER via the simulation of the MIMO system. The given expressions are then used to quantify the performance improvements attainable with minimum SER linear precoding over a correlated keyhole channel. I. INTRODUCTION work, this paper derives the exact expression for SER of OSTBCs over spatially correlated double Rayleigh fading keyhole MIMO channels with precoding in the transmitter. In particular, we derive easy to evaluate analytical expressions for SER of M-PSK, M-PAM, and M-QAM signaling. These results are generalizations of those in (6) to include precoding and spatial correlation in the keyhole channel. Numerical results are presented to confirm that our analytical expressions agree with those obtained by simulation of the OSTBC-MIMO systems. Based on the SER expressions, we also investigate the performance improvements achievable with linear pre- coders optimized for the correlation statistics of the keyhole MIMO channel. These precoders are found by minimizing the SER expressions with respect to the precoder matrix. It is well known that, when the transmitter has side information about the channel correlation matrix, then the performance of OSTBCs can be improved by using a precoder at the MIMO channel input, see (8), (9) and the references therein. To our knowledge, precoding for keyhole channels has not been considered before. The results presented in this paper show that a significant reduction in SER can be obtained at moderate to low channel signal to noise ratios, by including a minimum SER precoder in the transmitter. We also show that many properties of the minimum SER precoders for Rayleigh (10) and Ricean (9) MIMO channels also hold true for the double Rayleigh fading keyhole channel as well.

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