Cutoff rate of MIMO systems in Rayleigh fading channels with PSK signaling

We derive in this paper the cutoff rate R₀ of multiple-input-multiple-output (MIMO) space-time (ST) coding systems operating in Rayleigh fast fading channels with imperfect channel state information at the receiver (CSIR). In contrast to conventional cutoff rate analyzes where R₀ is treated as a continuous variable, we highlight in the paper that when the codeword length N is finite, there is a need to ldquoquantizerdquo R₀, as not all code rates are possible. Using the tight upper and lower bounds on the pair-wise error probability (PEP) in (Y. Li et al., 2007), we are able to derive in turn tight lower and upper bounds on the cutoff rate of MIMO ST coding systems. Our lower bound on R₀ is substantially tighter than that provided by the Chernoff bound for small and medium codeword length N. Asymptotically at large N, our lower bound coincides with the Chernoff bound. It is further shown in the paper that for some MIMO configurations, our upper bound on R₀ is simply that of our lower bound shifted by one unit of signal-to-noise-ratio (SNR). As a consequence, both bounds are tight at large SNR.