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A Non-Asymptotic Converse on the Maximal Coding Rate of Fading Channels with Partial CSIR

The problem of communication in Rayleigh fading channels with estimated channel state information at the receiver (CSIR) is investigated. Based on a related hypothesis testing problem in the Neyman-Pearson formulation, a non-asymptotic– in the codeword block-length–converse on the maximal coding rate is derived. The bound summarizes succinctly the effect of various system parameters that include the length of channel coherence interval, the length of the training and data intervals and the power allocated to training and data transmission. The bound is also studied in the asymptotic–in the codeword blocklength–regime and a particularly simple, non-trivial upper bound on the ergodic capacity of Raleigh fading channels with estimated CSIR is obtained. Finally, a second-order asymptotic expansion of the non-asymptotic converse is provided, which can be very useful in the study of latency-constrained communication systems.