Tight upper and lower bounds on the constrained capacity of non-coherent multi-antenna channels

Abstract

This paper first presents an optimal receiver and coding scheme for a multi-user, multi-receiver, non-coherent Rayleigh flat fading channel which achieves the channel's constrained capacity (i.e., the capacity for a fixed input distribution). The paper then goes on to analyze the optimal receiver and uses it to generate tight upper and lower bounds on the constrained capacity. Knowing this constrained capacity is essential to judge the efficiency of coding schemes for the channel; it performs the same function as BPSK capacity for the AWGN channel in judging LDPC codes. The paper then goes on to present a practicable correlation based receiver that uses a novel iterative channel estimation technique. The performance of this receiver remains close to the constrained capacity as long as the per-user SNR is low; there is no requirement on the aggregate SNR. With 50 users, 50 receivers and a brickwall fading channel with a coherence length of 200 symbols, for example, the correlation based receiver achieves a sum rate of 36 bits/sec/Hz, significantly greater than any current cellular standards.