Capacity of multiple one-bit transceivers in a Rayleigh environment

We analyze the channel capacity of a system with a large number of one-bit transceivers in a classical Rayleigh environment with perfect channel information at the receiver. With M transmitters and N =αM receivers, we derive an expression of the capacity per transmitter C, where C ≤ min(1,α), as a function of a and signal-to-noise ratio (SNR) ρ, when M → ∞. We show that our expression is a good approximation for small M, and provide simple approximations of C for various ranges of α and ρ. We conclude that at high SNR, C reaches its upper limit of one only if α > 1.24. Expressions for determining when C “saturates” as a function of α and ρ are given.