Fading channels with 1-bit output quantization: Optimal modulation, ergodic capacity and outage probability

The achievable rate of communications systems depends on the quantization resolution at the receiver. Earlier work has shown that the capacity of real-valued AWGN channels with 1-bit output quantization is achieved with BPSK. This paper studies optimal modulation schemes, the ergodic capacity and the outage probability for complex-valued fading channels with 1-bit output quantization, assuming full channel knowledge at the receiver. It is shown that circular symmetry with at most one amplitude per phase is a necessary condition for optimal modulation. Circular-symmetric PSK achieves the ergodic capacity in case of Rayleigh fading. Considering the outage probability for Rayleigh fading, L-PSK with large L shows the best performance among conventional modulation schemes.