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

Abstract

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.