Is Phase Shift Keying Optimal for Channels with Phase-Quantized Output?

Abstract

This paper establishes the capacity of additive white Gaussian noise (AWGN) channels with phase-quantized output. We show that a rotated $2^{b}$-phase shift keying scheme is the capacity-achieving input distribution for a complex AWGN channel with b-bit phase quantization. The result is then used to establish the expression for the channel capacity as a function of average power constraint $P$ and quantization bits $b$. The outage performance of phase-quantized system is also investigated for the case of Rayleigh fading when the channel state information (CSI) is only known at the receiver. Our findings suggest the existence of a threshold in the rate $R$, above which the outage exponent of the outage probability changes abruptly. In fact, this threshold effect in the outage exponent causes $2^{b}$-PSK to have suboptimal outage performance at high SNR.