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

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.