  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.
