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.

翻译：本文确定了具有分阶段量化输出的添加白高斯噪声(AWGN)渠道的能力。我们显示,旋转的2 ⁇ b$级转换键键键方案是具有美元-位数分数的复合AWGN频道的容量实现输入分布,结果被用来确定频道容量的表达方式,这是平均功率限制的函数,P美元和量度比特的函数。对于只有接收者才知道频道状态信息(CSI),Raylei 系统退出运行的情况也进行了调查。我们的调查结果表明,存在一个利率为$R$的阈值,超过该值的溢出概率会突变。事实上,这种退出的阈值效应导致高SNR(SN)的亚优度超值性差性能为$-PSK($-PSK)。