Several information-theoretic studies on channels with output quantization have identified the capacity-achieving input distributions for different fading channels with 1-bit in-phase and quadrature (I/Q) output quantization. However, an exact characterization of the capacity-achieving input distribution for channels with multi-bit phase quantization has not been provided. In this paper, we consider four different channel models with multi-bit phase quantization at the output and identify the optimal input distribution for each channel model. We first consider a complex Gaussian channel with $b$-bit phase-quantized output and prove that the capacity-achieving distribution is a rotated $2^b$-phase shift keying (PSK). The analysis is then extended to multiple fading scenarios. We show that the optimality of rotated $2^b$-PSK continues to hold under noncoherent fast fading Rician channels with $b$-bit phase quantization when line-of-sight (LoS) is present. When channel state information (CSI) is available at the receiver, we identify $\frac{2\pi}{2^b}$-symmetry and constant amplitude as the necessary and sufficient conditions for the ergodic capacity-achieving input distribution; which a $2^b$-PSK satisfies. Finally, an optimum power control scheme is presented which achieves ergodic capacity when CSI is also available at the transmitter.

翻译：在对输出量度的频道进行的若干信息理论研究中,我们考虑了在输出量化的频道上,对输出量化的频道进行了数种信息理论研究。我们首先考虑的是具有1比位的阶段和四级(I/Q)输出量化的不同淡化频道的容量化输入分布,但对于具有多比位的阶段化的频道,还没有提供能力化输入量分布的确切描述。在本文中,我们考虑了在输出量中具有多比位级量化的四种不同频道模型,并确定了每个频道模型的最佳输入量分配。我们首先考虑的是具有美元比位的复杂高斯频道,以1比位的分级输出,并证明能力化的发送量化分布是旋转的 2+B 级转换键(PSK) 。然后将分析扩大到多种淡化的情景。我们表明,在输出量化速度化的频道中,以$b美元比分级分级(LOS) 展示了每个频道状态信息(CSI) 也具备了在接收器中所需的精确度化能力。