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 bb -bit phase-quantized output and prove that the capacity-achieving distribution is a rotated 2b2^{b} -phase shift keying (PSK). The analysis is then extended to multiple fading scenarios. We show that the optimality of rotated 2b2^{b} -PSK continues to hold under noncoherent fast fading Rician channels with bb -bit phase quantization when line-of-sight (LoS) is present. When channel state information (CSI) is available at the receiver, we identify 2π2b\frac {2\pi }{2^{b}} -symmetry and constant amplitude as the necessary and sufficient conditions for the ergodic capacity-achieving input distribution; which a 2b2^{b} -PSK satisfies. Finally, an optimum power control scheme is presented which achieves ergodic capacity when CSI is also available at the transmitter.

中文翻译：

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相位量化通道的容量实现输入


对具有输出量化的信道的几项信息论研究已经确定了具有 1 位同相和正交 (I/Q) 输出量化的不同衰落信道的容量实现输入分布。然而，尚未提供具有多位相位量化的通道的容量实现输入分布的精确表征。在本文中，我们考虑在输出处具有多位相位量化的四种不同的通道模型，并确定每个通道模型的最佳输入分布。我们首先考虑具有 bb 位相位量化输出的复杂高斯信道，并证明容量实现分布是旋转的 2b2^{b} 相移键控 (PSK)。然后将分析扩展到多种衰落场景。我们表明，当存在视线 (LoS) 时，旋转 2b2^{b} -PSK 的最优性在具有 bb 位相位量化的非相干快衰落莱斯信道下继续保持。当信道状态信息（CSI）在接收器处可用时，我们将 2π2b\frac {2\pi }{2^{b}} -对称性和恒定幅度确定为遍历容量实现输入分布的充分必要条件； 2b2^{b} -PSK 满足。最后，提出了一种最佳功率控制方案，当 CSI 在发射机处也可用时，该方案可实现遍历容量。