The polar receiver architecture is a receiver design that captures the envelope and phase information of the signal rather than its in-phase and quadrature components. Several studies have demonstrated the robustness of polar receivers to phase noise and other nonlinearities. Yet, the information-theoretic limits of polar receivers with finite-precision quantizers have not been investigated in the literature. The main contribution of this work is to identify the optimal signaling strategy for the additive white Gaussian noise (AWGN) channel with polar quantization at the output. More precisely, we show that the capacity-achieving modulation scheme has an amplitude phase shift keying (APSK) structure. Using this result, the capacity of the AWGN channel with polar quantization at the output is established by numerically optimizing the probability mass function of the amplitude. The capacity of the polar-quantized AWGN channel with b1b_{1} -bit phase quantizer and optimized single-bit magnitude quantizer is also presented. Our numerical findings suggest the existence of signal-to-noise ratio (SNR) thresholds, above which the number of amplitude levels of the optimal APSK scheme and their respective probabilities change abruptly. Moreover, the manner in which the capacity-achieving input evolves with increasing SNR depends on the number of phase quantization bits.

中文翻译：

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极性量化高斯通道的容量实现输入


极化接收器架构是一种捕获信号的包络和相位信息而不是其同相和正交分量的接收器设计。多项研究已经证明了极化接收器对相位噪声和其他非线性的鲁棒性。然而，文献中尚未研究具有有限精度量化器的极地接收器的信息论限制。这项工作的主要贡献是确定输出端具有极性量化的加性高斯白噪声 (AWGN) 通道的最佳信令策略。更准确地说，我们表明容量实现调制方案具有幅度相移键控（APSK）结构。利用该结果，通过数值优化幅度的概率质量函数来确定输出端具有极性量化的 AWGN 信道的容量。还介绍了具有 b1b_{1} 位相位量化器和优化的单位幅度量化器的极性量化 AWGN 信道的容量。我们的数值研究结果表明存在信噪比 (SNR) 阈值，超过该阈值，最佳 APSK 方案的幅度级别数量及其各自的概率会突然变化。此外，容量实现输入随 SNR 增加而变化的方式取决于相位量化位数。