On the Capacity-Achieving Input of the Gaussian Channel with Polar Quantization

TL;DR

This paper determines the optimal input signaling for the Gaussian channel with polar quantization, revealing an APSK structure that maximizes capacity, and analyzes how capacity and signaling evolve with SNR and quantization bits.

Contribution

It identifies the capacity-achieving modulation scheme for the Gaussian channel with polar quantization and characterizes its capacity through numerical optimization, a novel theoretical insight.

Findings

Optimal signaling is APSK with amplitude phase shift keying.

Capacity exhibits SNR thresholds where optimal amplitude levels change.

The capacity depends on the number of phase quantization bits.

Abstract

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 $b_1$-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.