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

arXiv: https://arxiv.org/abs/2205.05850 · HTML: https://mlsanity.com/paper/2205.05850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 12 May 2022.

## Builds on (most cited first, 5 of 5)

- [On Minimizing Symbol Error Rate Over Fading Channels with Low-Resolution Quantization](https://mlsanity.com/paper/2106.11524/) (2021)
- [Low-Resolution Quantization in Phase Modulated Systems: Optimum Detectors and Error Rate Analysis](https://mlsanity.com/paper/1902.10896/) (2019)
- [Advanced Receiver Architectures for Millimeter Wave Communications with Low-Resolution ADCs](https://mlsanity.com/paper/2003.03683/) (2020)
- [Is Phase Shift Keying Optimal for Channels with Phase-Quantized Output?](https://mlsanity.com/paper/2101.09896/) (2021)
- [All-Digital LoS MIMO with Low-Precision Analog-to-Digital Conversion](https://mlsanity.com/paper/2108.01147/) (2021)

## Built on by (most cited first, 1 of 1)

- [Design and Analysis of Hardware-limited Non-uniform Task-based Quantizers](https://mlsanity.com/paper/2208.07525/) (2022)

## Abstract (arXiv)

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 b1-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.