Polar Decomposition of Mutual Information over Complex-Valued Channels

TL;DR

This paper introduces a polar decomposition of mutual information for complex channels with independent amplitude and phase, deriving bounds and demonstrating advantages of product-APSK over QAM in coded modulation.

Contribution

It proposes a novel polar decomposition of mutual information for complex channels and applies it to show the benefits of product-APSK over traditional QAM.

Findings

Cross term negligible at high SNR

Bounds for amplitude and phase mutual information terms derived

Product-APSK outperforms QAM in coded modulation

Abstract

A polar decomposition of mutual information between a complex-valued channel's input and output is proposed for a input whose amplitude and phase are independent of each other. The mutual information is symmetrically decomposed into three terms: an amplitude term, a phase term, and a cross term, whereby the cross term is negligible at high signal-to-noise ratio. Theoretical bounds of the amplitude and phase terms are derived for additive white Gaussian noise channels with Gaussian inputs. This decomposition is then applied to the recently proposed amplitude phase shift keying with product constellation (product-APSK) inputs. It shows from an information theoretical perspective that coded modulation schemes using product-APSK are able to outperform those using conventional quadrature amplitude modulation (QAM), meanwhile maintain a low complexity.