A General Conditional BER Expression of Rectangular QAM in the Presence of Phase Noise

TL;DR

This paper derives a closed-form BER expression for rectangular QAM considering phase noise, revealing how phase noise impacts different constellation sizes and shapes, with square QAM showing the best robustness.

Contribution

It introduces a new analytical BER expression for rectangular QAM under phase noise, enabling better understanding of phase noise effects on modulation schemes.

Findings

Phase noise impact on BER is proportional to constellation size.

Square QAM has lower phase noise-induced performance loss.

Derived BER expression applies to various rectangular QAM schemes.

Abstract

In this paper, we newly present a closed-form bit-error rate (BER) expression for an $M$-ary pulse-amplitude modulation ($M$-PAM) over additive white Gaussian noise (AWGN) channels by analytically characterizing the bit decision regions and positions. The obtained expression is then used to derive the conditional BER of a rectangular quadrature amplitude modulation (QAM) for a given value of phase noise. Numerical results show that the impact of phase noise on the conditional BER performance is proportional to the constellation size. Moreover, it is observed that given a constellation size, the square QAM achieves the lowest phase noise-induced performance loss compared to other rectangular constellations.