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

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