Performance of circular QAM constellations with time varying phase noise

Time varying phase noise is a limiting factor in highspeed wireless communication systems, e.g., microwave backhaul links in cellular networks. This paper seeks to investigate the performance of circular M-ary quadrature amplitude modulations (M-QAMs) in the presence of time varying phase noise. A new approximate union bound expression for the symbol-error probability (SEP) of a specific circular M-QAM constellation is derived. Numerical results show that this expression is accurate at medium-to-high signal-to-noise ratios (SNRs) for different constellation orders, M. Next, exact closed-form expressions for the SEP of binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) modulations in the presence of phase noise are derived. Extensive simulations are carried out to compare the performance of rectangular and circular QAM modulations in the presence of time varying phase noise, where it is demonstrated that circular QAM modulations can outperform their rectangular counterparts when considering the effect of time varying phase noise.