Error Probability of $ M$-Phase Signaling With Phase Noise Over Fading Channels

Abstract

This correspondence focuses on the analysis of average symbol error rate (ASER) of $M$ -ary phase-shift keying (MPSK) over $\boldsymbol {\kappa }$ - $\boldsymbol {\mu }$ , $ \boldsymbol {\eta }$ - $ \boldsymbol {\mu }$ , and $\boldsymbol {\alpha }$ - $\boldsymbol {\mu }$ fading channels subject to imperfect carrier phase recovery. The random phase noise is considered to be Tikhonov (or von Mises) distributed. Specifically, exact expressions for the ASER i) under non-fading scenario, ii) under $\boldsymbol {\kappa }$ - $\boldsymbol {\mu }$ , iii) $ \boldsymbol {\eta }$ - $ \boldsymbol {\mu }$ , and iv) $\boldsymbol {\alpha }$ - $\boldsymbol {\mu }$ fading channels, as well as v) their corresponding asymptotic behavior for high signal-to-noise ratio, (SNR) values are analytically obtained and evaluated. The derived expressions support arbitrary values of the fading parameters, namely $\boldsymbol {\alpha }$ , $ \boldsymbol {\kappa }$ , $\boldsymbol {\eta }$ and $ \boldsymbol {\mu }$ , and they are validated by reducing them to particular cases, for which results are available in the literature, and by means of simulations. Several important conclusions concerning the system performance as a function of the channel parameters and loop SNR are drawn.