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SUMMARYAnalytic expressions for the symbol-error probabilities of M-ary coherent phase shift keying (M-CPSK) detection with an imperfect local carrier reference phase in Nakagami-m fading and additive Gaussian noise are derived. Both the Tikhonov probability density function (PDF) and the uniform PDF of the carrier phase error are considered. We based our analyses on a newly derived expression for the Fourier coefficients of the PDF of the composite phase of the received signal impaired by Nakagami-m fading and additive Gaussian noise. We present a comparison of the results based on the Tikhonov PDF with those based on the uniform PDF in order to show substantial performance differences between these two-phase noise models.

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The moment-generating function (MGF) of the received signal-to-noise ratio (SNR) is a convenient tool in the performance analysis of modulation schemes in fading channels. In this letter, we derive the MGF for gamma-shadowed Ricean fading channels under the assumption that the average power of the Ricean fading is characterised by a gamma distribution. The MGF is expressed in a series form. An application of the derived MGF for evaluating the average bit error probability (ABEP) for binary differential phase-shift keying (DPSK) is given. The exact expression for ABEP and the corresponding asymptotic expression (assuming large SNR) are derived and mutually compared. The computational efficiency is elaborated on. Special cases of the exact expression for ABEP agree with corresponding known results.