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Error probability of partial-response continuous-phase modulation with coherent MSK-type receiver, diversity, and slow Rayleigh fading in Gaussian noise

This paper considers a class of constant-amplitude modulation schemes with good spectral main lobe and tail behavior. Detection is assumed to be coherent and the receiver is of offset-quadrature type, i.e., minimum shift keying (MSK) type, consisting of a linear filter in each quadrature arm followed by simple processing. Analytical error-probability formulas are derived for various modulation schemes and receiver filters for ideal diversity with maximal-ratio and selection combining. Independent slow Rayleigh fading in Gaussian noise is assumed and several numerical examples are given. Asymptotic behavior of the error probability for large signal-to-noise ratios is derived, and the relationship between the degree of smoothing in the partial-response continuous-phase modulation and the asymptotic error probability is shown for fading channels with and without diversity.