Differential detection of GMSK signals with postdetection MRC over correlated and unbalanced Nakagami-m fading channels

Differential detection with postdetection diversity reception of Gaussian minimum shift keying (GMSK) signals has become increasingly important owing to its widespread use in wireless communications. Its error analysis, however, is not available in the literature. The authors derive a bit-error probability expression for the differential detection of GMSK signals with post-detection maximal ratio combing (MRC) in additive white Gaussian noise and slow frequency-nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs) as well as different severity parameter m. The effects of arbitrary values of the fading severity parameter m and the arbitrary correlation between the unbalanced L diversity channels are considered. The derived expression can be easily computed via numerical integration routines, and hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.