Performance of GMSK with two-bit differential detection in a land mobile radio channel

The performance of two-bit differential detection of Gaussian minimum-shift keying (GMSK) in a cellular mobile communication channel is theoretically analyzed. The channel is modelled to reflect those encountered in a practical system; i.e., a frequency-selective fast Rayleigh-fading channel corrupted by cochannel interference and additive white Gaussian noise. A two-ray model for the channel is used and a single cochannel interferer is considered in the analysis. The Doppler effect is included as well. A closed-form expression for the probability of error is obtained. Numerical computation is used to obtain GMSK bit-error-rate performance for various combinations of channel parameters. The results are compared with those for limiter-discriminator detection with the same channel parameters. The performance of limiter-discriminator detection is found to be superior to that of two-bit differential detection. As two-bit differential detection is generally simpler to implement, the choice of detection method involves a performance versus complexity trade-off. The results presented can be used to make this trade-off.