Analytical computation of the error probability of (G)MSK with adaptive sampling in mobile radio channels with small delay spread

We compute analytically the error probability of (Gauss-filtered) minimum shift keying (G)MSK in mobile radio channels with delay spreads S much smaller than the bit length T. We include (i) the time dispersion of the channel in a general way, (ii) filtering of both the data sequence and the received signal, and (iii) noise. To realistically model a cordless communications system, we also choose the sampling time adaptively. We show that the errors due to ISI go like K(S/T)/sup 2/, where the proportionality constant K depends on the Gaussian filtering, the receiver filtering, and the sampling time. The chosen sampling instants for large group delays depend on the signal-to-noise ratios: for low SNR sampling times near the average mean delay are optimum, while at high SNR, sampling times that are shifted by approximately T/2 are optimum.