Error floor of MSK modulation in a mobile-radio channel with two independently fading paths

We investigate the error probability bit error rate (BER) of minimum shift keying (MSK) modulation with differential detection in a two-path fading channel without noise (error floor). We develop a new method for the computation of the BER: we show that errors occur if the phasors of the instantaneous impulse response fall into certain regions of the complex plane; then we average over the statistics of the phasors to arrive at the mean BER. With this method, we derive analytical expressions for the BER for arbitrary amplitude statistics of the paths. For the special case of two Rayleigh-fading paths with small delay, we find that the BER is proportional to the square of the mean delay spread (normalized to the bit length) if we sample between the two pulses. This proves the qualitative behavior of previous estimates, but our results allow also a more exact quantitative formulation. The quadratic dependence of the BER on the delay spread breaks down if we have one Rayleigh-fading and one Rician-fading path. We find that the bit combinations 1-11 and -11-1 do not lead to errors in the two-path model. However, additional Monte Carlo simulations show that these bit combinations do lead to errors in a three-path model.