Binary and quaternary differential coherent phase-shift keying schemes are widely used in digital wireless systems. In this paper, we derive a simple expression for the bit error rate performance of such schemes under postdetection equal-gain combining and fading channels. The analysis is based on a convergent infinite series for the probability density function of sums of random variables that has been derived using a Fourier series approximation method. Several fading conditions including arbitrarily correlated Nakagami-m, and independent Ricean slowly varying channels are investigated. The analytical study is also accompanied by using simulation techniques.