Pilot symbol assisted modulation (PSAM) has previously been shown to give good performance in flat fading, noise and cochannel interference. The present paper analyzes its performance in ISI due to frequency selective fading, and provides a similar analysis of differential detection for comparison. The paper also introduces a method for performing the formidable average over transmitted data patterns simply, and with an analytical result, PSAM is shown to be sensitive to RMS delay spread, though it always gives better performance than differential detection.>