It is well known that the optimum detector based on linear prediction, for frequency-nonselective (flat) fading channels, requires MP states for M-ary signalling, where P is the order of the prediction filter required to decorrelate the received signal. In this paper, we first derive a suboptimal linear predictive-based (SLP) detector for M-ary PSK by making a high SNR assumption. We then demonstrate using the concept of isometry that for M-ary PSK signalling, only MP-1 states are required for this SLP detector. The complexity reduction is achieved with no loss in symbol-error-rate performance compared to the case where MP states are used. As a corollary, we also show that for a first-order prediction filter and M-ary PSK signalling, the SLP detector is identical to the conventional differential detector. © 2001 Elsevier Science B.V.