On the performance of the quadratic receiver for Rayleigh fading channels

We investigate maximum likelihood sequence estimation (MLSE) of data sequences transmitted over time-varying frequency-selective Rayleigh fading channels. We present the optimal receiver designed to exploit perfect channel state information (CSI) at the beginning of the data sequence and the optimal receiver which does not use this information. For any given data sequence length, a performance range for the optimal detection can be identified: this range is lower bounded by the optimal receiver with perfect CSI and upper bounded by that without CSI. Furthermore, this range narrows for increasing data sequence lengths. The performance of these optimal receivers is compared to that of some suboptimal receivers based on per-survivor processing (PSP) which perform joint sequence detection and channel tracking using the least mean square (LMS) algorithm. In terms of performance, these suboptimal receivers are shown to be intermediate between the optimal receivers with and without initial CSI. In addition, we show that the performance of both optimal receivers degrades significantly if they are provided with imperfect information about the signal-to-noise ratio or channel delay profile-information which is not necessary to the suboptimal PSP-based receivers.