Tracking loop for fading dispersive channels

An optimum closed-loop symbol synchronizer operating over fading dispersive channels is developed. It is shown that the optimum tracking synchronizer is a multiplier that forms the product of the received signal and a filtered version of it, the filter impulse response is the first derivative with respect to time (or frequency) of the autocorrelation function of the signal part of the received waveform. It is proved that for small misalignment the control signal vector is an incrementally linear function of the error vector. For a Gaussian-shaped scattering function, a simple closed-loop structure is obtained and expressions for tracking error statistics are derived. The dependency of such statistics on the signal-to-noise ratio and on the spread of the channel is investigated