On sampling rate, analog prefiltering, and sufficient statistics for digital receivers

We consider the joint sequence estimation, timing and phase recovery for linear modulation. The paper differs from the classical ones in the sense that time-discrete algorithms suitable for fully digital receivers are discussed. Sufficient conditions are given such that the signal samples represent sufficient statistics. These conditions involve signal bandwidth, sampling/symbol rate and the analog prefilter characteristics. It is shown that the sampling rate need not be an exact multiple of the symbol rate, i.e., the samples can be taken from a free-running oscillator. All subsequent signal processing operations in the receiver then operate with the clock of this free-running oscillator. Timing recovery is then performed by a time-variant linear digital interpolator and a decimator. Carrier recovery and sequence estimation are performed at an average rate of one symbol per sample. The digital matched filter for this case is derived for an arbitrary colored noise spectrum