Symbol synchronizer performance affected by non-ideal interpolation in digital modems

Discusses the symbol synchronizer performance of a fully digitally implemented receiver, operating on a narrowband M-PSK signal (one-sided bandwidth not exceeding the symbol rate). The considered digital receiver operates on samples of the complex envelope r(t) of the received signal, taken by a fixed clock which is not synchronized to the transmitter clock. The synchronized samples required for the symbol synchronization algorithm are computed by interpolating between the available non-synchronized samples. Because of finite memory, interpolation is non-ideal; hence, some amount of distortion is introduced, which affects the performance of the symbol synchronizer. By means of theoretical analysis, the authors investigate the tracking performance of a specific decision-directed feedback synchronizer, assuming interpolation of orders zero, one and two. They show that non-ideal interpolation gives rise to a loop noise spectrum containing spectral lines, that mainly occur near f=0 when the number of samples per symbol is close to an integer. Unless a sufficiently small loop bandwidth is chosen, the contribution of these spectral lines could dominate the timing error variance, which then becomes much larger than for synchronized sampling