A Novel Interpolation Method for Maximum Likelihood Timing Recovery

An algorithm to recover bit timing is proposed which maximises a quadratic polynomial approximation to the log-likelihood function. The exact equation for the mean of the log-likelihood function derivative, i.e. the S-curve, is derived and shown to have a sine form. In each time interval the S-curve has two zeros. The zero corresponding to the maximum of the likelihood function is resolved using quadratic interpolation based on four samples per period. The resulting timing synchroniser has a simple open loop feedforward structure which has effectively no acquisition period. Receiver performances in terms of rms timing jitter and bit error rate (BER) are analysed and shown to agree closely with theoretical results.