Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
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An algorithm to recover bit timing is proposed which maximises a quadraticpolynomial approximation to the log-likelihood function. The exactequation for the mean of the log-likelihood function derivative, i.e. theS-curve, is derived and shown to have a sine form. In each time intervalthe S-curve has two zeros. The zero corresponding to the maximum of thelikelihood function is resolved using quadratic interpolation based onfour samples per period. The resulting timing synchroniser has a simpleopen loop feedforward structure which has effectively no acquisitionperiod. Receiver performances in terms of rms timing jitter and bit error rate (BER) are analysed and shown to agree closely with theoretical results.