Joint maximum-likelihood (ML) estimation of sampling phase error and data sequence allows timing recovery at low channel signal-to-noise ratios (SNRs). In per-survivor timing recovery of [1], joint ML estimation is done by generating a sampling phase error estimate for each branch in the Viterbi trellis using the local bit sequence implied in the given branch and readjusting the sampling position of the read signal for that branch for the next symbol cycle. The scheme effectively runs a separate parallel phase locked loop (PLL) as well as a sampling device for each of the branches in the trellis. In the phase-estimating maximum likelihood scheme of [2], on the other hand, phase estimation is also performed for each branch separately, but a delayed phase estimate common to all survivor paths is released to a global low pass filter whose output drives a voltage controlled oscillator (VCO) that in turn controls the sampling time of a single analog-to-digital converter (ADC). Thus, there exist parallel phase estimates incorporated into the Viterbi trellis branch metric computation but only one global PLL exists effectively. The phase error detector of [2] is also different from that of [1] in that [2] is based on maximizing the conditional probability density function of the overall error accumulated over a certain time window, given the phase offset, whereas [1] chooses the derivative of the accumulated error as the timing function.
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