Cost minimisation interpretation of fourth power phase estimator and links to multimodulus algorithm - Electronics Letters

Introduction: In burst-mode digital transmission systems adopting coherent demodulation, phase recovery within each burst becomes a crucial issue. Among the blind (or non-data-aided) carrier phase estimators available from the literature, perhaps the fourth power estimate appears to be the most popular. It is known to yield an approximate maximum likelihood estimator in the limit of small SNR [1]. Serpedin et al. have shown in [2] that several seemingly different phase estimators are in fact equivalent to the fourth power estimator. In this Letter we present a reinterpretation of the fourth power estimator in terms of the minimisation of a dispersion-based cost function. This cost has been recently proposed in the context of blind equalisation [3, 4] as the basis of the so-called multimodulus algorithm (MMA). One advantage of MMA over the standard constant modulus algorithm (CMA) [5] is precisely its ability to perform blind phase acquisition. Thus, this inherent phase recovery property of MMA can be seen as a ‘built-in’ fourth power estimator; consequently one cannot expect MMA to synchronise the phase with constellations for which the fourth power estimator is not well suited, such as M-PSK (M > 4).