Phase Estimation and Phase Ambiguity Resolution by Message Passing

Abstract

Abstract. Several code-aided algorithms for phase estimation have recently been proposed. While some of them are ad-hoc, others are derived in a systematic way. The latter can be divided into two different classes: phase estimators derived from the expectation-maximization (EM) principle and estimators that are approximations of the sum-product message passing algorithm. In this paper, the main differences and similarities between these two classes of phase estimation algorithms are outlined and their performance and complexity is compared. Furthermore, an alternative criterion for phase ambiguity resolution is presented and compared to an EM based approach proposed earlier.

Code-Aided Maximum-Likelihood Ambiguity Resolution Through Free-Energy Minimization

“…The ML criterion is the core of a number of ambiguity-resolution methods proposed in the literature, such as [20]- [22]. In these contributions, the ML solution is assumed to be intractable because the evaluation of the likelihood function p R|B (r|b) requires a summation over all possible sequences, i.e.,…”

“…In order to deal with this problem, so-called code-aided (CA) synchronization methods have been proposed in the technical literature, see e.g., [6]- [22]. The idea of CA synchronization is to take benefit from the knowledge of the code structure to improve the estimation quality.…”

“…Among CA ambiguity-resolution methods, one can distinguish between two main approaches: the authors either propose ad-hoc algorithms based on the fact that some decoder metrics vary as a function of the considered hypotheses [15]- [19], or place the CA ambiguity-resolution problem in the context of maximum a posteriori (MAP) or ML estimation, [20]- [22]. In the latter class of algorithms, [20] modifies the likelihood function by only keeping its largest term and decides whether the current estimate is true or not by a threshold decision on this modified likelihood function.…”

“…This approach has been given a more rigorous justification in [24]. Finally, in [22] the authors make their decision by maximizing a modified likelihood function, built by using the extrinsic probabilities delivered by the decoder as symbol a priori probabilities.…”

Joint iterative detection and decoding in the presence of phase noise and frequency offset

“…Step 1) evaluate coefficients , using the a priori information about code symbols (15), (16), and (17);…”