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. 1

Abstract—This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful error-correcting codes and operate at low signal-to-noise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a re-encoding (REEN) technique, an algorithm we previously derived from the expectation-maximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudo-ML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum–product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EM-based and the PML algorithms have excellent performance. The MS, PML, REEN, and EM-based algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance. Index Terms—Expectation-maximization (EM) algorithm, factor graphs, frame synchronization, turbo synchronization. I.

Abstract — This contribution considers the data-aided (DA) maximum-likelihood carrier phase ambiguity resolution algorithm for coded M-PSK signaling. We derive analytical performance results of the algorithm when operating in the presence of phase estimation errors. As the use of a pilot sequence reduces the spectral efficiency of the system, we determine analytically the minimal pilot sequence length for coded and uncoded systems such that the overall BER degradation due to phase ambiguity resolution errors is limited to an acceptable value. We show that powerful errorcorrecting codes require pilot sequences that are substantially longer than for uncoded transmission; however, these longer pilot sequences usually account for only a small fraction of the overall frame length. I.