Abstract
As many coded systems operate at very low signal-to-noise ratios, synchronization becomes a very difficult task. In many cases, conventional algorithms will either require long training sequences or result in large BER degradations. By exploiting code properties, these problems can be avoided. In this contribution, we present several iterative maximum-likelihood (ML) algorithms for joint carrier phase estimation and ambiguity resolution. These algorithms operate on coded signals by accepting soft information from the MAP decoder. Issues of convergence and initialization are addressed in detail. Simulation results are presented for turbo codes, and are compared to performance results of conventional algorithms. Performance comparisons are carried out in terms of BER performance and mean square estimation error (MSEE). We show that the proposed algorithm reduces the MSEE and, more importantly, the BER degradation. Additionally, phase ambiguity resolution can be performed without resorting to a pilot sequence, thus improving the spectral efficiency.
Highlights
In packet-based communications, frames arrive at the receiver with an unknown carrier phase
We evaluate the performance of the EM algorithm for phase estimation (PE) and Phase ambiguity resolution (PAR) when applied to a turbo-coded system with QPSK mapping
We will only consider the following schemes: (i) TPE: EM-2 + init(VV); L: the EM algorithms is executed 2M times with initial estimates given by (18); (ii) PAR: CORR + perfect fractional phase estimation” (FPE); L: the conventional PAR algorithm (6) under the assumption of perfect knowledge of εθ; (iii) PAR: REEN + perfect FPE; L: this algorithm is formally obtained by replacing the soft decisions μi in (15) by the data symbols obtained by re-encoding the decoded information sequence [12]
Summary
In packet-based communications, frames arrive at the receiver with an unknown carrier phase. Phase ambiguity resolution (PAR) can be accomplished by a data-aided (DA) algorithm that exploits the presence of a known pilot sequence in the transmitted data stream [2]. Conventional estimation algorithms perform well for uncoded systems, a different approach needs to be taken when powerful error-correcting codes are used. These codes operate typically at low SNR, making the estimation process more difficult. An EM-based algorithm was proposed in [8] but required certain approximations to operate in coded systems Apart from these ad hoc methods, a theoretical framework for code-aided estimation was proposed in [9] and applied to phase estimation. We demonstrate that the EM-based PE algorithm does not necessarily yield a substantial gain in terms of BER as compared to a conventional PE algorithm, the EM-based PAR algorithm is mandatory if we wish to avoid long pilot sequences
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