Soft-In Soft-Output Detection in the Presence of Parametric Uncertainty via the Bayesian EM Algorithm
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Soft-In Soft-Output Detection in the Presence of Parametric Uncertainty via the Bayesian EM Algorithm A. S. Gallo Department of Information Engineering, University of Modena and Reggio Emilia, via Vignolese 905, 41100 Modena, Italy Email: [email protected]
G. M. Vitetta Department of Information Engineering, University of Modena and Reggio Emilia, via Vignolese 905, 41100 Modena, Italy Email: [email protected] Received 30 April 2004; Revised 6 October 2004 We investigate the application of the Bayesian expectation-maximization (BEM) technique to the design of soft-in soft-out (SISO) detection algorithms for wireless communication systems operating over channels affected by parametric uncertainty. First, the BEM algorithm is described in detail and its relationship with the well-known expectation-maximization (EM) technique is explained. Then, some of its applications are illustrated. In particular, the problems of SISO detection of spread spectrum, singlecarrier and multicarrier space-time block coded signals are analyzed. Numerical results show that BEM-based detectors perform closely to the maximum likelihood (ML) receivers endowed with perfect channel state information as long as channel variations are not too fast. Keywords and phrases: expectation-maximization algorithm, soft-in soft-out detection, fading channels, space-time coding, OFDM.
1.
INTRODUCTION
In recent years, many research efforts have been devoted to the study of detection algorithms for digital signals transmitted over channels affected by random parametric uncertainty, like multipath fading channels and AWGN channels with phase jitter (see, e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] and references therein). In this field the attention has been progressively shifting from maximum likelihood (ML) sequence detection [2, 3, 4] to maximum a posteriori (MAP) symbol detection techniques [5, 6, 7, 8, 9, 10, 11, 12, 13] producing a posteriori probabilities (APPs) on the possible data decisions. This has been mainly due to the need of robust receiver structures for coded modulations and, more specifically, to the advent of the turbo processing principle applied to efficient iterative decoding of concatenated coding structures [14, 15, 16, 17, 18, 19, 20, 21, 22]. Such a principle has been also exploited to design iterative detection/equalization/decoding algorithms for interleaved coded signals transmitted over channels with memory This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
[10, 11, 12, 13, 23]. In all these cases good error performance is achieved by means of concatenated detection/decoding structures exchanging among each other soft information about the detected data. The basic building blocks of these structures are the so-called soft-in soft-out (SISO) modules [18, 22]. A wealth of technical papers on the design techniques for ML sequence detectors operating on channels
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