Impact of the Gaussian Approximation on the Performance of the Probabilistic Data Association MIMO Decoder
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Impact of the Gaussian Approximation on the Performance of the Probabilistic Data Association MIMO Decoder Justus Ch. Fricke Information and Coding Theory Lab, Faculty of Engineering, University of Kiel, Kaiserstraße 2, 24143 Kiel, Germany Email: [email protected]
Magnus Sandell Toshiba Research Europe Ltd., Telecommunications Research Laboratory, 32 Queen Square, Bristol BS1 4ND, UK Email: [email protected]
Jan Mietzner Information and Coding Theory Lab, Faculty of Engineering, University of Kiel, Kaiserstraße 2, 24143 Kiel, Germany Email: [email protected]
Peter A. Hoeher Information and Coding Theory Lab, Faculty of Engineering, University of Kiel, Kaiserstraße 2, 24143 Kiel, Germany Email: [email protected] Received 1 March 2005; Revised 24 July 2005; Recommended for Publication by Michael Gastpar The probabilistic data association (PDA) decoder is investigated for use in coded multiple-input multiple-output (MIMO) systems and its strengths and weaknesses are determined. The conventional PDA decoder includes two approximations. The received symbols are assumed to be statistically independent and a Gaussian approximation is applied for the interference and noise term. We provide an analytical formula for the exact probability density function (PDF) of the interference and noise term, which is used to discuss the impact of the Gaussian approximation in the presence of a soft-input soft-output channel decoder. The results obtained resemble those obtained for the well-known PDA multiuser detector in coded CDMA systems for which similar investigations have been done before. Keywords and phrases: probabilistic data association, MIMO systems, stochastic approximation, iterative methods, interference.
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INTRODUCTION AND BACKGROUND
Probabilistic data association (PDA) has originally been developed for target tracking by Yaakov Bar-Shalom in the 1970s. Since then, it has been applied in many different areas, including digital communications. In the area of digital communications, the PDA algorithm is a reduced complexity alternative to the a posteriori probability (APP) decoder/detector/equalizer. Near-optimal results were demonstrated for a PDA-based multiuser decoder (MUD) for code division multiple access (CDMA) systems [1, 2]. Recently, 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.
probabilistic data association has been shown to achieve good results in multiple-input multiple-output (MIMO) systems [3, 4]. In [5], a PDA was presented for turbo equalization of a single antenna system. It should also be noted that the Gaussian assumption made in the PDA decoder is used in several other MUD detection schemes, especially when applying iterative detection and decoding schemes, for example, [6, 7, 8]. In [9], it was shown that the performance of a coded CDMA system with PDA decoder degrades if the number of users is not large enough. In t
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