Conference Paper

On the analysis of the MAP equalizer performance within an iterative receiver

ISECS, Sfax, Tunisia
DOI: 10.1109/SPAWC.2004.1439281 Conference: Signal Processing Advances in Wireless Communications, 2004 IEEE 5th Workshop on
Source: IEEE Xplore

ABSTRACT We consider an iterative receiver composed of a maximum a posteriori (MAP) equalizer and a MAP decoder. During the iterations, the equalizer and the decoder exchange extrinsic information and use them as a priori in order to improve their performance. We propose here to study analytically the impact of the a priori information provided by the channel decoder on the equalizer performance. We show that it is equivalent to a gain in terms of signal-to-noise ratio (SNR) and we provide an analytical expression. Simulation results show that this expression approximates quite well the SNR gain.

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    • "At high SNR, the term corresponding to the upper bound will dominate the sum of the probabilities of the error events (because of the exponential decrease of the Q (.) function). Thus the overall probability of error can be approximated by [4]: "
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    ABSTRACT: To combat the effects of intersymbol interference, the optimal equalizer to be used is based on maximum a posteriori (MAP) detection. We consider the case where the MAP equalizer is provided with a priori information on the transmitted data, as in a turbo equalizer. We propose to study analytically the impact of the a priori on the MAP equalizer performance. We distinguish two cases: the case of unreliable a priori and the case of reliable a priori. We show that when the a priori is reliable, it is better to perform the detection of the transmitted symbols based on the a posteriori outputs of the MAP equalizer rather than on the a priori only. In a turbo equalizer, the equalizer and the decoder exchange extrinsic log likelihood ratios (LLRs). We propose here to study analytically their distribution. The aim of this study is to perform in the future the analytical convergence analysis of turbo equalizers using the MAP equalization.
    Signal Processing Advances in Wireless Communications, 2005 IEEE 6th Workshop on; 07/2005
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    • "Dans la suite, nous proposons de calculer la probabilité d'erreur totale de l'´ egaliseur et de trouver la distribution des LRV extrinsèques LRV ext eg (s k ). Nous généralisons les résultats de [4] et distinguons deux cas : le cas d'informations a priori peu fiables (μ eg faible) et le cas d'informations a priori fiables (μ egélevé ). "
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    ABSTRACT: Afin de combattre les effets des interférences entre symboles (IES), l'égaliseur optimal à utiliser est basé sur le critère Maximum a posteriori (MAP). Nous considérons le cas où l'égaliseur MAP est alimenté par des informations apriori sur les données émises, comme pour un turbo égaliseur. Nous proposons d'étudier analytiquement l'impact de l'a priori sur les performances de l'égaliseur MAP. Nous distinguons deux cas d'étude : le cas où les informations a priori sont fiables et le cas où elles ne sont pas fiables. Dans un turbo égaliseur, l'égaliseur et le décodeur s'échangent des Logarithmes du Rapport de Vraisemblance (LRV) extrinsèques pour améliorer les performances au fil des itérations. Nous proposons ici d'étudier analytiquement la distribution de ces LRV. Le but de cette étude est d'effectuer de manière analytique, dans un travail futur, l'analyse de la convergence des turbo égaliseurs utilisant un égaliseur MAP.
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    • "Moreover, we have m ≥ 2. Thus, a lower bound for˜E m = ε m 2 + 4mµ 2 is given by bound(µ 2 ) = d 2 min + 8µ 2 . (26) In [5] "
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    ABSTRACT: In this paper, we consider an iterative receiver composed of a maximum a posteriori (MAP) equalizer and a MAP decoder. During the iterations, the equalizer and the decoder exchange extrinsic information and use them as a priori in order to improve their performance. We consider here an iterative receiver including a channel estimator. We propose to study analytically the impact of both the a priori information and the channel estimation errors on the equalizer performance. We show that it is equivalent to a shift in terms of signal-to-noise ratio (SNR) and we provide an analytical expression. Simulation results show that the analytical expression we give approximate quite well the equalizer performance.
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