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On the Convergence of Iterative Receiver Algorithms Utilizing Hard Decisions

Abstract

The convergence of receivers performing iterative hard decision interference cancellation (IHDIC) is analyzed in a general framework for ASK, PSK, and QAM constellations. We first give an overview of IHDIC algorithms known from the literature applied to linear modulation and DS-CDMA-based transmission systems and show the relation to Hopfield neural network theory. It is proven analytically that IHDIC with serial update scheme always converges to a stable state in the estimated values in course of iterations and that IHDIC with parallel update scheme converges to cycles of length 2. Additionally, we visualize the convergence behavior with the aid of convergence charts. Doing so, we give insight into possible errors occurring in IHDIC which turn out to be caused by locked error situations. The derived results can directly be applied to those iterative soft decision interference cancellation (ISDIC) receivers whose soft decision functions approach hard decision functions in course of the iterations.

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Correspondence to Wolfgang H. Gerstacker.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Rößler, J.F., Gerstacker, W.H. On the Convergence of Iterative Receiver Algorithms Utilizing Hard Decisions. EURASIP J. Adv. Signal Process. 2009, 803012 (2010). https://doi.org/10.1155/2009/803012

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Keywords

  • Neural Network
  • Stable State
  • Quantum Information
  • General Framework
  • Transmission System