Performance Evaluation of Linear Turbo Receivers Using Analytical Extrinsic Information Transfer Functions
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Performance Evaluation of Linear Turbo Receivers Using Analytical Extrinsic Information Transfer Functions ´ Cesar Hermosilla Department of Electronic Engineering, Technical University Federico Santa Mar´ıa, Valpara´ıso 239-0123, Chile Email: [email protected]
´ Leszek Szczecinski ´ Institut National de la Recherche Scientifique-Energie, Mat´eriaux,et T´el´ecommunications, Universit´e du Qu´ebec Montreal, Quebec, Canada J3X 1S2 Email: [email protected] Received 13 October 2003; Revised 16 July 2004 Turbo receivers reduce the effect of the interference-limited propagation channels through the iterative exchange of information between the front-end receiver and the channel decoder. Such an iterative (turbo) process is difficult to describe in a closed form so the performance evaluation is often done by means of extensive numerical simulations. Analytical methods for performance evaluation have also been proposed in the literature, based on Gaussian approximation of the output of the linear signal combiner. In this paper, we propose to use mutual information to parameterize the logarithmic-likelihood ratios (LLRs) at the input/output of the decoder, casting our approach into the framework of extrinsic information transfer (EXIT) analysis. We find the EXIT functions of the front-end (FE) receiver analytically, that is, using solely the information about the channel state. This is done, decomposing the FE receiver into elementary blocks described independently. Our method gives an insight into the principle of functioning of the linear turbo receivers, allows for an accurate calculation of the expected bit error rate in each iteration, and is more flexible than the one previously used in the literature, allowing us to analyze the performance for various FE structures. We compare the proposed analytical method with the results of simulated data transmission in case of multiple antennas transceivers. Keywords and phrases: iterative receivers, turbo processing, performance analysis, MIMO systems.
1.
INTRODUCTION
The iterative processing based on the so-called turbo principle, introduced to decode the parallel-concatenated codes (turbo codes) [1], was shown to be a powerful tool approaching the limit of globally optimal receivers. In serially concatenated coding schemes, where the propagation channel is the inner code of rate one, the turbo principle has been used in the problem of temporal equalization [2, 3], spatial separation in multiple-input multiple-output (MIMO) receivers [4, 5], and multiuser detection (MUD) [6, 7, 8]. In the above-mentioned serial concatenation schemes, a generic turbo receiver (T-RX) is composed of a soft-input soft-output (SISO) front-end (FE) receiver and a SISO channel decoder. Both devices, exchanging information using logarithmic-likelihood ratios (LLRs) defined for the coded bits, are separated by the mandatory (de)interleaver whose role is to decorrelate the LLRs. The optimal calculation of LLRs in the FE receiver may be computationally demanding
for high-dimensional sy
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