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Bounds on SIMO and MIMO Channel Estimation and Equalization with Side Information

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Abstract

Constrained Cramér-Rao bounds are developed for convolutive multi-input multi-output (MIMO) channel and source estimation in additive Gaussian noise. Properties of the MIMO Fisher information matrix (FIM) are studied, and we develop the maximum rank of the unconstrained FIM and provide necessary conditions for the FIM to achieve full rank. Equality constraints on channel and signal parameters provide a means to study the potential value of side information, such as training symbols (semi-blind case), constant modulus (CM) sources, or known channels. Nonredundant constraints may be combined in an arbitrary fashion, so that side information may be different for different sources. The bounds are useful for evaluating the performance of SIMO and MIMO channel estimation and equalization algorithms. We present examples using the constant modulus blind equalization algorithm. The constrained bounds are also useful for evaluating the relative value of different types of side information, and we present examples comparing semi-blind, constant modulus, and known channel constraints. While the examples presented are primarily in the communications context, the CRB framework applies generally to convolutive source separation problems.

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Authors and Affiliations

  1. Army Research Laboratory, AMSRL-CI-CN, 2800 Powder Mill Road, Adelphi, MD, 20783, USA

    Brian M. Sadler, Terrence Moore & Ananthram Swami

  2. Department of Electrical Engineering, Bucknell University, Lewisburg, PA, 17837, USA

    Richard J. Kozick

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  1. Brian M. Sadler
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  2. Richard J. Kozick
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  3. Terrence Moore
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  4. Ananthram Swami
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Sadler, B.M., Kozick, R.J., Moore, T. et al. Bounds on SIMO and MIMO Channel Estimation and Equalization with Side Information. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 30, 107–126 (2002). https://doi.org/10.1023/A:1014046808970

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