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MIMO linear equalization with an H∞ criterion

Hassibi, Babak and Erdogan, Alper T. and Kailath, Thomas (2006) MIMO linear equalization with an H∞ criterion. IEEE Transactions on Signal Processing, 54 (2). pp. 499-511. ISSN 1053-587X. doi:10.1109/TSP.2005.861888.

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In this paper, we study the problem of linearly equalizing the multiple-input multiple-output (MIMO) communications channels from an H∞ point of view. H∞ estimation theory has been recently introduced as a method for designing filters that have acceptable performance in the face of model uncertainty and lack of statistical information on the exogenous signals. In this paper, we obtain a closed-form solution to the square MIMO linear H∞ equalization problem and parameterize all possible H∞-optimal equalizers. In particular, we show that, for minimum phase channels, a scaled version of the zero-forcing equalizer is H∞-optimal. The results also indicate an interesting dichotomy between minimum phase and nonminimum phase channels: for minimum phase channels the best causal equalizer performs as well as the best noncausal equalizer, whereas for nonminimum phase channels, causal equalizers cannot reduce the estimation error bounds from their a priori values. Our analysis also suggests certain remedies in the nonminimum phase case, namely, allowing for finite delay, oversampling, or using multiple sensors. For example, we show that H∞ equalization of nonminimum phase channels requires a time delay of at least l units, where l is the number of nonminimum phase zeros of the channel.

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Additional Information:© 2006 IEEE. Reprinted with permission. Manuscript received July 12, 2004; revised April 13, 2005. [Posted online: 2006-01-16] The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Nicholas D. Sidiropoulos.
Subject Keywords:H∞ estimation, linear equalization, minimum phase channels, multiple-input multiple-output (MIMO) equalization, risk sensitive estimation, robustness
Issue or Number:2
Record Number:CaltechAUTHORS:HASieeetsp06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6790
Deposited By: Archive Administrator
Deposited On:21 Dec 2006
Last Modified:08 Nov 2021 20:37

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