Fast maximum likelihood for blind identification of multiple FIR channels

This paper develops a fast maximum likelihood method for estimating the impulse responses ofmultiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The twostep maximum likelihood(TSML) method is shown to be high-SNR efficient, i.e., attaining the Cramer-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML, method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established Copyright Information: All rights reserved unless otherwise indicated. Contact the author or original publisher for any necessary permissions. eScholarship is not the copyright owner for deposited works. Learn more at http://www.escholarship.org/help_copyright.html#reuse IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 44, NO. 3, MARCH 1996 66 1 Fast Maximum Likelihood for Blind Identification of Multiple FIR Channels Yingbo Hua, Senior Member. IEEE AbstructThis paper develops a fast maximum likelihood method for estimating the impulse responses of multiple FIR channels driven by an arbitrary unknown input. The resulting method consists of two iterative steps, where each step minimizes a quadratic function. The two-step maximum likelihood (TSML) method is shown to be high-SNR efficient, i.e., attaining the CramCr-Rao lower bound (CRB) at high SNR. The TSML method exploits a novel orthogonal complement matrix of the generalized Sylvester matrix. Simulations show that the TSML method significantly outperforms the cross-relation (CR) method and the subspace (SS) method and attains the CRB over a wide range of SNR. This paper also studies a Fisher information (FI) matrix to reveal the identifiability of the M-channel system. A strong connection between the FI-based identifiability and the CR-based identifiability is established.