Ng, Michael K. A fast algorithm for blind channel identification. (English) Zbl 1006.65033 Electron. J. Math. Phys. Sci. (EJMAPS) 1, No. 1, 92-103 (2002). A signal is transmitted by two channels and the noisy outputs are measured. The blind channel identification problem is to recover the transfer functions of the channels from the outputs and the noise information. Using second order statistics, and assuming some restrictions, the problem can be formulated as an eigenvalue problem for the covariance matrix of the two outputs placed in one vector. This covariance matrix has four Toeplitz blocks. The vector of the channel coefficients is the eigenvector corresponding to the smallest eigenvalue.Exploiting the displacement rank of the matrix, a fast algorithm of W. F. Trench [SIAM J. Matrix Anal. Appl. 9, No. 2, 181-193 (1988; Zbl 0647.65017)] is used to solve this problem. The complexity is \(O(4Nn)\) with \(N\) the number of iterations and \(n\) the number of filter coefficients. Reviewer: Adhemar Bultheel (Leuven) MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 62G30 Order statistics; empirical distribution functions 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 65Y20 Complexity and performance of numerical algorithms Keywords:Toeplitz-block matrix; eigenvalues; blind channel identification problem; second order statistics; covariance matrix; eigenvector; displacement rank; algorithm; complexity Citations:Zbl 0647.65017 PDFBibTeX XMLCite \textit{M. K. Ng}, Electron. J. Math. Phys. Sci. (EJMAPS) 1, No. 1, 92--103 (2002; Zbl 1006.65033) Full Text: EuDML EMIS