An algorithm for short-block data detection in the near-to-Toeplitz case

Crozier et al. (1990, 1992) have developed schemes for estimating transmitted data on a block-by-block rather than symbol-by-symbol basis. In general, this requires the solution of a linear system of equations with a near-to-Toeplitz structure. In this paper, we apply the algorithm of Cybenko and Berry (1990) for the efficient solution of near-to-Toeplitz linear systems of equations to the data detection problem of Crozier et al. The algorithm of Cybenko and Berry is based upon the use of hyperbolic Householder transformations and is asymptotically more efficient in terms of the number of operations than a direct method of solution based, say, upon the use of a general Cholesky linear system solver. Because near-to-Toeplitz matrices can be very ill conditioned, even when the matrix is small, the application of Bischof's (1990) incremental condition estimator (ICE) algorithm is shown to be useful in detecting such ill conditioning.