Taylor series approximation of semi-blind best linear unbiased channel estimates for the general linear model

We present a low complexity approximate method for semi-blind best linear unbiased estimation (BLUE) of a channel impulse response vector (CIR) for a communication system, which utilizes a periodically transmitted training sequence, within a continuous stream of information symbols. The algorithm achieves slightly degraded results at a much lower complexity than directly computing the BLUE CIR estimate. In addition, the inverse matrix required inverting the weighted normal equations to solve the general least squares problem may be pre-computed and stored at the receiver. The BLUE estimate is obtained by solving the general linear model. The Gauss-Markoff theorem gives the solution in this paper. In the present work we propose a Taylor series approximation in which the full Taylor formula is described. The algorithms give better performance than correlation channel estimates and previous approximations used, (S. Ozen et al., Nov. 2003), at only a slight increase in complexity. The linearization procedure used is similar to that used in the linearization to obtain the extended Kalman filter, and the higher order approximations are similar to those used in obtaining higher order Kalman filter approximations, (A. Gelb et al., 1974).