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Abstract-A semiblind iterative algorithm to construct the best linear unbiased estimate (BLUE) of the channel impulse response (CIR) vector h for communication systems that utilize a periodically transmitted training sequence within a continuous stream of information symbols is devised. The BLUE CIR estimate for the general linear model y = Ah + w, where w is the correlated noise, is given by the Gauss-Markoff theorem. The covariance matrix of the correlated noise, which is denoted by C(h), is a function of the channel that is to be identified. Consequently, an iteration is used to give successive approximations h (k) , k = 0, 1, 2, . . . to h BLUE , where h (0) is an initial approximation given by the correlation processing, which exists at the receiver for the purpose of frame synchronization. A function F (h) for which h BLUE is a fixed point is defined. Conditions under which h BLUE is the unique fixed point and for which the iteration proposed in the algorithm converges to the unique fixed point h BLUE are given. The proofs of these results follow broadly along the lines of Banach fixed-point theorems.

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 infomation symbols. The algorithm achieves slightIy degraded results at a much lower complexity than directly computing the BLUE CIR estimate. In addition, the inverse matrix required to invert 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, y = Ah + w +-n , for h , where w is correlated noise and the vector n is an AWGN process, which is uncorrelated with w . The Gauss -