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Semiblind BLUE channel estimation with applications to digital television
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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 hBLUE, 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 hBLUE is a fixed point is defined. Conditions under which hBLUE is the unique fixed point and for which the iteration proposed in the algorithm converges to the unique fixed point hBLUE are given. The proofs of these results follow broadly along the lines of Banach fixed-point theorems.