Semiblind BLUE Channel Estimation With Applications to Digital Television

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