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 to invert the weighted normal equations to solve the general least squares problem may be precomputed 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 solution is given by theIn the present work we propose a Taylor series approximation for the functionL for each¯xed vector of received symbols, y, and each¯xed convolution matrix of known transmitted training symbols, A: We describe the full Taylor formula for this function,and describe algorithms using, respectively,¯rst, second and third order approximations. The algorithms give better performance than correlation channel estimates and previous approximations used, [15], at only a slight increase in complexity. The linearization procedure used is similar to that used in the linearization to obtain the extended Kalman lter, and the higher order approximations are similar to those used in obtaining higher order Kalman¯lter approximations, [7]

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Semiblind BLUE Channel Estimation With Applications to Digital Television

Pladdy¹,

OzenOzen²,

Nerayanuru

et al. 2006

IEEE Trans. Veh. Technol.

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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.

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

Cited by 3 publications

References 13 publications

Best linear near unbiased estimation for nonlinear signal models via semi-infinite programming approach

Best linear near unbiased estimation for nonlinear signal models via semi-infinite programming approach

Taylor series approximation for low complexity semi-blind best linear unbiased channel estimates for the general linear model with applications to DTV

Semiblind BLUE Channel Estimation With Applications to Digital Television

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