Taylor series approximation of semi-blind BLUE channel estimates with applications to DTV

Abstract

We present a low-complexity method for approximating the semi-blind best linear unbiased estimate (BLUE) of a channel impulse response (CIR) vector for a communication system, which utilizes a periodically transmitted training sequence. The BLUE, for h, for the general linear model, y ¼ Ah þ w þ n, where w is correlated noise (dependent on the CIR, h) and the vector n is an Additive White Gaussian Noise (AWGN) process, which is uncorrelated with w is given by h ¼ (A T C(h) À1 A) À1 A T C(h) À1 y. In the present work, we propose a Taylor series approximation for the function F(h) ¼ (A T C(h) À1 A) À1 A T C(h) À1 y. We describe the full Taylor formula for this function and describe algorithms using, first-, second-, and third-order approximations, respectively. The algorithms give better performance than correlation channel estimates and previous approximations used, at only a slight increase in complexity. Our algorithm is derived and works within the framework imposed by the ATSC 8-VSB DTV transmission system, but will generalize to any communication system utilizing a training sequence embedded within data.