Optimal Least Squares Deterministic Parameter Estimation from a Class of Block-Circulant-with-Circulant-Block Linear Model

This paper investigates the least-squares (LS) estimation of unknown deterministic parameters from a standard linear model characterized by a class of block-circulant-with-circulant-block (BCCB) matrix. We propose a method for designing the BCCB system matrix coefficients to minimize the mean square error incurred by the LS estimate, under certain equality and inequality constraints. By exploiting the eigenvalue characteristic of BCCB matrices, precise analysis is undertaken to derive a closed-form solution. The considered optimization problem arises in the study of blind channel estimation for single-carrier block transmission with cyclic prefix; the presented analysis reveals several key features associated with the BCCB family, and shows an original investigation of the BCCB matrix structure for facilitating linear optimal parameter estimation