A Full Second-Order Statistical Analysis of Strictly Linear and Widely Linear Estimators with MSE and Gaussian Entropy Criteria

Abstract Novel physical insights are provided into second-order weight error bounds for both strictly linear (SL) and widely linear (WL) estimators for noncircular Gaussian data, under both mean square error (MSE) and Gaussian entropy criteria. This is achieved by first defining complementary weight error variances of these estimators and by further exploiting the so obtained additional degrees of freedom, related to complex noncircularity. Next, the strong uncorrelating transform (SUT) is employed for a joint diagonalization of both the input covariance matrix and the complementary covariance matrix, to allow for the boundedness of complementary weight error variances for different estimators to be addressed. Furthermore, a joint consideration of both the standard and complementary weight error variance analyses is shown to make it possible to measure weight error power distribution of these estimators over both real and imaginary data channels, an important finding which is not possible to obtain through the standard variance analysis only. Simulations in both system identification and channel estimation settings support the analysis.