IEEE Trans. on Information Theory, Vol.46, No.7, pp. 2544-2560, November 2000.
Bounds for the MSE Performance of Constant Modulus Estimators
P. Schniter and C.R. Johnson, Jr.
Abstract
The constant modulus (CM) criterion has become popular in the design
of blind linear estimators of sub-Gaussian independent and identically
distributed (i.i.d.) processes transmitted through unknown linear
channels in the presence of unknown additive interference. In this
paper, we present an upper bound for the conditionally unbiased
mean-squared error (UMSE) of CM-minimizing estimators that depends
only on the source kurtoses and the UMSE of Wiener estimators. Further
analysis reveals that the extra UMSE of CM estimators can be
upper-bounded by approximately the square of the Wiener (i.e.,
minimum) UMSE. Since our results hold for vector-valued finite-impulse
response/infinite-impulse response (FIR/IIR) linear channels,
vector-valued FIR/IIR estimators with a possibly constrained number of
adjustable parameters, and multiple interferers with arbitrary
distribution, they confirm the longstanding conjecture regarding the
general mean-square error (MSE) robustness of CM estimators
