The Godard or the constant modulus algorithm (CMA) is an effective technique for blind receiver design in communications. However, due to the complexity of the Constant Modulus (CM) cost function, the performance of CM receivers has primarily been evaluated using simulations. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function. The following question, while resolvable numerically for a specific example, remains unanswered in a generic manner: In the presence of channel noise, where are the CM local minima and what are their mean-squared errors (MSE)? In this paper, a geometrical approach is presented that relates CM to Wiener (or minimum MSE) receivers. Given the MSE and the intersymbol/user interference of a Wiener receiver, a sufficient condition is given for the existence of a CM local minimum in the neighborhood of the Wiener receiver. MSE bounds on CM receiver performance are derived and shown to be tight in simulations. The analysis shows that, while in some cases the CM receiver performs almost as well as the (nonblind) Wiener receiver, it is also possible that, due to its blind nature, CM receiver may perform considerably worse than a (nonblind) Wiener receiver.Index Terms-Adaptive filters, blind deconvolution, constant modulus algorithm (CMA), equalization, intersymbol interference, local convergence, Wiener receiver.
This paper investigates connections between (nonblind) Wiener receivers and blind receivers designed by minimizing the constant modulus (CM) cost. Applicable to both T-spaced and fractionally spaced FIR equalization, the main results include 1) a test for the existence of CM local minima near Wiener receivers; 2) an analytical description of CM receivers in the neighborhood of Wiener receivers; 3) mean square error (MSE) bounds for CM receivers. When the channel matrix is invertible, we also show that the CM receiver is approximately colinear with the Wiener receiver and provide a quantitative measure of the size of neighborhoods that contain the CM receivers and the accuracy of the MSE bounds.
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