Sensitivity of the linearly-constrained constant-modulus cost function

The authors present results from the application of the linearly constrained constant-modulus (LCCM) adaptive algorithm to a perturbed array environment. Assuming a narrowband signal model, analytic expressions are derived for the feasible gain values on the signal in the presence of general array perturbations and ambient white noise. The feasible gain values are found to be the roots of a cubic equation that is parameterized by the number of array elements, the signal-to-noise ratio, the modulus factor, the kurtosis of the signal of interest, and the angle between the true signal steering vector, and the perturbed steering vector. A principal result of the analysis is that LCCM is robust in the presence of array perturbations but is sensitive to the modulus factor value. A simulation is included that compares the sensitivity to perturbations of the techniques of linearly constrained minimum power, unconstrained constant-modulus, and LCCM. Experimental results are presented on a four-element square array with half-wavelength spacing which is used to receive a QPSK signal arriving from a presumably known direction