  The family of constant-modulus algorithms is widely used in wireless
communication systems and in radar. The classical constant-modulus adaptive
(CMA) algorithm, however, fails to lock onto a single mode when used in
conjunction with an antenna array. Instead, it equalizes the entire spatial
spectrum. In this paper, we describe in full detail our recently proposed
approach for the separation of multiple users in a radio system with frequency
reuse, such as a cellular network, making use of the CMA algorithm. Based on
the observation that the differential filter weights resemble a superposition
of the array steering vectors, we cast the original task to a
direction-of-arrival estimation problem. With rigorous theoretical analysis of
the array response based on the discrete-space Fourier transform we elaborate a
solution that solves the problem by finding the roots of a polynomial equation.
We provide a numerical example to demonstrate the validity of the approach
under high-SNR conditions. In addition, we propose a more general preprocessor
for the CMA array which allows the modulated signals to differ in amplitude. As
a byproduct, the preprocessor yields a low-cost estimate of the number of
concurrent users, i.e. the model order, by simply counting the roots with the
strongest response.
