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.
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