A class of constant modulus algorithms for uniform linear arrays with a conjugate symmetric constraint

A class of constant modulus algorithms (CMAs) subject to a conjugate symmetric constraint is proposed for blind beamforming based on the uniform linear array structure. The constraint is derived from the beamformer with an optimum output signal-to-interference-plus-noise ratio (SINR). The effect of the additional constraint is equivalent to adding a second step to the original adaptive algorithms. The proposed approach is general and can be applied to both the traditional CMA and its all kinds of variants, such as the linearly constrained CMA (LCCMA) and the least squares CMA (LSCMA) as two examples. With this constraint, the modified CMAs will always generate a weight vector in the desired form for each update and the number of adaptive variables is effectively reduced by half, leading to a much improved overall performance.