A new approach to adaptive beamforming is presented. The method is based on the property of cyclostationary signals to generate spectral lines when they pass through certain nonlinear transformations. The beamformer coefficients are selected according to a new optimization objective, which consists on minimizing the mean square error between the array output after the nonlinearity and a complex exponential. This approach optimally extracts any signal that generates a spectral line at the same frequency as the reference complex exponential. A gradient-based algorithm is derived to compute the optimum weights. Since the proposed cost function is a nonconvex function of the array coefficients, minima are analyzed for the three most common types of perturbations found in communications: Gaussian noise, multiple interferences, and multipath propagation. It is demonstrated via analysis and simulations that minima correspond to points where output noise power is minimized, interferences are canceled, and intersymbol interference is removed, i.e., the beamformer eliminates the distortion introduced by the radiocommunication channel.
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