Adaptive beamforming with real-valued coefficients based on uniform linear arrays

A class of adaptive beamforming algorithms with real-valued coefficients is proposed based on the uniform linear array structure by introducing a preprocessing transformation matrix. It is derived from the beamformer with a minimum mean square error (MSE) or a maximum output signal-to-interference-plus- noise ratio (SINR), depending on the specific design criteria. The key parameter of the transformation matrix takes different values for different beamforming scenarios and three representative examples are studied: the linearly constrained minimum variance beamformer (and the generalized sidelobe canceller), the reference signal based beamformer, and the class of blind beamformers based on the constant modulus algorithm. Its advantage is twofold: 1) with real-valued coefficients, the computational complexity of the overall system is reduced significantly; 2) a faster convergence speed is achieved and given the same stepsize, the system arrives at a lower MSE (or a higher output SINR).