Beampattern optimization for sensor arrays based on covariance matrix weighting

Three optimal beamforming methods for sensor arrays of arbitrary geometry and element directivity were developed. The first one minimizes the square errors between the design beam and the desired beam while keeping unity output in the look direction. This method can design the beam according to the desired beam response. The second approach maximizes the array gain while keeping mainlobe direction and contolling the maximum sidelobe level. The third method minimizes the sidelobe level while keeping unity output in the look direction. These three methods can all overcome the two questions of second statistical weighted beamforming methods, which are the higher sidelobe and negative values in the beam patterns. They are converted to a convex form as the so called second-order cone programming and easily solved using well-developed interior-point methods. Results of computer simulation and lake-experiment for a circular array show superior performance of the proposed methods developed compared to the existing optimal beamforming methods.