BEAMPATTERN SYNTHESIS WITH LINEAR MATRIX INEQUALITIES USING MINIMAL ARRAY SENSORS

A new beampattern synthesis formulation is proposed to compute the minimum number of array sensors required. In order to satisfy all the prescribed speciflcations of the beampattern, the proposed method imposes linear matrix inequality (LMI) constraints on the beampattern as developed by Davidson et al., which remove the need to discretize the beampattern region. As the proposed formulation is quasi-convex, an iterative procedure is used to decompose it into a systematic sequence of convex feasibility problems, in order to flnd the minimum number of sensors. The proposed method guarantees convergence if the globally optimum solution lies in the search interval, which is easy to ensure at the start of the search.