Accurate and Efficient Shaped Power Pattern Synthesis for Arbitrary Antenna Arrays via Beam-Space Semidefinite Relaxation Method

In this communication, a beam-space semi-definite relaxation (BS-SDR) method is presented for synthesizing shaped power patterns of arbitrary antenna arrays. Different from the original semi-definite relaxation (SDR) method which optimizes all the element excitations directly, the proposed BS-SDR method constructs several analytical pencil beams whose directions cover the desired mainlobe region as well as the notch area, and the excitations for each beam basis are analytically obtained by solving the maximum Rayleigh quotient problem. Then, the proposed method optimizes only a few beam coefficients in the SDR frame to approximate the desired power pattern characteristics. In this way, the number of optimization variables can be significantly reduced, thus remarkably improving the time efficiency of the SDR-based shaped pattern synthesis. Several examples of synthesizing different shaped patterns for linear and conformal antenna arrays are provided to validate the effectiveness and advantages of the proposed method.