Convex Beam Synthesis for System-Oriented Noisy and Optimal Antenna Arrays

This letter describes the system-oriented convex optimization framework for antenna array beam synthesis problems in noisy environments. Each antenna signal reception is modeled as a combination of propagation delays in terms of linear, time-invariant Padé approximations, and noise terms affecting each antenna. Considering the desired signal and jammers as reference and disturbance inputs, respectively, the antenna array input–output relationships are used to formulate a semidefinite convex optimization problem to optimize the antenna weight coefficients and to optimize the number of antenna elements for desired signal gain and jammer null levels. The numerical results demonstrate the efficacy of the proposed framework for the number and weights of an array.