An Analytical Solution for Weighted Least-Squares Beampattern Synthesis Using Adaptive Array Theory

The adaptive array theory has been successfully employed to the weighted least-squares (WLS)-based beampattern synthesis of arbitrary arrays for adjusting the weighting coefficients of WLS cost function, which enables flexible control of both mainlobe and sidelobe responses. However, the problem with the existing WLS beampattern synthesis approach is that the weighting coefficients, interpreted as "artificial interferers," are adjusted in an ad hoc way since some key user parameters used therein need to be chosen via a tedious trial-and-error process. Moreover, it may not guarantee that the desired beampattern control objective can be met. To deal with the problem, this communication establishes theoretically the relationship between the weighting coefficients of WLS cost function and the desired array response and proposes an analytical solution for the WLS beampattern synthesis, which can guarantee the objective of desired beampattern control without fine-tuning of any user parameters. The effectiveness of the proposed solution is further verified by several numerical examples of beampattern synthesis for linear and planar arrays.