Linear Phase Beampattern Design with Set-theoretic Methods

We study a nonconvex beampattern design problem with magnitude constraints in the angular domain. By imposing a linear-phase constraint on the beampattern, we simplify the original nonconvex problem to a convex one. This simplification, which originates in the design of digital filters, has also been applied to beampattern design, albeit without considering potential performance impairments. In this study, we assess this performance degradation empirically, and derive new projection-based algorithms. Specifically, we propose a low-complexity extrapolated projection method to solve the simplified problem, and we compare its performance to the widely-used projections onto convex sets algorithm. Moreover, our simulations show that adding the additional constraint does not impair the sidelobe suppression in many practical cases.