Mask-free beampattern shaping for active reconfigurable intelligent surface-aided transmit array

This paper utilizes a closely-deployed active reconfigurable intelligent surface (RIS) to assist the transmit array for significantly reducing sidelobe levels without a mainlobe gain loss. To avoid pre-specifying a sub-optimal pattern mask, we jointly design the transmit weights and active RIS reflection coefficients by maximizing the ratio between minimal mainlobe gain and peak sidelobe level. Under the constraints of transmit power, total power consumption and maximum amplification factor of active RIS, and acceptable mainlobe ripple, we formulate the proposed beampattern shaping into a nonconvex constrained optimization problem. Then we customize an effective algorithm based on the alternating direction method of multipliers (ADMM) framework to tackle variable-coupled nonconvex constraints, wherein we specially solve the subproblems related to the transmit weights and active RIS reflection coefficients by leveraging consensus ADMM and quadratically constrained quadratic program with one constraint techniques simultaneously. Numerical results show that the proposed array yields markedly lower sidelobe levels and a slightly higher mainlobe gain than conventional and passive RIS-aided ones. The mechanism is that the beampattern component yielded by the reflection path has almost opposite phase and identical amplitude in the sidelobe region as that of the direct path, dramatically canceling the sidelobes.