Adaptive beamformers are an integral part of most radar and sonar target detection systems. They can be subject to large sidelobes and mainlobe squinting due to sensor perturbations, pointing error, and/or low sample support. In radar and sonar systems, this behavior can lead to increased false alarms from clutter, reverberations, and unexpected interferers.

In this work, a general framework for adaptive and non-adaptive beampattern synthesis based on minimum mean-square error (MMSE) beamforming with quadratic beampattern constraints is presented. Main beam and sidelobe pattern control is achieved by imposing a set of inequality constraints on the weighted mean-square error between the adaptive pattern and a desired beampattern over a given angular region. An iterative procedure for satisfying the constraints is developed which can be applied as post-processing to standard the standard MMSE beamformer. The technique is used to synthesize a nearly uniform sidelobe level quiescent pattern for a circular array under development for airborne radar, and to control sidelobe levels for the same array in an adaptive manner. Performance results using data provided by Lincoln Lab show that under low sample support conditions, sidelobes can be effectively suppressed while maintaining high signal-to-interference plus noise ratio, and deep nulls on clutter and interferers