Adaptive Beamforming With Continuous/Discrete Phase Shifters via Convex Relaxation

Adaptive antenna array employing phase shifters only can reduce the hardware cost and power consumption, but the related optimization is well understood to be difficult to solve. In this paper, we examine the use of both continuous phase shifters (CPS) and discrete phase shifters (DPS) in antenna array for adaptive interference suppression. First, we formulate the phase-only tuning problem with CPS via quadratically constrained quadratic program (QCQP), which can be approximated through semidefinite relaxation (SDR) and solved by convex-optimization solvers efficiently. We also demonstrate that quantizing such results directly may not necessarily give acceptable performance. Then, we propose to use binary quadratic program (BQP) for the optimization of the adaptive beamformer utilizing DPS with an arbitrary number of control bits to specify the phase-shift levels. The resultant BQP can be relaxed and solved efficiently too. Moreover, due to the similarity between the CPS and DPS formulation, we can mix them in a single beamforming scheme to provide additional compromises between the output signal-to-interference and noise ratio (SINR) performance and implementation cost. Simulations show that in the considered interference-limited environment, our proposed beamformers with CPS, DPS, and hybrid phase shifters (HPS) give desirable results as expected.