Frequency invariant beamformer design exploiting SRV-constrained array response control

Array response control (ARC)-based techniques, recently proposed for deterministic beamformer design, offer flexibility and reduced computational complexity but are typically limited to narrowband beampatterns. This paper considers the problem of frequency invariant (FI) deterministic wideband beamformer design and introduces a spatial response variation (SRV)-constrained ARC framework. The SRV translates to a virtual colored noise in ARC-based techniques to realize the FI property over a wideband. Furthermore, in order to solve a phase ambiguity issue in ARC, two design principles, namely the FI maximum magnitude response (FI-MMR) and the FI low pattern distortion (FI-LPD) are presented to realize accurate ARC with a constant beamwidth over a wide frequency range. In particular, the FI-MMR principle maximizes the magnitude response at the main-beam point for a focused FI beam, thus achieving a high array gain in sensing applications. Meanwhile, the FI-LPD principle offers a low pattern distortion for a shaped FI beam, which enables accurate beampattern control at one intended point while reducing the pattern distortion at other points. By applying these two principles, two low-complexity FI deterministic wideband beamforming algorithms for focused and, respectively, shaped beampattern design are developed. Numerical results validate the effectiveness of the proposed algorithms under arbitrary array configurations.