Design of Real-Valued Wideband Beamformers Using an Adaptive-Array-Theory-Inspired WLS: Theory and Algorithm

• Published in: IEEE transactions on signal processing Vol. 70; pp. 1 - 15
• Main Authors: Feng, Congwei, Chen, Huawei
• Format: Journal Article
• Language: English
• Published: New York IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: adaptive array theory; Adaptive control; Algorithms; Arrays; Beamforming; Broadband; Cost function; Exact solutions; frequency-invariant beamformers; Mathematical analysis; Narrowband; Real-valued wideband beamformers; Signal processing; weighted least squares; Weighting functions; wideband beampattern control
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2022.3221541

The weighted least squares (WLS)-based beamformer design can achieve flexible beampattern control via adjusting the WLS weighting function inspired by the adaptive array theory (AAT). Nevertheless, the weighting function is conventionally adjusted in an ad hoc way, and precise beampattern control cannot be guaranteed. Although an analytical solution for the weighting function adjustment was proposed very recently, it is only applicable to complex-valued narrowband beamformers. In some applications such as acoustic/seismic array processing, however, real-valued wideband beamformers are required, since acoustic/seismic signals are usually unmodulated, real-valued and wideband. This paper studies the theory and design of real-valued wideband beamformers using an AAT-inspired WLS, which can achieve precise wideband beampattern control. The main contributions of this paper include: i) we theoretically prove the existence of the WLS weighting function for the real-valued wideband beamformers to achieve precise control of wideband beampatterns, and derive the corresponding analytical solutions; ii) we provide the insights into the impact of the weighting function on the cost function, which is useful to find the optimum solution for the weighting function among multiple feasible solutions; and iii) we propose an algorithm for the design of real-valued wideband beamformers using the proposed AAT-inspired WLS, which does not require to fine-tune any user parameters, and can guarantee precise control of wideband beampatterns as demonstrated by the simulation results.