Non-Uniform Decomposition Method Used for Obtaining the Frequency-Constrained Matrix of Broadband Laguerre Beamforming
Shurui Zhang, Qiong Gu, Xun Wu, Jie Luo, Weixing Sheng · IEEE Wireless Communications Letters · 2022
Adaptive Laguerre processing is an attractive spatio-temporal method of designing broadband beamformers. In this letter, a novel approach of directly obtaining the low-dimensional frequency-constrained matrix of adaptive spatio-temporal broadband Laguerre beamforming, namely, the non-uniform decomposition method frequency-constrained Laguerre beamformer (NUDM-FCLB), is proposed. The NUDM-FCLB utilizes non-uniform decomposition method to rapidly construct the low-dimensional frequency-constrained matrix of Laguerre beamformer without adding any computational complexity. More importantly, the proposed constrained matrix guarantees the Laguerre beamformer’s distortion-less response to the broadband signals of interest. Compared with the singular value decomposition for the high-dimensional frequency-constrained matrix to derive the reduced-rank ones, the proposed NUDM-FCLB can directly derive the low-dimensional frequency-constrained matrix without any extra complex multiplication and exhibit satisfactory performance in terms of broadband beamforming. The effectiveness and correctness of proposed algorithm is verified by numerical simulations.