Hexagonal Array Fourier Transform Adaptive Beamforming And Its RLS Algorithmic Implementation

Hexagonal arrays have the best spatial sampling characteristics and are widely used in practice. To a Sonar system, signal processing is its most important part while beamforming is the core component of modern Sonar signal processing system. Since beamforming is a computation intensive algorithm, how to implement beamforming efficiently becomes an important problem especially in large aperture Sonar systems. Besides conventional beamforming, to suppress the strong interferences which are common in ocean environment, adaptive beamforming attracts great concern in recent research. LMS (Least Mean Square) and RLS (Recursive Least Square) are two popular adaptive algorithms. RLS algorithm has good performance especially in non-stationary environment. However, the conventional RLS (CRLS) algorithm is numerically unstable and its use is limited in practice. Combining RLS algorithm with Inverse QR Decomposition (IQRD), we develop a numerical stable IQRD-RLS adaptive beamforming algorithm.The basic operation of both conventional beamforming and adaptive beamforming is the inner product of weighting vector and data vector. The inner product of such two vectors is essentially a spatial Fourier transform. The weighting vector of conventional beamforming is the array response vector under plane-wave assumption, while the weighting vector of adaptive beamforming is the pre-whitened array response vector (left multiplied by the correlation matrix of interference plus noise) under plane-wave assumption. There is a duality between spatial filtering which is based on frequency-domain Fourier transform and temporal filtering which is based on time-domain Fourier transform. We illustrate the consistency between temporal processing and spatial processing, and establish beamforming, just as temporal filtering, under Fourier transform framework. For the hexagonal array used, we carry out theoretical research and computer simulation adopting hexagonal fast Fourier transform (HFFT) in conjunction with IQRD-RLS algorithm. Finally the lake experimental data processing verifies that the hexagonal fast Fourier transform-Inverse QR Decomposition RLS (HFFT-IQRD-RLS) beamforming algorithm enjoys a good performance.The main results include:(1) Expressed conventional and adaptive beamforming under Fourier transform framework. Improving their computational efficiency through the use of Fast Fourier Transform.(2) Researched on the numerical stability of RLS algorithm in a precision-limited system. Verified that IQRD-RLS adaptive beamforming algorithm is more numerical stable than CRLS algorithm through computer simulation.(3) Used hexagonal Fourier transfoim and its corresponding fast algorithm toimplement conventional/adaptive beamforming on hexagonal arrays. Combining hexagonal Fourier transform and IQRD-RLS algorithm to develop HFFT-IQRD-RLS beamforming algorithm which reduces computational complexity significantly as well as ensuring reasonable performance. (4) Employed the data from a lake experiment to verify HFFT-IQRD-RLS algorithm's steady performance such as DoA (Direction of Arrival) estimation, interference nulling etc.