# Optimized Sonar Broadband Focused Beamforming Algorithm
## 1 Introduction  
Beamforming can obtain array directivity in a predetermined direction, and it can improve the signal-to-noise ratio of the received signal. Space interference is suppressed through spatial filtering. Beamforming can realize target bearing estimation for multiobject resolution. It has a significant role in the estimation of the target location, distance, and depth. It can also offer information for target recognition [1]. The narrowband signal contains minimal information about the targets, such that the broadband signal is chosen for parameter estimation, target detection, and feature extraction. Broadband signal beamforming processing has two methods: The incoherent signal-subspace method (ISM) and the coherent signal-subspace method (CSM). Compared with that of the ISM method, the focusing operation of the CSM algorithm can fully integrate the broadband information and make the covariance matrix of the focused signal keep full rank, thereby effectively solving the problem of broadband beamforming. The CSM algorithm has small computational complexity and high estimation precision; it can effectively overcome the problems in signal offset, extension, detection, and resolution threshold, and it can solve the multipath problem [2; 3; 4]. In the CSM algorithm, the broadband signal is first divided into several narrowband signals in different frequencies, and all the narrowband signals are then mapped to the same reference frequency by the focusing matrix, where the narrowband beamforming algorithm can be used to achieve broadband focused beamforming [5; 6]. The structure of the focusing matrix is the core of the CSM algorithm, and the structure method of the focusing matrix plays a decisive role in the estimation of the performance of the CSM algorithm. The final focus effect in the estimation of the focusing matrix is determined by two factors: Initial direction estimation and focusing frequency choice. The deviation of these two factors would significantly decrease thefinal focusing effects, and it can even disable the algorithm. To solve this problem, the robust Capon beamforming (RCB) algorithm is used to correct the focusing matrix; it improves the focusing effect by considering the deviation of initial direction estimation [7; 8; 9]. The second-order cone programming (SOCP) method to compensate for the error of the focusing matrix was used in Reference [10]. However, neither of these methods considered the influence of the focusing frequency. In this paper, we propose an optimized sonar broadband focused beamforming algorithm. We used the RCB algorithm to correct the focusing matrix, and the focusing frequency problem was considered. The broadband signals were focused on the optimal focusing frequency by the corrected focusing matrix such that the wideband beamforming was transformed into a narrowband problem. Finally, the focused narrowband signals were beamformed by the second-order cone programming algorithm. The proposed method is derived in the next section. Section 3 reports simulation studies and performance analysis. Water pool experiments are reported in Section 4.