# Smart Ocean: A New Fast Deconvolved Beamforming Algorithm for Multibeam Sonar
## 1 Introduction  
Smart Ocean engineering systematically integrates a variety of marine sensors, including underwater acoustic sensors and underwater acoustic sensor networks [1; 2; 3; 4], to develop and utilize a rich variety of resources. Multibeam sonar is one of the main underwater acoustic sensors for remotely sensing seabed characteristics. Multibeam sonar can provide the full sea depth, wide coverage, and high precision seabed topography, surficial seabed type information, and two-dimensional images of targets in the water column, all of which play an important role in the smart ocean, and the performance of multibeam sonar is seriously affected by the robust high-resolution beamforming algorithm.  
In the field of beamforming, we usually multiply the data vector obtained at the same time by the weighted vector of a fixed value to obtain the maximum response in one or more directions, which is usually called conventional beamforming (CBF). The advantage of CBF is that it is robust and it can work in the condition of a low signal-to-noise ratio (SNR). However, CBF suffers from fat beams and high-level side lobes, and it cannot detect a weak signal among loud interfering sources.  
To overcome the shortcomings of CBF, some high-resolution beamforming methods based on the inverse of the signal covariance matrix have been proposed. The minimum-variance distortionless response (MVDR) and multiple signal classification (MUSIC) are representative methods. These algorithms yield narrow beam widths and low side lobe levels, and therefore they allow for better interference rejection and detection of targets with a small bearing separation. At the same time, thesealgorithms are known to be sensitive to the signal mismatches [5]. To minimize the sensitivity for producing a wider beam in the target/interference look direction while keeping the side lobe level low, the MVDR algorithm has been modified with additional constraints, such as the white noise gain (WNG) constraint [6] or distributed sources constrains [7]. In addition, another problem with these high-resolution algorithms is that the signal covariance matrix is usually not known, which is replaced by the sample covariance matrix. Assuming that the signal is stationary, the sampled covariance matrix requires many samples of signals (usually 2-3 times the number of sensors) to guarantee rapid convergence and minimum power loss in the beam output [8]. For a nonstationary environment, such as a moving target with a high bearing rate, the number of samples available for a covariance matrix that is estimated without violating the stationary condition can be relatively small, which causes a snapshot deficient condition [9]. These high-resolution algorithms usually have a poor performance under these conditions.  
Deconvolved beamforming was first proposed by [PERSON] [5], and it has been applied to low-frequency line arrays, which works very well, yields narrow beam widths, and low side lobe levels. However, the Richardson-Lucy (R-L) deconvolution algorithm, which is used in [PERSON]'s paper, requires a huge amount of calculation. Based on [PERSON]'s paper, we further study the implementation of the R-L deconvolution algorithm and propose a new fast R-L deconvolution algorithm, which can greatly improve the efficiency of the original R-L algorithm. We applied the new fast R-L deconvolution algorithm to high frequency line arrays, and it obtained satisfactory results.