# Smart Ocean: A New Fast Deconvolved Beamforming Algorithm for Multibeam Sonar
## 3 Experimental Results  
### Computation Complexity Analysis  
To compare the computation complexity (here we use the length of time of computing to scale) of the four R-L algorithms, we compared and analyzed the case where the computation complexity varies as the beam number \(N\) grows when the iteration results are the same (we specify for the convenience of description that the effect of a certain number of calculation times with the Algorithm 1 iteration is the standard, and the other algorithms utilize it as the terminating condition for the iteration). Figure 3a shows that the time consumption of Algorithm 1 increased rapidly as beam number \(N\) grew. The time consumptions of Algorithm 2 and Algorithm 3 were roughly equivalent, but for Algorithm 3, it was a little less. Algorithm 4 had the least amount of calculation, which hardly increased as beam number \(N\) grew. When the beam number \(N\) equaled 3200, the time that Algorithm 1 consumed was about 150 times that of Algorithm 4, and the times that Algorithm 2 and Algorithm 3 consumed were about 12 times that of Algorithm 4. In addition, the ratio further increased as the beam number grew. Figure 3c shows a case where the theoretical amount of calculation (here we only take the time that multiplication needs into account) varies along with the growing of the beam number. This curve tendency is consistent with the experimental results.  
Next, we kept the beam number \(N\) constant and analyzed a case where the amount of calculation varied along with the different iteration results (for the convenience of description, we allow the  
Figure 3: (**a**) The actual time consumption (computation complexity) and beam number \(N\), (**b**) actual time consumption and iterative number (the higher the iterative number is, the better the results are) of the R–L algorithm, (**c**) theoretical computation complexity and beam number \(N\), (**d**) theoretical computation complexity and iterative number of R–L algorithm.  
number of iterations of Algorithm 1 to represent the effect of the iteration). The higher the number of times of the iteration, the better the results were. As shown in Figure 2(b), the time consumption of Algorithm 1 increased linearly as the iterative number grew. Algorithm 2 and Algorithm 3 consumed almost the same amount of time, and Algorithm 4 consumed the least amount of time. When the iterative number of Algorithm 1 was equal to 3200, the time consumption of Algorithm 1 was about 80 times that of Algorithm 4, and the time consumptions of Algorithm 2 and Algorithm 3 were about 9 times that of Algorithm 4. In addition, the ratio further increased as the beam number grew. Figure 2(d) shows a case where the theoretical amount of calculation varies along with the iterative number of the R-L algorithm (Algorithm 1) growing. This curve tendency is consistent with the experimental results.  
Overall, we obtained the conclusion that the computation efficiency of the fast R-L algorithm (Algorithm 2) utilizing the FFT technique was greatly improved compared to the R-L algorithm (Algorithm 1). The computation efficiency of the fast-accelerated R-L algorithm (Algorithm 4) was further improved compared to the accelerated R-L algorithm (Algorithm 3). The fast-accelerated R-L algorithm (Algorithm 4) had the highest computation efficiency. Because of such a high computation efficiency, the R-L algorithm that would have required a large amount of time for calculation could be implemented in a very short time. This greatly improves the efficiency of data processing and makes the application to high-resolution multibeam sonar system in real-time possible. In the subsequent experimental data processing, we will use Algorithm 4 for the deconvolved beamforming.  
The computing platform used in this experiment was an Intel(r)Core(TM) i5-6400 CPU with 2.7 GHz.