Improvement of the calculation for planar array directivity index

The planar array directivity index calculated by the formula in the book of "Sonar for Practising Engineers" is usually used to estimate sonar detection range. However, the estimated result is different from actual calculated value. In many other existing formulas for estimating directivity index of planar array at home and abroad, there are some other problems, such as large errors, complex expressions, or unclear theoretical derivation. In view of the fact that the accuracies of many domestic and foreign directivity index estimation formulas of planar array are different, the improved theoretical derivation and comparative analysis are made in this paper, so that the estimated value can be closer to the true value. In addition, the corresponding simulation analysis and verification are performed. The result proves that the estimation formula in this paper is closer to the true results and it is applicable to other curved arrays such as cylindrical array.