Structural optimization of nested circular arrays under compressed sensing theory

To reduce the cost of microphone array, the array structure can be optimized by optimization algorithm without affecting the location accuracy. In this paper, a sparse optimization mathematical model of microphone array structure was established under the framework of compressed sensing theory. With the minimum mean value of non-diagonal elements in Gram matrix as the optimization objective, the sparse optimal structure of 31-element nested circular array was designed by adaptive genetic algorithm, and the optimal array configuration and fitness convergence curves at different frequencies were analyzed. The performance of the optimized microphone array was verified by simulation and experiment. The results show that the root-mean-square error of the optimized array is similar to the error of the full array, and even slightly smaller than the error of the full array, indicating that the optimized array has a similar or even slightly better location performance than the full array.