Abstract: A nongrid sparse array optimization method was proposed to reduce the hardware cost of the portable 3D imaging sonar system and guarantee the performance of beam pattern of the array． Based on the cross array， the element position perturbation was introduced into the simulation annealing ( SA) algorithm to achieve the nongrid sparse optimization for the cross array and decrease the element number． Based on multiplefrequency transmitting beamforming and parallel subarray receiving beamforming algorithms，a new energy function for the SA algorithm was defined to make the sparse cross array has a realtime imaging property and lower computational requirement． Finally， the proposed method was employed to optimize a cross array with 100 +100 elements． The experiment results demonstrate that the nongrid sparse array obtained by the proposed method can achieve the presupposed beam pattern performance and own realtime imaging property and low computational requirements． Compared with the existing literature， the sparse array has the fewest active elements while maintaining the same beam pattern performances． 

Key words:  imaging sonars, sensor arrays, simulated annealing, beamforming