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Phase-only nulling under sidelobe and mainlobe constraints is a problem of interest in array synthesis which is a nonlinear problem without analytical solution. To reduce the computational cost of phase-only array nulling on-line, this paper proposes a real-time phase-only array synthesis method based on the deep neural network. The on-line real-time prediction of element excitation phase is achieved by the trained neural network which can be done off-line. The performance of the trained neural network is related with the number of data. Firstly, in order to obtain a large enough database for the deep neural network efficiently, a multi-task phase-only array synthesis model with nulling operation and sidelobe control is relaxed to a convex problem and solved by direct iterative rank refinement. Then, the deep neural network is devised to emulate the phase array nulling behavior. This is carried out by the design of the structure of the network, the dataset structure and the loss function of the network. To validate the performance of the deep neural network, the phase-only nulling of 10-element and 16-element linear array based on the deep neural network is realized and tested. Experimental results demonstrate that the proposed real-time array synthesis method not only satisfies the desired array pattern property but also shows robustness to the array imperfections. Robustness is validated with Monte Carlo test.

Real-Time Phase-Only Nulling Based on Deep Neural Network With Robustness