Abstract
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.
Highlights
Antenna array pattern synthesis is to generate the specific pattern by determining the amplitudes, phases or positions of the array elements, which is widely used in radar, sonar and communication systems [1]–[4]
The learning rate is decreased adaptively according to the value of Huber Loss of the proposed deep neural network (DNN) model. 20000 input-output pairs of data is used to train the network within 100 epochs
The on-line phase-only array synthesis based on the DNN is more efficient in terms of computation time
Summary
Antenna array pattern synthesis is to generate the specific pattern by determining the amplitudes, phases or positions of the array elements, which is widely used in radar, sonar and communication systems [1]–[4]. For the sake of preparing a large enough dataset for the DNN in acceptable time, the model is relaxed to a convex problem by semidefinite relaxing and solved by direct iterative rank refinement(DIRR), which converges fast in getting the approximated rank one solution of the phase-only array nulling. The optimization is to minimize the power at the interference directions while satisfying the following constraints: preserving the desired direction power which is expressed by constraint (a), maintaining the direction stable which is described with constraint (b), forcing the array element amplitude unchanged while alternating the phase of the elements to form nulls in the array pattern which is shown in constraint (c) and remaining the rank of matrix X to one which is denoted as constraint (d). Because of the generalization ability, the trained DNN can predict the phases of the array elements with similar performance of the original array synthesis model even though the input of the network never appears in the trainset.
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