Focused energy delivery with protection for precision electronic warfare

Focused energy delivery is a technique for precisely bringing energy to a specific target area. This paper deals with focused energy delivery by using an ultrasparse array and its application to precision electronic warfare (PREW). To take advantage of the prior information about the regions that need to be protected while delivering energy, the standard focused energy delivery model is modified by specifying protected regions more precisely to provide better overall performance in PREW scenarios. Besides the commonly used performance metric of minimum energy difference between the target region and the protected region, two new metrics that are more meaningful in PREW scenarios are presented. Then, by appropriately synthesizing the covariance matrix of the transmitted waveform, focused energy delivery is formulated as two different optimal design problems with these two performance metrics as their optimization objective functions, respectively. The first optimization problem is expressed as a semidefinite programming (SDP) problem that can be efficiently solved by using standard libraries. The second one, however, is shown to be a mixed Boolean SDP problem.We approximately solve it using two different techniques: 1) convex relaxation and 2) approximation of the objective function using a smooth function before optimizing it via general nonlinear programming. Numerical results are provided to demonstrate the advantages of the proposed algorithms over other focused energy delivery algorithms.