Sparse Antenna Array Optimization with the Cross-Entropy Method

The interest in sparse antenna arrays is growing, mainly due to cost concerns, array size limitations, etc. Formally, it can be shown that their design can be expressed as a constrained multidimensional nonlinear optimization problem. Generally, through lack of convex property, such a multiextrema problem is very tricky to solve by usual deterministic optimization methods. In this article, a recent stochastic approach, called Cross-Entropy method, is applied to the continuous constrained design problem. The method is able to construct a random sequence of solutions which converges probabilistically to the optimal or the near-optimal solution. Roughly speaking, it performs adaptive changes to probability density functions according to the Kullback-Leibler cross-entropy. The approach efficiency is illustrated in the design of a sparse antenna array with various requirements.