Sparse Antenna Array Optimization With the Cross-Entropy Method

• Published in: IEEE transactions on antennas and propagation 2011-08, Vol.59 (8), p.2862-2871
• Main Authors: Minvielle, P., Tantar, E., Tantar, A., Berisset, P.
• Format: Article
• Language: English
• Subjects: Antenna arrays; Antenna design; Antenna radiation patterns; Antennas; Applied sciences; Arrays; Constraints; Cost engineering; cross-entropy; Directive antennas; Exact sciences and technology; Monte Carlo methods; Nonlinearity; Optimization; phased array; Probability density functions; Radiocommunications; stochastic optimization; Telecommunications; Telecommunications and information theory
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2011.2158941

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.