Sparse arrays with the minimum number of elements: Recent advances

The design of maximally sparse arrays able to radiate focused beam patterns satisfying a given upper bound power mask is a research area of increasing interest. The synthesis problem can be formulated with proper constraints on the cardinality of the solution space, i.e. its ℓ₀-norm. As the latter is a non-convex constraint, a different solution needs to be exploited. In this communication an innovative synthesis approach which optimizes both excitation weights and sensor positions of an array radiating pencil beam-patterns is discussed. The solution algorithm is based on sequential convex optimizations including a reweighted ℓ₁-norm minimization. Numerical tests, referred to benchmark problems, show that that proposed synthesis method is able to achieve maximally sparse linear arrays, also compared with the best results reported in the literature, obtained by means of global optimization schemes.