Non-uniform array pattern synthesis using reweighted ℓ1-norm minimization

This paper presents a new array pattern synthesis algorithm by reweighted ℓ1-norm minimization and convex optimization. A virtual uniform array with much smaller element spacing and a weight matrix are created first; then, we obtain a weight vector by solving a weighted ℓ1-norm minimization convex problem, and update the weight matrix by the weight vector. Some entries of the weight vector are so small and thus negligible without significantly changing the array pattern performance. Based on this notion, the pruned weight vector becomes a sparse weight vector, and a non-uniform array is formed according to the nonzero valued positions of the sparse weight vector. Determining the weight vector, updating the weight matrix and creating a non-uniform array are repeated until the final array synthesis performance is satisfactory. After optimizing the array geometric construction, we obtain the optimal weight vector of the non-uniform array by using convex optimization. One numerical example is presented to show the high efficiency of achieving the desired radiation pattern with the minimum number of antenna elements.