Minimising number of perturbed elements in linear and planar adaptive arrays with broad nulls using compressed sensing approach

Abstract

Here, a new algorithm, based on compressed sensing (CS), is presented for generating broad nulls in linear and planar adaptive antenna arrays through the control of only a small number of elements. In particular, sparse recovery theorem and convex optimisation are used to generate the broad nulls by perturbing the complex weights of a minimum number of elements. The problem is first formulated as a sparse recovery problem and then relaxed to the form of a convex optimisation problem. In addition to the nulling constraints, another constraint is added to ensure that the perturbed elements do not cause a pointing error in the synthesised array pattern. Also, one more constraint is used to set a predefined peak value for the array response in the sidelobe region. The optimisation problem is then solved iteratively using the iterative re-weighted l 1 -norm minimisation technique to reduce the number of perturbed array elements to the lowest possible number while satisfying the constraints on the radiation pattern. Simulations were conducted for linear and planar arrays. The results show that the proposed algorithm is capable of forming the required nulls by changing the complex weights of only a small percentage of the array elements.