Sparse Linear Array Synthesis Using Exponential Analysis

This paper presents an exponential analysis technique for synthesizing a sparse non-uniform linear array using equidistant samples of the array factor of a dense uniform linear array. The problem statement is explored in a realistic production noise setting (i.e., we model uncertainties/tolerances during production as Gaussian noise), which motivates some slight oversampling. The collected samples are organized in the form of a Hankel matrix. A Cadzow iteration provides an accurate lower-rank approximation of the Hankel matrix. This lower-rank Hankel matrix is then used to obtain an equivalent sparse reduced array that accurately approximates the performance of the original dense array. Numerical experiments demonstrate that the newly developed method is more robust and accurate compared to the methods previously reported.

I. Introduction

Modern wireless communication systems frequently employ antenna arrays because of their high gain and beam-forming capabilities. Recently, unequally spaced sparse arrays that utilize fewer antenna elements are becoming increasingly popular, in terms of reducing the system complexity, cost and power consumption, as well as minimizing the effects of mutual coupling. Several techniques are employed to synthesize sparse linear and planar arrays. Some notable optimization methods include the genetic algorithm [1], where the antenna element positions are optimized in order to achieve a minimum peak sidelobe level, keeping the number of elements and their complex excitations fixed, and simulated annealing [2], where a stochastic method is utilized for synthesizing a planar array from a fully sampled array with half-wavelength element spacing. While these iterative methods have shown promising results for small arrays, they have a tendency to be trapped into local optima resulting in significant computation time when the array is large. Other optimization techniques for array sparsification are presented in [3], [4] and [5]. In [3], a sequence of weighted l₁ convex optimization problems are solved to synthesize a sparse array, and in [4] a multi-objective optimization problem is solved to minimize the number of elements and the peak sidelobe level. In [5], a Bayesian compressive sensing inversion algorithm is proposed to solve a sparseness constrained optimization problem, in order to minimize the number of elements in the array. Other than these iterative methods, non-iterative algorithms using subspace based methods have also been proposed to synthesize sparse linear [6], [7] and planar arrays [8]. Using matrix pencil based algorithms, the methods have successfully reconstructed focused or shaped beam patterns with fewer elements, while also significantly reducing the computation time, when compared to the iterative methods.