Pattern Synthesis Using Fourier Transforms

Abstract

Many adaptive phased array radar (APAR) high-resolution spectral estimation techniques are used to determine far field signal power and location. Once this information is known, placing nulls at these locations to cancel jammers can be accomplished through a proper choice of antenna weights. The antenna weight and angular pattern domains are related through Fourier transformation. To obtain a fine sampling in the angular domain in order to accurately specify the desired nulls, it is required to extend the antenna aperture by padding it with zeros. However, in the final weight vector applied to the antenna output, the contribution of these extra elements must be zero since they do not correspond to available antenna elements. This provides two sets of constraints on the solution: the set of desired nulls in the angular domain and the available aperture in the weight domain. A method of finding a solution that matches constraints in both the time and frequency domains is the Gerch-berg-Saxton algorithm, which is often applied to image reconstruction. This paper describes an investigation into the behavior of this algorithm as applied to the discrete, one-dimensional antenna pattern synthesis case. The algorithm is presented in matrix/vector form, and its transient and steady state responses are derived. To assist in this analysis, we introduce a new matrix operator that greatly simplifies the required derivations. Computer simulation and numerical evaluations of the analytical results are included to demonstrate the applicability of the algorithm to pattern synthesis.