Consistency of Constraints on Nulls and on Dynamic Range Ratio in Pattern Synthesis for Antenna Arrays

Given an antenna array of N elements, we deal with the problem of finding an array pattern that approximates a desired pattern, while: a) null constraints are imposed in M(les N - 2) assigned directions; b) an upper bound D is imposed on the dynamic range ratio (DRR) of the excitations. At first we show that the system of constraint equations has solutions if and only if D ges D₀, where D₀ is a parameter depending on the null directions, and describe a method to evaluate D₀. Then we propose two simple and fast algorithms to solve the synthesis problem and show their effectiveness by numerical examples. Statistical results show that usually D₀ = 1 when M is small compared to N, thus exact nulls can be formed for any D ges 1. This result provides an insight into the numerical results.