Design of Frequency-Hopping Waveforms Based on Ambiguity Function

Abstract

Integrated sidelobe level(ISL) criterion and the maximal sidelobe level(MSL) criterion are used to design frequency-hopping waveforms based on ambiguity functions respectively in this paper. Some simulation results are given and analyzed. The performance of the proposed algorithm is validated by numerical simulations. Frequency-hopping coding is a kind of orthogonal signals which can be used in radar and sonar systems. And frequency- hopping coding such as Costas arrays (1, 2) has good autocorrelation property. However, for radar and sonar systems, their properties of ambiguity function are mainly considered. In this paper, frequency-hopping waveforms are designed based on ambiguity functions. The results are achieved by minimizing two cost functions which measure the integrated sidelobe level(ISL) and the maximal sidelobe level(MSL) of the autocorrelation function respectively. In this paper, cost functions are defined based on ISL criterion and MSL criterion respectively, and some results are achieved based on genetic algorithm. The remainder of this paper is organized as follows. Section Ⅱ presents the ambiguity function of frequency-hopping waveforms and cost functions designed in this paper, and formulates the problem of designing frequency-hopping waveforms. In section Ⅲ, we introduce the genetic algorithm to optimize frequency-hopping waveforms sets. And design results and their curves of ambiguity functions are presented in Section Ⅳ. Finally, some conclusions are drawn in section Ⅴ.