CAJ | 학술논문

针对声呐低截获波形设计，提出了一种基于有限域理论的Costas编码脉冲串跳频信号构建方法。该方法根据整数集合生成有限域的充分性定理和有限域中本原元的存在性定理，在给定素数p的条件下，构造了包含p个元素的有限域，给出了该有限域中本原元的求解方法以及递推公式，该方法可以通过大数值模除运算来构造高阶次Costas阵列。实验结果表明，基于有限域理论的Costas编码脉冲串跳频信号具有较小的非循环互相关系数和“图钉”状的模糊度函数，具有好的多普勒频率分辨率和时延分辨率，对于低截获声呐设计具有重要的实用价值。
침대성눌저절획파형설계，제출료일충기우유한역이론적Costas편마맥충천도빈신호구건방법。해방법근거정수집합생성유한역적충분성정리화유한역중본원원적존재성정리，재급정소수p적조건하，구조료포함p개원소적유한역，급출료해유한역중본원원적구해방법이급체추공식，해방법가이통과대수치모제운산래구조고계차Costas진렬。실험결과표명，기우유한역이론적Costas편마맥충천도빈신호구유교소적비순배호상관계수화“도정”상적모호도함수，구유호적다보륵빈솔분변솔화시연분변솔，대우저절획성눌설계구유중요적실용개치。
Based on the analysis of the demand of sonar signal waveform design, Doppler frequency resolution and delay resolution, we design a frequency hopping coded signal based on Costas sequence for detecting underwater target while maintaining low interception probability for active sonar.A construction method based on finite fields for generating Costas sequence is also proposed.According to a sufficient theorem of generating a finite field by integer set and an existence theorem of primitive elements in this finite field, a finite field with p elements is constructed with a given prime number p.Primitive elements in this finite field are calculated by procedures and recurrence for-mula listed in this paper.High-order Costas sequence can also be obtained by using large number modulo operation based on this method.Computer simulation results and their analysis show preliminarily that frequency hopping Cos-tas sequence coded signal based on finite field theory has small acyclic cross-correlation coefficient and pushpin shaped ambiguity function.Because of its good Doppler frequency resolution and time delay resolution, this signal is of practical importance in LPI sonar design.