The Optimal Frequency Hopping Patterns And Their Application In Frame Synchronization System

Telemetry is a wireless communication method that has been widely used in the research fileds of military,national,and scientific.For example,the systems of such as carrying space shuttles,Beidou navigation satellites,weather monitoring satellites and resource survey satellites,especially in the system of aviation and aerospace,telemetry technology plays an extremely important role.Frame synchronization is a synchronization technology commonly used in current aviation and aerospace telemetry communication systems.By inserting a one-dimensional pseudo-random sequence into the head of each frame of data as a frame synchronization flag,frame synchronization is completed using the correlation of frame synchronization codes.For long-distance wireless communications such as aviation and aerospace,there are various uncertain interference situations when signals are transmitted in space,leading to errors in frame synchronization symbols,then causing miss detection and false alarms at the receiving end.In order to solve the problem of insufficient synchronization performance of the one-dimensional frame synchronization code,the anti-interference ability of the system can be improved by improving the interference resistance of the frame synchronization code.In this dissertation,the optimal frequency hopping pattern is used as the frame synchronization sequence,its excellent performance of autocorrelation and cross-correlation can effectively improve the frame synchronization performance of the telemetry system.Firstly,based on the research of frame synchronization system,this dissertation briefly introduces the principle and structure of the frame synchronization system,and analyzes key performance indicators such as miss detection and false alarm of the frame synchronization system,and the system structure and frame structure of PCM telemetry frame synchronization system are briefly described.Finite fields and Costas arrays are the keys to constructing the optimal frequency hopping pattern,so a method for constructing finite field by using field extensions is introduced,and in the next the basic theory of finite fields and the algebraic structure and characteristics of Costas arrays are introduced.Then the method of constructing Welch Costas arrays and Golomb Costas arrays based on finite fields is introduced,and to obtain the optimal frequency hopping pattern with a gap line by cyclically shifting the Welch Costas arrays in the vertical direction,ant to obtain the optimal frequency hopping pattern with one-gap line or one-gap column by cyclically shifting the Golomb Costas arrays in the vertical direction or horizontal direction.Finally,the autocorrelation performance of the one-dimensional Barker code,the auto/cross-correlation performance of the Welch Costas array,and the autocorrelation/cross-correlation performance of the optimal frequency hopping patterns are compared through simulation.This dissertation presents the frame structure and system model of the telemetry frame synchronization system based on the optimal frequency hopping pattern,and the simulation analysis shows that the optimal frequency hopping pattern has excellent autocorrelation and Cross-correlation performance while the value of the max time delay and the max Doppler frequency shift less than the acceptable maximum.Therefore,the reasonable design of the optimal frequency hopping pattern by estimating the maximum Doppler frequency shift can effectively improve the anti-interference ability of the telemetry system and the frame synchronization performance.