Application Research On Optimal Frequency Hop-ping Patterns In OFDM System

OFDM is a widely used modulation technology in modern communication systems.It uses overlapping and orthogonal subcarriers for multi-carrier modulation,which can overcome frequency selective fading and improve spectral efficiency while having high data rate.However,OFDM has serious problems: Inter-Carrier Interference caused by time delay and Doppler shift.The common solution to the Inter-Carrier Interference caused by time delay is to insert Cyclic Prefix,but there is no effective solution to the Inter-Carrier Interference caused by Doppler shift.In this thesis,the method of applying the optimal frequency hopping pattern in OFDM system can solve the Inter-Carrier Interference caused by time delay and Doppler shift simultaneously.Based on the introduction of the principle of OFDM,this thesis studies the traditional frequency hopping technology and Costas arrays,and then puts forward the method of constructing the optimal frequency hopping pattern based on the algebraic Costas arrays,and proposes that the optimal frequency hopping pattern is applied to the OFDM system to eliminate or reduce the inter-carrier interference.Only the frequency hopping patterns with sharp autocorrelation and the lowest cross-correlation can be called the optimal frequency hopping patterns.This thesis studies the autocorrelation function and cross-correlation function of the arrays obtained by cyclic shift of Costas arrays.It is found that the arrays retain the sharp autocorrelation property of Costas arrays and have the lowest cross-correlation.Then,the optimal frequency hopping patterns is applied to OFDM communication system,and the design scheme of users’ frequency hopping patterns for cellular mobile communication system architecture is provided.By hopping the frequency according to the frequency hopping patterns,the Inter-Carrier Interference caused by time delay and Doppler shift in OFDM system can be eliminated or reduced.Simulation results show that the optimal frequency hopping patterns have the lowest cross-correlation property in the range of delay or Doppler shift constraints,and the designed users’ optimal frequency hopping patterns have sharp autocorrelation and the lowest cross-correlation property in the delay and Doppler shift constrained system.