Two-Dimensional Hamming Correlation Analysis Of Cubic Polynomial And Cartesian Product Frequency Hopping Sequence

Frequency hopping communication is a communication mode in which both communication receiving and receiving sides synchronously change frequency,and has good anti-interference and multiple access performance.In frequency hopping code division multiple access communication systems,the size of the Hamming correlation is an important measure of communication effectiveness.The frequency hopping sequence set has a good Hamming correlation in the low/no hit zone,which is beneficial to eliminate or reduce the interference in the communication system and is more favorable for the signal transmission in the communication system.In an actual communication system,signals not only undergo time shift but also undergo frequency shifts,causing mutual collisions between frequency gaps and seriously affecting communication quality.Therefore,it is necessary to extend the study of one-dimensional time-hopping of frequency hopping sequences to the study of two-dimensional time-shift and frequency shift of frequency hopping sequences.In this paper,we study the average Hamming correlation performance of the set of frequency hopping sequences in the cubic polynomial of the time-frequency low hit zone and the Hamming correlation of the set of hopping sequences in Cartesian product.Firstly,the related concepts and theorems of two-dimensional periodic hopping sequence sets and two-dimensional periodic Hamming correlation theorems of low/no hit zone frequency hopping sequences are introduced.And using the matrix transformation method to construct a set of hopping sequence sequences satisfying the two-dimensional periodic Hamming correlation theorems.Secondly,On the basis of the two-dimensional periodic average Hamming correlation theorems in the time-frequency low hit zone,the sequence parameters of the frequencyhopping sequence set constructed by cubic polynomials are studied,and the frequency number,sequence period,number of sequences,and total number are analyzed respectively.The properties of Hamming self/cross-correlation function values and mean Hamming self/cross-correlation function values,and using knowledge of finite fieldtheory and number theory,proved that the set of frequency-hopping sequences constructed by cubic polynomials meets the time-frequency two-dimensional periodic average Hamming correlation theorems.Finally,This paper promotion the characteristics of the one-dimensional periodic Cartesian product hopping sequence set in the time-frequency low hit zone to the twodimensional periodic Cartesian product hopping sequence set,and uses the different properties of the base sequence to construct two different Cartesian product hopping frequencies.Sequence sets,using the knowledge of Chinese surplus theory,analyzes the Hamming correlation of the constructed frequency hopping sequences.The constructed Cartesian product frequency hopping sequence sets satisfy the time-frequency low hit zone two-dimensional Hamming correlation theorems.