Analysis And Construction Of Time-Frequency Two-Frequency Two-Dimensional Hamming Correlation Frequency Hopping Sequence

Frequency hopping communication is widely used in radar,nuclear submarine,radio communication,base station communication and other fields to avoid the enemy’s interference and interception through frequency hopping.The frequency hopping is based on the frequency hopping sequence,which shows that the frequency hopping sequence plays an important role in the frequency hopping communication system.Frequency hopping sequences are divided into optimal,suboptimal and non optimal levels,which are mainly measured by the theory of hamming correlation function.In recent years,the research of sequences mainly focuses on the construction of sequences and the theory of hamming correlation function.With the exponential growth of the number of communication users,in order to achieve more accurate and efficient information transmission,based on the traditional one-dimensional hamming correlation function,this paper considers the influence of doppler frequency shift on information communication,constructs a frequency hopping sequence set with more sequences and longer cycle length,and evaluates the performance of the sequence from the perspective of time-frequency two-dimensional;at the same time,when measuring the frequency hopping sequence The cycle is replaced by a part of the cycle,so as to speed up the relevant detection calculation.Firstly,the relation between time-frequency two-dimensional periodic hamming correlation function and difference filling and the relation between difference filling and frequency hopping sequence are established;the method of constructing frequency hopping sequence based on combinatorial design theory,time-frequency two-dimensional periodic hamming correlation analysis and its construction examples are given.It lays a foundation for constructing FH sequence set indirectly in the futureSecondly,based on the fact that some frequency gaps move out of the set of frequency gaps to become non effective ones with the influence of time delay and frequency offset,the concept of partial periodic hamming correlation function in two-dimensional time-frequency low impact area is given.In this new context,the upper and lower bounds of partial periodic hamming correlation function in two-dimensional time-frequency low impact area are deduced,Then,the theoretical bound of the partial periodic hamming correlation function in the frequency-domain aperiodic shift time-frequency two-dimensional low impact area is derived,and the theoretical bound of the partial periodic hamming correlation function in the frequency-domain aperiodic shift time-frequency two-dimensional low impact area,the mathematical bound of the periodic hamming correlation function in the frequency-domain aperiodic shift time-frequency two-dimensional low impact area,and the theoretical bound of the periodic hamming correlation function in the frequency-domain aperiodic shift time-frequency two-dimensional low impact area are derived The theoretical bound of periodic hamming correlation function in frequency domain is wrong.Finally,based on the concept of time-frequency shift inequivalence,a method of constructing a long and large number of time-frequency two-dimensional partial periodic low collision region frequency hopping sequence set based on cartesian product mathematical theory is proposed.The frequency-domain aperiodic shift time-frequency two-dimensional partial periodic hamming correlation function is defined to analyze the obtained cartesian product frequency hopping sequence set.Then,multiple types of frequency hopping sequence set are analyzed The time-frequency shift is not equivalent,and the time-frequency two-dimensional partial periodic hamming correlation of frequency-domain aperiodic shift is given.