The Constructions Of Frequency Hopping Sequence Set With Time-frequency Two-dimensional Low Or No Hit Zone And The Research Of Costas Array Pair

QS-FH-CDMA system based on frequency hopping sequence with low or no hit zone is a kind of superior frequency hopping communication method.It is found that,in the actual system,frequency hopping sequence not only has time shift,but has frequency shift as well.,resulting in collision with other frequency hopping sequence,affecting the communication quality.Therefore,it is necessary to extend the one-dimensional hit zone,which only considers the time shift to the two-dimensional collision zone considering both time shift and frequency shift.Costas array is a special permutation matrix.Its special array structure makes it has the ideal auto-correlation performance.The frequency hopping sequence obtained by using Costas array has the ideal Hamming auto-correlation characteristic and good Hamming cross-correlation characteristic.It has been found that the address code sequence used by the transmitting end and the address code sequence used by the receiver can not be the same,and the receiving can be realized as long as they meet certain relevant conditions.Firstly,the upper bound of the auto-correlation function of the time-frequency two-dimensional periodic Hamming correlation function is proved,which provides theoretical support for constructing the frequency hopping sequence with time-frequency two-dimensional low hit zone.It is found a kind of property of frequency hopping sequence with time-frequency two-dimensional no hit zone.This property gives an effective method to determine the size of two-dimensional aperiodic no hit zone.Two kinds of constructions of frequency hopping sequence set with time-frequency two-dimensional low or no hit zone are proposed.One method constructs the frequency hopping sequence set with time-frequency two-dimensional periodic low hit zone based on the RS code.At the same time,The frequency sequence set also satisfies the condition of the frequency hopping sequence set with time-frequency two-dimensional aperiodic low hit zone.Another method splices and transforms line vector to construct the frequency hopping sequence set with time-frequency two-dimensional aperiodic no hit zone.Secondly,according to the special matrix form of Costas array,the properties of thecorrection function of Costas array are obtained.At the same time,it proves the uniqueness of the Costas array pair,which ensures theoretically the only reception of the signal.the four-point properties of Costas array pair including transformation properties is studied.In order to facilitate the further study of the Costas array.Finally,a two-dimensional shift frequency hopping sequence pair corresponding to Costas array is discussed.And the equality relation between correction functions is obtaine’d,and the uniqueness of the two-dimensional shift frequency hopping sequence is proved.