The Bound Of Frequency Hopping Sequences And Design Of Several Classes Of Optimal Frequency Hopping Sequences

Frequency hopping (FH) multiple-access (MA) spread-spectrum (SS) systems, with its anti-jamming, secure, and MA properties, have found many applications in Bluetooth, military radio communications, mobile communications, modern radar and sonar echolocation systems. FH sequences play a very important role in FH communication system. In this dissertation, theoretical bounds for FH sequences, FH sequence set with good aperiodic Hamming correlation, FH sequence set with good partial Hamming correlation, and low-hit-zone FH sequence set with good partial Hamming correlation are investigated.First of all, theoretical bounds for FH sequences are investigated in this dissertation. The bounds for FH sequences, with respect to the size of the frequency slot set, the sequence length, the family size, the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are established. The new bounds are tighter than the Peng-Fan aperiodic Hamming correlation bounds. A bound on the FH sequence set with respect to the size of the frequency slot set, the sequence length, the family size, the maximum periodic Hamming correlation is established. The new bound is tighter than the Singleton bound on FH sequence set. Furthermore, by introducing the Mobius function, the Singleton bound on FH sequence set is improved. In addition, an upper bound on the family size of FH sequence set with respect to the size of the frequency slot set, the sequence length and the maximum aperiodic Hamming correlation is established. A new bound on the maximum partial Hamming correlation of FH sequence set with respect to the size of the frequency slot set, the sequence length, the family size, and the length of correlation window is established. Then, the dissertation proves that there does not exist an optimal FH sequence set of family size M and length N over a frequency slot set of size q with respect to the Niu-Peng-Liu-Liu bound for all correlation window length L≤N when N>q2/M and q≥2.Based upon an FH sequence set with optimal partial Hamming correlation for a given correlation window length, a class of optimal FH sequence set with respect to the Niu-Peng-Liu-Liu bound is constructed by utilizing interleaving techniques. Based on the m sequence, a class of optimal FH sequence set with respect to the Niu-Peng-Liu-Liu bound is constructed. Then, based on this class of FH sequence set, a new class of optimal FH sequence set is constructed by interleaving techniques.Thereafter, the dissertation focuses on FH sequence set with good aperiodic Hamming correlation and the corresponding constructions are given. Based on the Reed-Solomon code, a class of FH sequence set with large family size is obtained, whose parameters meet the upper bound on the family size of FH sequence set under aperiodic Hamming correlation with equality. The FH sequence set is optimal with respect to the upper bound. From generalized m sequences (GM sequences) and generalized Gordon-Mills-Welch sequences (GGMW sequences), two classes of FH sequence sets under aperiodic Hamming correlation are also presented, whose parameters meet the upper bound with equality. The two classes of FH sequence sets are optimal with respect to the upper bound. Based upon an optimal FH sequence set with respect to the aperiodic Hamming correlation lower bound, a class of FH sequence set with optimal aperiodic Hamming correlation is constructed by utilizing interleaving techniques. In addition, based on m sequences, a class of one-coincidence FH sequence sets under aperiodic Hamming correlation is proposed. By employing the one-coincidence FH sequence sets, a class of FH sequence sets with optimal aperiodic Hamming correlation is also constructed by interleaving techniques.Finally, the partial Hamming correlation of FH sequences with low hit zone is studied. From an FH sequence set with optimal partial Hamming correlation for all correlation window length, a class of FH sequence set with low hit zone is constructed. The FH sequence set with low hit zone is optimal with respect to the Niu-Peng-Liu-Liu bound for all correlation window length. From an m sequence of degree 2, a class of optimal low-hit-zone FH sequence set for all correlation window length is constructed by interleaving techniques.