The Bound And Design Of Hopping Spreading Sequences

The spreading sequences play a very important role in spread spectrum communication system. In general, the goodness of the spreading sequences determines largely the level of the multiple-access interference and multipath interference of the corresponding system, influences the performance and capacity of the corresponding systems directly. The frequency hopping sequence spreading spectrum communication is an important way of spreading spectrum communication, it uses the spreading spectrum sequence is known as frequency hopping sequence. The theory of frequency hopping sequence design includes two primary research aspects:the theoretical bounds and sequence design. In this paper, theoretical bounds for the conventional frequency hopping sequences and the low hit zone frequency hopping sequences are investigated; the constructions and analysis of frequency hopping sequences are also carried out.First of all, the theoretical bounds on the Hamming correlation and the partial Hamming correlation of frequency hopping sequences (FHSs) are investigated. For any FHS sets, the average periodic Hamming correlation theoretical restriction relation (theoretical bound) that is satisfied by some parameters, such as the sequence length, the family size, the size of the frequency slot set, the average periodic Hamming autocorrelation sidelobe and the average periodic Hamming crosscorrelation value are established. The theoretical bound on the maximum aperiodic Hamming correlation of FHS with LHZ. the maximum aperiodic Hamming correlation of FHS are also established. In addition, the theoretical bound for maximum aperiodic Hamming correlation are tighter than the known bound. Besides, the theoretical bounds on the partial Hamming correlation of FHSs are investigated. The theoretical bounds on the maximum periodic partial Hamming correlation of LHZ FHS, the average periodic partial Hamming correlation of LHZ FHS, the maximum periodic partial Hamming correlation of FHS and the average periodic partial Hamming correlation of FHS are established. These bounds that are satisfied by some parameters, such as the sequence length, the family size, the size of the frequency slot set, the maximum (average) periodic partial Hamming autocorrelation sidelobe and the maximum (average) periodic partial Hamming crosscorrelation value, are established. It is shown that the new bounds include the known Eun-Jin-Hong-Song bounds, Peng-Fan-Lee bounds, Peng-Fan bounds and Lempel-Greenberger bounds as special cases.Thereafter, the relationship between single FHS and LHZ FHS set are given, and the new design of optimal LHZ FHS sets is proposed based on interleaving technique. By the new design, new classes of optimal LHZ FHS sets with new and flexible parameters are obtained. The proposed construction improved the known construction by Ma and Sun. The generalized relationship between FHS and LHZ FHS set are established, and the generalized design of optimal LHZ FHS sets is also proposed. Moreover, new classes of optimal LHZ FHS sets with large family size are obtained by the new design. Besides, the construction of shift sequence sets is given. It is shown that all the sequences in the proposed FHS sets are shift distinct.Next, based on the generalized m-sequence and generalized Gordon-Mills-Welch sequence over a polynomial residue class ring, a new class of frequency hopping/time hopping sequence set with good partial Hamming correlation properties is investigated. The new sets are with flexible parameters. By the parameters choosen, the optimal frequency hopping/time hopping sequence sets meeting partial Hamming correlation bound for any correlation window are proposed.Finally, a new family of cubic+constant frequence hopping/time hopping sequences with large family size is proposed. Further, the average Hamming correlations for the new cubic+constant hopping sequences and some known cubic polynomial hopping sequences are derived analytically. It is shown that these cubic polynomial hopping sequences are optimal with respect to our new bound on the average Hamming correlation.