Research On The Partial Hamming Correlation Properties Of Low-hit-zone Frequency Hopping Sequences

With good anti-jamming performance, system safety and reliability, multiple access,etc., frequency hopping (FH) communication systems have found wide applications in both military communications and civil communications. On the other hand, for an FH commu-nication system, the degree of its multiple access interference to a certain extent depends on the Hamming correlation performance of the frequency hopping sequences (FHSs) it used.Therefore, FHSs play a critical role in FH communication systems. In order to meet the need of practical communication environment, the concepts of low-hit-zone (LHZ) FHSs and par-tial Hamming correlation emerged. Moreover, the conventional frequency hopping sequence(FHS) sets are specials cases of LHZ-FHS sets when the LHZ equals the sequence length minus 1, and the periodic Hamming correlation or the aperiodic Hamming correlation is a special case of the partial Hamming correlation when the correlation window length equals the sequence length or the sequence length minus the time delay length respectively. The the-oretical research of FHSs mainly includes the theoretical bounds of FHSs and the designs of FHSs which can (approximately) reach the theoretical bounds. In this dissertation, the theo-retical bounds on the average partial Hamming correlation of FHS sets, and on the maximum partial Hamming correlation of LHZ-FHS sets are studied; LHZ-FHS sets with good periodic Hamming correlation property or optimal partial Hamming correlation property, and FHS sets with good aperiodic Hamming correlation property are also investigated.In the first, for given sequence length, family size and alphabet size, the theoretical con-straint to which the average partial Hamming autocorrelation and the average partial Ham-ming cross-correlation of a conventional FHS set should be subject is discussed, and then a new theoretical bound on the average partial Hamming correlation of a conventional FHS set is established. Moreover, for given sequence length, family size, alphabet size, low-hit-zone and correlation window length, the theoretical constraint to which the maximum partial Hamming correlation of an LHZ-FHS set should be subject is also discussed, and then a new theoretical bound on the maximum partial Hamming correlation of an LHZ-FHS set is derived. Compared with corresponding existing theoretical bounds, these two new ones are tighter.Secondly, based on the excellent shift-and-add property and ideal k-tuple distribution property of m-sequences, two classes of LHZ-FHS sets with optimal periodic Hamming cor-relation property are introduced by using m-sequences and their decimated ones. Further-more, through using the decimated sequences of m-sequences, a class of LHZ-FHS sets with optimal partial Hamming correlation property under all the correlation window lengths is constructed.Next, under the conditions of with and without shift sequence, the methods to design LHZ-FHS sets via interleaving techniques are presented. So that, three classes of LHZ-FHS sets with different parameters and good periodic Hamming correlation property are recom-mended.Subsequently, based on the theory of Cartesian product, three new constructions of LHZ-FHS sets are introduced. Meanwhile, we pay our attention to the maximum periodic Ham-ming correlation within the LHZ of the constructed FHS sets in the first construction, and to the maximum partial Hamming correlation within the LHZ of the constructed FHS sets in the rest constructions. Besides, based on the quadratic polynomials in the finite field, a class of FHS sets which has optimal partial Hamming correlation property and will be chose as a part of component FHS sets is obtained. On the basis of above three constructions, by choosing appropriate component FHS sets, six new classes of LHZ-FHS sets are recommended. In ad-dition, the former two classes of LHZ-FHS sets have optimal periodic Hamming correlation property, and the last four classes of LHZ-FHS sets have optimal partial Hamming correlation property under all the correlation window lengths.Finally, based on FHS sets with optimal partial Hamming correlation property, a method to construct new FHS sets is proposed. Through this method, the parameters of the newly constructed FHS sets can be flexibly chose, such that a large number of new FHS sets can be obtained. In addition, the newly constructed FHS sets can have good aperiodic Hamming correlation property under some conditions. Based on the existing two classes of FHS sets with optimal partial Hamming correlation property, two new classes of FHS sets with good aperiodic Hamming correlation property are introduced. Moreover, with the aid of the plat-form Matlab, the aperiodic Hamming correlation performance of all new FHS sets we may get can be analyzed as long as the based FHS set is fixed, which does provide convenience in the selections of appropriate parameters of new FHS sets.