Investigation Of Novel Spreading Sequences And Their Theoretical Bounds

The spreading sequences play a very important role in Code Division Multiple Access (CDMA) techniques. In general, the goodness of the spreading sequences determines largely the level of the multiple-access interference and multipath interference of CDMA system, therefore directly influences the performance and capacity of the CDMA systems. The theory of spreading sequence design includes two primary research aspects, i.e. the theoretical bounds and sequence design. In this thesis, theoretical bounds for the conventional spreading sequences and the new type of spreading sequences are investigated; the constructions and analysis of novel spreading sequences are also carried out, together with their applications in quasi-synchronous (QS) CDMA communication systems.First of all, based on Levenshtein's "weight vector method", several new theoretical bounds for the conventional binary direct spreading sequences and the conventional direct spreading sequences over complex roots of unity are established by selecting special weight vector. That is, new mathematics inequalities are derived to disclose the relationship between the sequence length, the family size, the maximum aperiodic autocorrelation sidelobe and the maximum aperiodic crosscorrelation value. It is shown that these new theoretical bounds are tighter than the existing bounds, such as Sarwate bounds, Welch bounds, Levenshtein bounds and Boztas bounds.Based on the concepts of generalized orthogonal (GO) direct spreading sequences, by merging "weight vector method" with the theory of low/zero correlation zone (LCZ/ZCZ), an effective new method called "correlation zone method' is proposed for deriving theoretical bounds of GO sequence sets. Using "correlation zone method', the theoretical bounds for the periodic (aperiodic) GO binary sequence and the periodic (aperiodic) GO sequences over complex roots of unity are established. It is shown that these new theoretical bounds include the existing Tang-Fan bounds on GO sequences, the known Sarwate bounds, Welch bounds, Levenshtein bounds and Peng-Fan bounds on conventional sequences, as special cases. In addition, the theoretical bounds for GO functions are tighter under some circumstances.Thereafter, the theoretical bounds on frequency hopping (FH) sequences are investigated. For the conventional FH sequence sets, several new theoretical restriction relations (theoretical bounds) that are satisfied by some parameters, such as the sequence length, the family size, the size of the frequency slot set, the maximum periodic (aperiodic) Hamming autocorrelation sidelobe and the maximum periodic (aperiodic) Hamming crosscorrelation value, are established. It is shown that the new periodic FH bounds include the known Lempel-Greenberger bounds and Seay bounds as special cases. Besides, the aperiodic FH bounds have not yet been previously reported.The concepts and properties of the no/low hit zone (NHZ/LHZ) on the FH sequences are then discussed in details, together with the theoretical bounds of periodic Hamming correlation functions on generalized orthogonal FH sequence sets. For GO FH sequence set, new theoretical inequalities are derived to disclose the relationship between sequence length, family size, size of the frequency slot set, correlation zone, maximum periodic Hamming autocorrelation sidelobe in the correlation zone and maximum periodic Hamming crosscorrelation value in the correlation zone. It is shown that the existing bounds on the conventional FH sequences, such as Lempel-Greenberger bounds, Seay bounds and Peng-Fan bounds, as well as the known Ye-Fan bounds on FH sequences with the no hit zone, are only special cases of the presented bounds.Next, the constructions and characteristics of the direct sequences are discussed. In order to judge the goodness of ZCZ direct sequence sets, a new concept, called ZCZ characteristic, is proposed. Then by defining a sequence operation called "correlation product", and establishing its basic properties, a new approach to construct sets of sequences with large zero correlation zone is presented. According to the proposed ZCZ characteristic measure, the new construction is near optimal with respect to the ZCZ bound. Besides, constructions and characteristics of frequency/time hopping (TH) sequences are also discussed. A general quadratic FH/TH sequences, a general cubic FH/TH sequences and polynomial FH/TH sequences are proposed and investigated in details. Based on the finite field theory, it is shown that the new frequency/time hopping sequence sets possess large family size and good Hamming correlation properties. Moreover, accurate analytical formulas for the average number of hits, the probability of full collisions on general...