Constructions On Orthogonal Sequence Sets Suitable For The Code Division Multiple Access Systems

Pseudo random sequences have been widely used in CDMA communication system,encoding,cryptography,radar and other fields.This dissertation researches the constructions of orthogonal sequence sets,orthogonal sequence sets with zero correlation zone and Z-complementary sequence sets.Firstly,a large family of orthogonal sequence sets is investigated based on the theo-ry of the Boolean functions.By the classical Maiorana-McFarland?M-M?construction,a large class of orthogonal sequence sets is constructed.Next we assign these sequences to a regular tessellation of hexagonal cells in such a way that the correlation between code-words assigned to adjacent cells is zero,while the correlation between codewords assigned to non-adjacent cells is small.To avoid a hard combinatorial problem of assigning several such orthogonal sets to a single cell,meanwhile preserving the orthogonality to adjacent cells,this method is combined with the so-called vectorial bent function direct sum used for extending the length of these codewords to the desired length.This allows us to increase the number of orthogonal sequences per cell without modifying the original assignment found for small suitably chosen8).In order to apply a similar approach for resolving the problem of assigning orthogonal sets when m is even,we specify a modified design method.The obtained results are compared with previous results,we construct orthogonal sequence sets are arranged to be far better than the previous results.Secondly,we construct a new class of orthogonal sequence sets with zero correlation zone by combining the orthogonal sequences with complementary sequences.We construct a class of orthogonal sequences of length 2⁴such that there are 2²orthogonal sequences per cell,the reuse distance=4.Combining with the vectorial bent function direct sum,we can extend the length of these codewords to the desired length.Next we extend the binary orthogonal sequences to-ary orthogonal sequences such that there are⁸-1)orthogonal sequences per cell.We construct a family of orthogonal sequence sets with zero correlation zone property,meanwhile preserving the orthogonality to adjacent cells,and also having the same reuse distance with the obtained orthogonal sequence sets.Finally,the design of the Z-complementary sequences is studied.Based on the Boolean functions,we give a construction of Z-complementary sequences of length 2⁸+3)+2⁸+2)+2⁸+1)with ZCZ width 2⁸+3),where8)is a nonnegative integer.Each sequence of the Z-complementary pairs has low PMEPR?2.57.We propose the concept of the partiallysequences.Employing the partiallysequences and the complementary pairs,we present a construction of Z-complementary pairs of lengthwith ZCZ width?-4?,wheredenotes the length of the partiallysequences anddenotes the length of complementary pairs.Each sequence of the Z-complementary pairs has low PMEPR.