New direction in spreading sequence design and the related theoretical bounds

For quasi-synchronous (QS) CDMA systems, in order to eliminate the multiple access interference and multipath interference, it is required to design a set of spreading sequences which are mutually orthogonal within a designed shift-zone, called orthogonal zone. Unfortunately, for normal spreading sequences where the orthogonal zone equals to the sequence length, according to Welch bounds and other sequence bounds, in theory, it is impossible to construct such an ideal set of sequences. For traditional orthogonal sequences, such as Walsh sequences, the orthogonality can only be achieved at an orthogonal point; in other words, the orthogonality is destroyed whenever there is a relative shift between the sequences, i.e. their orthogonal zone is 0. In this paper, new concepts of generalized orthogonality (GO) and generalized quasi-orthogonality (GQO) are proposed, resulting a new direction of sequence design. Besides, selected GO/GQO sequence designs and their theoretical periodic and aperiodic bounds also are presented.