Optimal Polyphase Asymmetric ZCZ Sequence Sets Including Uncorrelated Sequences

Abstract

The present paper proposes a new method for constructing polyphase asymmetric zerocorrelation zone (A-ZCZ) sequence sets using discrete Fourier transform (DFT) matrices and orthogonal codes. The proposed method can generate A-ZCZ sequence sets that cannot be obtained using known methods. The newly obtained A-ZCZ sequence sets include optimal ZCZ sequence sets. In addition, two arbitrary sequences that belong to different sequence subsets become uncorrelated sequences. The proposed method is expected to be usefu1 for reducing or avoiding inter-cell interference from adjacent cells in approximately synchronized code-division multiple-access (AS-CDMA) systems.

A New Construction of Asymmetric ZCZ Sequence Sets

“…Up to now, certain constructions of A-ZCZ sequence sets have been reported [11]- [21]. Torii et al proposed several types of polyphase A-ZCZ sequence sets based on perfect sequences in [11]- [16], and based on DFT matrices in [17]. These resultant sequence sets have larger ZCCZ lengths than the mathematical upper bound of conventional ZCZ sequence sets.…”

“…The parameters of the A-ZCZ sequence sets can approach or almost approach the theoretical bound only if the uncorrelated ZCZ sequence set was optimal or quasi-optimal. In [17], polyphase A-ZCZ sequence sets were constructed from the P-dimension DFT matrices and the orthogonal matrices of order M. The number of subsets is determined by P/M , which represents that the closer of P and M means the less of number of subsets. In addition, the obtained A-ZCZ sequence sets were optimal when M = P/N .…”

Constructions of polyphase ZCZ sequence sets with low cross‐correlation property

“…The latter is referred to as ICI. To reduce or remove ICI from adjacent cells, some progress on the construction of multiple sequence sets has been made recently [17–28]. Asymmetric ZCZ (A‐ZCZ) sequence sets consist of multiple ZCZ sequence subsets and the CCF between two arbitrary sequences from different subsets has a large zero‐cross‐correlation zone (ZCCZ) [17].…”

“…If the sequence subsets of an A‐ZCZ sequence set are assigned to adjacent cells in QS‐CDMA systems, the asymmetric property can be useful in reducing or avoiding ICI. [18, 19] constructed polyphase A‐ZCZ sequence sets based on DFT matrices and interleaved technique, respectively. The ZCZ sequences from different subsets of these A‐ZCZ sequence sets are uncorrelated.…”

An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length

“…In order to overcome the above shortcoming, a new class of zero correlation zone (ZCZ) sequence set referred as asymmetric ZCZ (A-ZCZ) sequence set has recently been proposed [10,4,5,12,15,14,11,13]. An A-ZCZ sequence set consists of multiple C-ZCZ sequence subsets, and the cross-correlation function (CCF) of two sequences which belong to different subsets has a wider ZCZ than that of arbitrary two sequences in the same subset.…”