Construction method of optimal codebook based on Zadoff-Chu matrix

Yubo LI; Shengyi LIU; Jingjing ZHANG; Dongyan JIA

doi:10.11959/j.issn.1000-436x.2020021

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Construction method of optimal codebook based on Zadoff-Chu matrix

Papers | 更新时间：2024-06-05

- Construction method of optimal codebook based on Zadoff-Chu matrix
- Journal on Communications Vol. 41, Issue 3, Pages: 112-119(2020)
- 作者机构：
  
  1. 燕山大学信息科学与工程学院，河北秦皇岛 066004
  2. 河北省信息传输与信号处理重点实验室，河北秦皇岛 066004
  3. 河北科技师范学院数学与信息科技学院，河北秦皇岛 066004
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61501395)
- DOI：10.11959/j.issn.1000-436x.2020021
  CLC： TN911.2
- Online First：2020-03，
  
  Published：25 March 2020
- 稿件说明：
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Yubo LI, Shengyi LIU, Jingjing ZHANG, et al. Construction method of optimal codebook based on Zadoff-Chu matrix[J]. Journal on Communications, 2020, 41(3): 112-119.
DOI：

Yubo LI, Shengyi LIU, Jingjing ZHANG, et al. Construction method of optimal codebook based on Zadoff-Chu matrix[J]. Journal on Communications, 2020, 41(3): 112-119. DOI： 10.11959/j.issn.1000-436x.2020021.

摘要

具有低相关性质的码本在同步码分多址系统（CDMA）、量子信息理论以及压缩感知领域都有重要应用。为扩展码本数量，放宽了变换矩阵的限制条件。基于Zadoff-Chu矩阵，利用差集、几乎差集以及有限域特征和构造了新的码本，得到的码本依照Welch界限或Levenstein界是最优或几乎最优的。通过实验仿真发现，基于该类码本构造的确定性测量矩阵在压缩感知中具有良好的性能。

Abstract

Codebooks with low-coherence have wide utilization in code division multiple access (CDMA) communications

quantum information theory

compressed sensing and so on.In order to expand the number of codebooks

the restrictions on the transformation matrix were relaxed.Based on the Zadoff-Chu matrix

new codebooks were constructed using the difference set

almost difference set

and finite field character sum.The proposed codebooks were optimal or near optimal according to the Welch bound or Levenstein bound.Through experimental simulation

it is found that the deterministic measurement matrices constructed using these codebooks also have good performance in the process of compressed sensing.

关键词

Keywords

references

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