基于Zadoff-Chu矩阵的最优码本构造方法

Construction method of optimal codebook based on Zadoff-Chu matrix

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。

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.