Construction method of optimal codebook based on Zadoff-Chu matrix

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.

Keywords

• codebook
• difference set
• almost difference set
• Welch bound
• Levenstein bound