基于Zadoff-Chu矩阵的最优码本构造方法

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

Abstract

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.

Key words: codebook, difference set, almost difference set, Welch bound, Levenstein bound

CLC Number:

TN911.2

Yubo LI,Shengyi LIU,Jingjing ZHANG,Dongyan JIA. Construction method of optimal codebook based on Zadoff-Chu matrix[J]. Journal on Communications, 2020, 41(3): 112-119.

Figures/Tables 2

方法	码本参数	最大相关幅度值	最优性	矩阵Φ	集合D
文献[4,18]	(p,K)	$I_{\max} (C_{Φ}) = \sqrt{\frac{p - K}{(p - 1) K}}$	Welch界最优	IDFT矩阵	差集
文献[5]	$(p, \frac{p - 1}{2})$	$I_{\max} (C_{Φ}) = \frac{1 + \sqrt{p}}{p - 1}$	Welch界渐进最优	Hadamard矩阵	几乎差集
文献[19]	$(q - 1, \frac{q}{p^{2}} - 1)$	$I_{\max} (C_{Φ}) = \frac{(p^{2} - 1) \sqrt{q}}{\sqrt{q} - p^{2} }$	Welch界几乎最优	IDFT矩阵	二元序列支撑集
文献[20]	$(q, \frac{p - 1}{2 p} (q + \sqrt{q}) + 1)$	$I_{\max} (C_{Φ}) = \frac{1}{K} \frac{(p + 1) \sqrt{q}}{2 p}$	Welch界几乎最优	Hadamard矩阵	二元序列支撑集
定理2	(p,K)	$I_{\max} (C_{Φ}) = \sqrt{\frac{p - K}{(p - 1) K}}$	Welch界最优	Zadoff-Chu矩阵	差集
定理3	$(p, \frac{p - 1}{2})$	$I_{\max} (C_{Φ}) = \frac{1 + \sqrt{p}}{p - 1}$	Welch界渐进最优	Zadoff-Chu矩阵	几乎差集
定理4	(q ²+q-1,q)	$I_{\max} (C_{Φ} \cup ξ_{K}) = \frac{1}{\sqrt{q}}$	Levenstein界渐进最优	Zadoff-Chu矩阵	Eisenstein sum定义的集合

References 22

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