Construction of Multi-Dimensional Periodic Complementary Array Sets

Fanxin ZENG  Zhenyu ZHANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.7   pp.1392-1395
Publication Date: 2010/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1392
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
multi-dimensional array,  periodic complementary array set,  perfect array,  impulsive periodic autocorrelation function,  

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Multi-dimensional (MD) periodic complementary array sets (CASs) with impulse-like MD periodic autocorrelation function are naturally generalized to (one dimensional) periodic complementary sequence sets, and such array sets are widely applied to communication, radar, sonar, coded aperture imaging, and so forth. In this letter, based on multi-dimensional perfect arrays (MD PAs), a method for constructing MD periodic CASs is presented, which is carried out by sampling MD PAs. It is particularly worth mentioning that the numbers and sizes of sub-arrays in the proposed MD periodic CASs can be freely changed within the range of possibilities. In particular, for arbitrarily given positive integers M and L, two-dimensional periodic polyphase CASs with the number M2 and size L L of sub-arrays can be produced by the proposed method. And analogously, pseudo-random MD periodic CASs can be given when pseudo-random MD arrays are sampled. Finally, the proposed method's validity is made sure by a given example.