Parameterization of Perfect Arrays of Real Numbers

A perfect array is an array for which the autocorrelation function is impulsive. A parameterization of perfect arrays of real numbers is presented. Perfect arrays are represented by trigonometric functions. Three formulae are obtained according to the parities of the size of the array. Examples corresponding to each formula are shown. In the case of 6×6 arrays, the existence of a set of perfect arrays having integer components is shown.

[1]  Takafumi Hayashi,et al.  Binary array set having a cross-shaped zero-correlation zone , 2004, IEEE Signal Processing Letters.

[2]  Takafumi Hayashi,et al.  Parameterization of perfect sequences , 2010, TENCON 2010 - 2010 IEEE Region 10 Conference.

[3]  Pingzhi Fan,et al.  Two Types of Polyphase Sequence Sets for Approximately Synchronized CDMA Systems , 2003, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[4]  Naoki Suehiro,et al.  A signal design without co-channel interference for approximately synchronized CDMA systems , 1994, IEEE J. Sel. Areas Commun..

[5]  R. E. Challis,et al.  Pseudo random binary sequence techniques for ultrasonic NDE of high loss materials , 1994 .

[6]  M. Antweiler,et al.  Perfect binary arrays , 1989 .

[7]  P. Wild,et al.  Infinite families of perfect binary arrays , 1988 .

[8]  H. D. Luke,et al.  Sequences and arrays with perfect periodic correlation , 1988 .

[9]  Tao Jiang,et al.  A Novel Class of 2-D Binary Sequences With Zero Correlation Zone , 2010, IEEE Signal Processing Letters.

[10]  J.J. Garcia,et al.  Using Golay complementary sequences for multi-mode ultrasonic operation , 1999, 1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No.99TH8467).

[11]  Chris J. Mitchell,et al.  Constructing new perfect binary arrays , 1988 .