Generation of Long Perfect Gaussian Integer Sequences


主讲人:李崇道 台湾义守大学




内容介绍:A Gaussian integer is a complex number whose real and imaginary parts are both  integers. A Gaussian integer sequence is called perfect if it satisfies the  ideal periodic auto-correlation functions. That is, let S=(s(0),s(1),...,s(N-1))  be a complex sequence of period N, where s(t)=u(t)+v(t)i for u(t),v(t), and i=.  The complex sequence S is said to be a perfect Gaussian integer sequence if is  nonzero for and is zero for any ,where denotes the conjugate of a complex number  . Recently, the perfect Gaussian integer sequences have been widely used in  modern wireless communication systems, such as code division multiple access and  orthogonal frequency-division multiplexing systems. In this research, two  different methods are presented to generate the long perfect Gaussian integer  sequences with ideal periodic auto-correlation functions. The key idea of the  proposed methods is to use a short perfect Gaussian integer sequence together  with the polynomial or trace computation over an extension field to construct a  family of the long perfect Gaussian integer sequences. The period of the  resulting long sequences is not a multiple of that of the short sequence, which  has not been investigated so far. Compared with the already existing methods,  the proposed methods have three significant advantages that a single short  perfect Gaussian integer sequence is employed, the long sequences consist of two  distinct Gaussian integers, and their energy efficiency is monotone increasing.