Orthogonal periodic sequences with two complex numbers derived from M‐sequences

Abstract

The periodic sequence for which the sidelobe of the autocorrelation function is zero is called an orthogonal sequence. The orthogonal sequence is applied to various problems such as synchronization of communication and radar ranging. As a general method to generate the orthogonal sequence, the method to form the discrete‐Fourier transform of the periodic sequence with a constant amplitude is known. This paper proposes a method of generating the orthogonal sequence with an element of the sequence being composed of two complex numbers (orthogonal periodic sequence with two complex numbers). The method does not use the discrete‐Fourier transform, but maps the elements of the M‐sequence on Galois field GF(2) to complex numbers. Then the properties of the orthogonal sequence are discussed from the geometrical viewpoint and the range for which the orthogonal periodic sequence with two complex numbers exists is indicated.

Digital simulation of fault location on EHV lines using wideband spread spectrum techniques

“…The MLS orthogonal codes [63] are derived from the MLS codes by replacing each code value -1, +1 with complex numbers A.,, A+j respectively. Provided the complex numbers are chosen correctly the resulting code is orthogonal.…”