In this paper, a novel algorithm is proposed to generate orthogonal periodic sequences whose components consist of at most q complex numbers. In this algorithm, orthogonal periodic sequences are generated by means of mappin M-sequences on GF(q) into complex perio%ic sequences.The mapping functions are derived in simple formulas. The mathematical properties have been studied and it is shown that polyphase orthogonal periodic sequences and real orthogonal periodic sequences are derived as the particular cases of t h e orthogonal periodic sequences.
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.
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