Abstract
This paper proposes a class of pseudo-polyphase orthogonal sequence sets with good cross-correlation property. Each set, composed of N pseudo-polyphase orthogonal sequences, is introduced from a maximum length sequence (m-sequence) by the inverse DFT, where N is the period of sequences.
A periodic sequence is called an orthogonal sequence, when the autocorrelation function is 0 in every term except for period-multiple-shift terms. It is known that a polyphase periodic sequence is transformed into an orthogonal sequence by the DFT or by the inverse DFT. There are N way for transforming a shifted m-sequence by the inverse DFT matrix, because an m-sequence is a periodic sequence of period N. So, we obtain N pseudo-polyphase orthogonal sequences by transforming the shifted m-sequences with the inverse DFT.
The absolute values of (N−1) terms in any obtained sequence are the same value \(\sqrt {\frac{{N + 1}}{N}}\). The absolute value of remained one term in the sequence is \(\sqrt {\frac{1}{N}}\). So, the obtained sequences can be called a pseud-polyphase orthogonal sequence.
The absolute values of (N−1) terms in any crosscorrelation function between two different sequences in a set are the same value \(\sqrt {\frac{{N + 1}}{N}}\). The absolute value of the remained one term is 1/N. So, these sequences have good crosscorrelation property.
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© 1991 Springer-Verlag Berlin Heidelberg
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Suehiro, N. (1991). Pseudo-polyphase orthogonal sequence sets with good cross-correlation property. In: Sakata, S. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1990. Lecture Notes in Computer Science, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54195-0_43
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DOI: https://doi.org/10.1007/3-540-54195-0_43
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