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# Pseudo-polyphase orthogonal sequence sets with good cross-correlation property

• Naoki Suehiro
Submitted Contributions Error Correcting Codes: Theory And Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)

## 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.

## Keywords

Discrete Fourier Transform Binary Sequence Periodic Sequence Orthogonal Sequence Maximum Length Sequence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1991

## Authors and Affiliations

• Naoki Suehiro
• 1
1. 1.Faculty of EngineeringTokyo Engineering UniversityTokyoJapan