A Class of Optimal One-Coincidence Frequency-Hopping Sequence Sets with Composite Length

Wenli REN  Fang-Wei FU  Feng WANG  Jian GAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.11   pp.2528-2533
Publication Date: 2017/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.2528
Type of Manuscript: LETTER
Category: Communication Theory and Signals
frequency-hopping sequence,  maximum Hamming correlation,  power residue theory,  interleaving technique,  

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In this letter, we first investigate some new properties of a known power residue frequency-hopping sequence (FHS) set which is established as an optimal one-coincidence frequency-hopping sequence (OC-FHS) set with near-optimal set size. Next, combining the mathematical structure of power residue theory with interleaving technique, we present a new class of optimal OC-FHS set, using the Chinese Remainder Theorem (CRT). As a result, one optimal OC-FHS set with prime length is extended to another optimal OC-FHS set with composite length in which the construction preserves the maximum Hamming correlation (MHC) and the set size as well as the optimality of the Lempel-Greenberger bound.