A lower bound on the average Hamming correlation of frequency-hopping sequence sets

Aixian Zhang; Zhengchun Zhou; Keqin Feng

doi:10.3934/amc.2015.9.55

Article Contents

2015, Volume 9, Issue 1: 55-62. Doi: 10.3934/amc.2015.9.55

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A lower bound on the average Hamming correlation of frequency-hopping sequence sets

1.
Department of Mathematical Sciences, Xi'an University of Technology, Xi'an, Shanxi 710048
2.
School of Mathematics, Southwest Jiaotong University, Chengdu, 610031
3.
Department of Mathematical Sciences, Tsinghua University, Beijing 100084

Received: April 30, 2014

Revised: July 31, 2014

Published: January 2015

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Abstract

The average Hamming correlation is an important indicator of frequency-hopping sequences (FHSs) which measures the average performance of FHSs employed in practical frequency-hopping multiple access (FHMA) communication systems. In this paper, a lower bound on average Hamming auto- and cross correlations of an FHS set is derived. It generalizes and improves the lower bound proposed recently by Peng, Niu and Tang. A simple necessary and sufficient condition for an FHS set to meet the new bound is given. Based on this condition, two classes of FHS sets whose average Hamming correlations reach the proposed bound are introduced.

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Mathematics Subject Classification: Primary: 94A05, 94B60; Secondary: 05B10.

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