Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(4): 040509    DOI: 10.1088/1674-1056/20/4/040509
GENERAL Prev   Next  

Multirate diversity strategy of fractal modulation

Yuan Yong(袁勇),Shi Si-Hong(史思红), and Luo Mao-Kang(罗懋康)
Institute of Mathematics, Sichuan University, Chengdu 610065, China
Abstract  Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment.
Keywords:  multirate diversity      fractal modulation      homogeneous signals      fractal signals  
Received:  19 July 2010      Revised:  02 December 2010      Accepted manuscript online: 
PACS:  05.45.Df (Fractals)  
  01.20.+x (Communication forms and techniques (written, oral, electronic, etc.))  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10731050) and the Program for Changjiang Scholars and Innovative Research Team in University of the Ministry of Education of China (Grant No. IRTO0742).

Cite this article: 

Yuan Yong(袁勇),Shi Si-Hong(史思红), and Luo Mao-Kang(罗懋康) Multirate diversity strategy of fractal modulation 2011 Chin. Phys. B 20 040509

[1] Mandelbort B B 1983 The Fractal Geometry of Nature (New York: W H Freeman and Company) p. 98
[2] Feder J 1988 Fractals (New York: Plenum) p. 56
[3] Tricot C 1995 Curves and Fractal Dimension (New York: Springer-Verlag) p. 67
[4] Bamsley M F 1993 Fractals Everywhere 2nd edn. (New York: Academic Press Professional) p. 33
[5] Wornell G W and Oppenheim A V 1992 IEEE Trans. on Information Theory 38 785
[6] Ptasinski H S and Fellman R D 1994 Proceedings of the SPIE Wavelet Applications Conference 2242 78
[7] Ptasinski H S and Fellman R D 1994 Proceedings of the IEEE SUPERCOMM/Int. Comm. Conf. 3 1551
[8] Wornell G W 1996 Proceedings of the IEEE 84 586
[9] Manglani M J and Bell A E 2001 Proceedings of the IEEE MILCOM 2 845
[10] Bell A E and Manglani M J 2002 Proceedings of the IEEE ICASSP 3 2813
[11] Atzori L, Giusto D D and Murroni M 2002 IEEE Trans. on Broadcasting 48 103
[12] Mallet S G 1989 IEEE Trans. Pattern Anal. Machine Intell. PAMI-11 674
[13] Daubechies I 1988 Commun. Pure Appl. Math. 41 909
[14] Daubechies I 1992 Ten Lectures on Wavelets (Philadelphia: SIAM Pub) p. 53
[15] Grossman A and Morlet J 1984 SIAM J. Mathemat. Analysis 15 723
[16] Haar A 1990 Math. Ann. 69 331
[17] Strang G 1994 American Scientist 82 250
[18] Strang G 1989 SIAM Rev. 31 614
[19] Strang G and Nguyen T Q 1996 Wavelets and Filter Banks (Wellesley, MA: Wellesley-Cambridge) p. 235
[20] Mallet S G 1989 Trans. Am. Math. Soc. 315 69
[21] Sun X J, Yuan Y and Tang B 2009 Journal of System Simulation 21 3842 (in Chinese)
[22] Cha G M and Xiong X Z 2002 Spread Spectrum Communication (Xián: Xidian University Press) p. 5 (in Chinese) endfootnotesize
[1] Multifractal analysis of the software evolution in software networks
Meili Liu(刘美丽), Xiaogang Qi(齐小刚), and Hao Pan(潘浩). Chin. Phys. B, 2022, 31(3): 030501.
[2] Fractal sorting vector-based least significant bit chaotic permutation for image encryption
Yong-Jin Xian(咸永锦), Xing-Yuan Wang(王兴元), Ying-Qian Zhang(张盈谦), Xiao-Yu Wang(王晓雨), and Xiao-Hui Du(杜晓慧). Chin. Phys. B, 2021, 30(6): 060508.
[3] Analysis and implementation of new fractional-order multi-scroll hidden attractors
Li Cui(崔力), Wen-Hui Luo(雒文辉), and Qing-Li Ou(欧青立). Chin. Phys. B, 2021, 30(2): 020501.
[4] Analysis of secondary electron emission using the fractal method
Chun-Jiang Bai(白春江), Tian-Cun Hu(胡天存), Yun He(何鋆), Guang-Hui Miao(苗光辉), Rui Wang(王瑞), Na Zhang(张娜), and Wan-Zhao Cui(崔万照). Chin. Phys. B, 2021, 30(1): 017901.
[5] Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes-Vanstone elliptic curve cryptosystem
Zeyu Liu(刘泽宇), Tiecheng Xia(夏铁成), Jinbo Wang(王金波). Chin. Phys. B, 2018, 27(3): 030502.
[6] Detection of meso-micro scale surface features based on microcanonical multifractal formalism
Yuanyuan Yang(杨媛媛), Wei Chen(陈伟), Tao Xie(谢涛), William Perrie. Chin. Phys. B, 2018, 27(1): 010502.
[7] Multifractal modeling of the production of concentrated sugar syrup crystal
Sheng Bi(闭胜), Jianbo Gao(高剑波). Chin. Phys. B, 2016, 25(7): 070502.
[8] Exploring the relationship between fractal features and bacterial essential genes
Yong-Ming Yu(余永明), Li-Cai Yang(杨立才), Qian Zhou(周茜), Lu-Lu Zhao(赵璐璐), Zhi-Ping Liu(刘治平). Chin. Phys. B, 2016, 25(6): 060503.
[9] Multifractal analysis of white matter structural changes on 3D magnetic resonance imaging between normal aging and early Alzheimer's disease
Ni Huang-Jing (倪黄晶), Zhou Lu-Ping (周泸萍), Zeng Peng (曾彭), Huang Xiao-Lin (黄晓林), Liu Hong-Xing (刘红星), Ning Xin-Bao (宁新宝), the Alzheimer's Disease Neuroimaging Initiative. Chin. Phys. B, 2015, 24(7): 070502.
[10] Directional region control of the thermalfractal diffusion of a space body
Qiao Wei (乔威), Sun Jie (孙洁), Liu Shu-Tang (刘树堂). Chin. Phys. B, 2015, 24(5): 050504.
[11] Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions
Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi. Chin. Phys. B, 2014, 23(7): 070505.
[12] Row-column visibility graph approach to two-dimensional landscapes
Xiao Qin (肖琴), Pan Xue (潘雪), Li Xin-Li (李信利), Mutua Stephen, Yang Hui-Jie (杨会杰), Jiang Yan (蒋艳), Wang Jian-Yong (王建勇), Zhang Qing-Jun (张庆军). Chin. Phys. B, 2014, 23(7): 078904.
[13] Adaptive step-size modified fractional least mean square algorithm for chaotic time series prediction
Bilal Shoaib, Ijaz Mansoor Qureshi, Shafqatullah, Ihsanulhaq. Chin. Phys. B, 2014, 23(5): 050503.
[14] A fractal approach to low velocity non-Darcy flow in a low permeability porous medium
Cai Jian-Chao (蔡建超). Chin. Phys. B, 2014, 23(4): 044701.
[15] A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction
Bilal Shoaib, Ijaz Mansoor Qureshi, Ihsanulhaq, Shafqatullah. Chin. Phys. B, 2014, 23(3): 030502.
No Suggested Reading articles found!