An Improved multiple fractal algorithm

Transcription

1 Advanced Scence and Technology Letters Vol.31 (MulGraB 213), pp An Improved multple fractal algorthm Yun Ln, Xaochu Xu, Jnfeng Pang College of Informaton and Communcaton Engneerng Harbn Engneerng Unversty, Harbn, Chna {lnyun, xuxaochun, Abstract. Multple fractal dmensons can depct the geometry characterstc of the sgnals from dfferent levels, thus t can extract the features of dfferent sgnals. The paper proposed an mproved algorthm of multple fractal dmenson, t changed the calculaton method of tradtonal multple fractal dmenson whch accumulated the dmensons characterstcs. It ncreased the regularty and gathered degrees of the sgnals characterstcs, under the condton that the basc computatonal complexty of algorthm was not changed. Smulaton results show that, for the classfcaton of dfferent sgnals, the mproved algorthm has better property. Keywords: Multple Fractal mensons; Geometry Characterstc; Sgnal Feature 1 Introducton Radar echoes usually contans a lot of nformaton related to the target feature and a varety of stray echoes, therefore, t has been a hot topc that how to extract the characterstcs of radar ntra-pulse sgnal n the low SR envronments whch n order to dentfy the radar sgnals. For the feature of the radar ntra-pulse sgnals characterstcs, the theory of sgnal complexty characterstcs, entropy theory and fractal theory get the more extensve applcaton. References [1] used the sgnals complexty feature box dmenson and ndex entropy double complexty characterstcs to dentfy the communcaton sgnals acheved a better result. References[2] mproved the tradtonal box dmenson, although t ncreases a certan amount of calculaton, the recognton effect have been sgnfcantly mproved. References[3-4] appled the multfractal spectrum characterstcs to the dentfcaton of the radar sgnals ntra-pulse modulaton characterstcs. References [] provded the method calculatng dscrete sgnals multfractal spectrum characterstcs and annotated the meanng of multple fractal dmenson spectrum. From the pont of vew of the measure, fractal dmenson [6] whch usually used to represent the degree of rregularty fractal sets expanded the dmenson from nteger to fracton and broke through the boundary that general topologcal dmenson s nteger. Thus It has been a wde range of applcaton n varous felds. The paper mproved multple fractal dmenson characterstcs after comparng wth the tradtonal multple fractal dmenson characterstcs. The smulaton results showed that compared wth the tradtonal algorthm, t decreased amount of calculaton and ISS: ASTL Copyrght 213 SERSC

2 Advanced Scence and Technology Letters Vol.31 (MulGraB 213) far more stable than tradtonal multple fractal dmenson algorthm and had better applcaton value. 2 Multracal theory 2.1 Tradtonal mult-fractal dmenson algorthm Multple fractal dmensons can descrbe the features of the objects n varous ways. The method to defne the tradtonal multple fractal dmenson s as follows: The research object dvded nto mcro-regons, suppose the length of the regon sε, then the probablty densty functon of ths regon P can be descrbe by the scalng exponentα : α P = ε, = 1, 2,, (1) on-ntegerα was generally called sngularty exponent, ts value was related to X ε whch was the probablty weghted the regon. efned the functon ( ) summaton of all regons: X ( ε ) = P = 1 From ths, the further defnton of the generalzed fractal dmenson was: ln ( ε ) = 1 1 ln X 1 = lm = lm (2) 1 ε ln ε 1 ε ln ε fferent showed dfferent property of probablty characterstc area, by means of weghted summaton processng, we dvded a sgnals nto numerous regons wth dfferent sngular degree. Thus we could know the refned structure of nternal sgnals step by step. P 2.2 Improved mult-fractal dmenson algorthm The paper mproved the mult-fractal dmenson algorthm. In the evaluaton process of, we cancel the summaton of probablty n dfferent regons and calculate the multfractal characterstcs of sgnals whch n dfferent levels drectly..and the mproved multple efned the functon X ( ε ) : X ( ) fractal dmenson s : ε = P ( ε ) ln ( P ) 1 ln X 1 = lm = lm 1 ε ln ε 1 ε ln ε (3) Copyrght 213 SERSC 18

3 Advanced Scence and Technology Letters Vol.31 (MulGraB 213) s the value of mproved multple fractal dmenson at present. and both could descrbe the sgnals characterstcs n dfferent levels, the result of showed the sgnals dstrbuton characterstcs n each level. It reduced an addton summaton and had a better feature extracton effect. 3 Smulaton results and analyss On the bass of the multple fractal dmenson, n the SR for 1dB condtons, we got the numercal value of four dfferent knds of radar sgnals: chrp sgnal, stepped freuency sgnal, freuency shft keyng sgnal and phase shft keyng sgnal, and drew multple fractal dmenson. Fgure 1 and fgure 2 showed the smulaton results. lnx lnx (a) lne (b) lne 2 1 lnx 1 lnx 1 - (c) lne - (d) lne (a) Chrp sgnal (b) Stepped freuency sgnal (c) Freuency shft sgnal (d) Phase shft sgnal Fg. 1. Four knds of radar sgnal tradtonal multple fractal dmensons 186 Copyrght 213 SERSC

4 Advanced Scence and Technology Letters Vol.31 (MulGraB 213) 1 1 lnx lnx (a) lne 1-1 (b) lne 1 lnx lnx (c) lne -1 (d) lne (a) Chrp sgnal (b) Stepped freuency sgnal (c) Freuency shft sgnal (d) Phase shft sgnal Fg. 2. Four knds of radar sgnal mproved multple fractal dmensons Abscssa ln e represent lnε n the formula (2), ordnate ln x represent ( ) ln X ε n the Formula X ( ε ) = P. = 1 4 Concluson The paper proposed an mproved algorthm of multple fractal dmensons. The algorthm cancels the summaton of characterstc parameter n dfferent levels compared wth the tradtonal one. In the premse of smplfed algorthm, the radar sgnal s multple fractal dmensons we extract had better stablty and lay a better foundaton for the rest of the classfer recognton work. Acknowledgment. Ths work s supported by the aton ature Scence Foundaton of Chna o and , and the Fundamental Research Funds for the Central Unverstes o. HEUCFZ1129, o. HEUCF1381 and o. HEUCF Copyrght 213 SERSC 187

5 Advanced Scence and Technology Letters Vol.31 (MulGraB 213) References 1. Avc,., sala zéza, C., Berbneau, M., etal. An ntellgent system usng adaptve wavelet entropy for automatc analog modulaton dentfcaton[c]. GLOBECOM - IEEE Global Telecommuncatons Conference (21) 2. Ataollah Ebrahmzadeh. Automatc Modulaton Recognton Usng RBF and Effcent Features n Fadng Channels [C]. 29 1st Internatonal Conference on etworked gtal Technologes (29) 3. Hua Jng-yu, Meng L-mn, Xu Zh-jang, etal. An adaptve sgnal-to-nose rato estmator n moble communcaton channels[j]. vol. 2(3), pp: gtal Sgnal Processng(21) 4. Mahmoud, Almorad, Karm, Mahmood. Parameter estmaton of nosy autoregressve sgnals[c] th Iranan Conference on Electrcal Engneerng(21). Shermeh Ataollah Ebrahmzadeh, Ghazalan, Reza. Recognton of communcaton sgnal types usng genetc algorthm and support vector machnes based on the hgher order statstcs[j].vol. 2(6), pp: gtal Sgnal Processng (21) 188 Copyrght 213 SERSC