Correlation Models for Shadow Fading Simulation
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1 Correlation Model for Shadow Fading Simulation IEEE 80.6 Preentation Submiion Template (Rev. 8.3) Document Number: IEEE S80.6m-07/060 Date Submitted: Source: I-Kang Fu, Chi-Fang Li, Ting-Chen Song, Wern-Ho Sheen NCTU / ITRI tomtom@itri.org.tw 00 Ta Hueh Road, Hinchu, Taiwan 300, ROC whheen@itri.org.tw Venue: IEEE 80.6 Seion #48, Orlando, USA Bae Document: IEEE C80.6m-07/060 Purpoe: TGm Evaluation Methodology development Notice: Thi document ha been prepared to ait IEEE It i offered a a bai for dicuion and i not binding on the contributing individual() or organization(). The material in thi document i ubject to change in form and content after further tudy. The contributor() reerve() the right to add, amend or withdraw material contained herein. Releae: The contributor grant a free, irrevocable licene to the IEEE to incorporate material contained in thi contribution, and any modification thereof, in the creation of an IEEE Standard publication; to copyright in the IEEE name any IEEE Standard publication even though it may include portion of thi contribution; and at the IEEE ole dicretion to permit other to reproduce in whole or in part the reulting IEEE Standard publication. The contributor alo acknowledge and accept that thi contribution may be made public by IEEE IEEE 80.6 Patent Policy: The contributor i familiar with the IEEE 80.6 Patent Policy and Procedure < including the tatement "IEEE tandard may include the known ue of patent(), including patent application, provided the IEEE receive aurance from the patent holder or applicant with repect to patent eential for compliance with both mandatory and optional portion of the tandard." Early dicloure to the Working Group of patent information that might be relevant to the tandard i eential to reduce the poibility for delay in the development proce and increae the likelihood that the draft publication will be approved for publication. Pleae notify the Chair <mailto:chair@wireleman.org> a early a poible, in written or electronic form, if patented technology (or technology under patent application) might be incorporated into a draft tandard being developed within the IEEE 80.6 Working Group. The Chair will dicloe thi notification via the IEEE 80.6 web ite <
2 Correlation Model for Shadow Fading Simulation I-Kang Fu, Chie-Fang Li, Ting-Chen Song, Wern-Ho Sheen NCTU / ITRI
3 Outline Shadow Fading Model for Sytem Level Simulation Auto-correlation Model for Shadow Fading Cro-correlation Model for Shadow Fading 3
4 Shadow Fading Model for Sytem Level Simulation The hadow fading effect i uually modeled by a log-normal random variable in ytem level imulation It mean m i uually given a 0dB, and the tandard deviation σdb depend on the propagation environment (ex. 8dB for urban). Thi random variable i normal ditributed in db When doing the ytem level imulation, a normal ditributed random variable can be dropped from time to time to repreent the hadow fading for each radio link. The typical way i to drop the random variable independently for different time and for different radio link i.e. the hadow fading effect for each radio link at each time intance are imulated in uncorrelated manner 4
5 Auto-correlation Model for Shadow Fading However, the hadow fading effect of the ame radio link i highly correlated for the nearby location. A imple and well accepted auto-correlation model wa propoed by Gudmundon [] for thi effect: the correlation of ignal ample eparated by k ampling intance: e D R ( k) = a k vt / D a = e D σ a ε D v T i the tandard deviation of hadow fading model i the correlation coefficient i the correlation between two location eparated by ditance D i the mobile velocity i the ampling interval 5
6 Auto-correlation Model for Shadow Fading The aforementioned model wa reference by [] and modified a: d cor de-correlation ditance; it definition here i the ditance eparation at which the correlation coefficient reduce to ½. Δx the ditance between two obervation location ρ the correlation coefficient Simulation Methodology: If L i the log-normal component at poition P, L i for P which i x away from P. Then L i normally ditributed in db with mean ρ( x)l and variance (-ρ( x) )σ. derived in next page Vx - ln d cor r ( Vx) = e 6
7 Auto-correlation Model for Shadow Fading Conider X and Y are Normal ditributed random variable. Given Y=y and correlation coefficient a ρ, then the ditribution of (X Y=y) can be obtained a [3]: m, m and, are the mean and variance of X and Y f f ( x y) = X Y ( x, y) f ( y) -! x m x m y m y m!! y - m! - r +! -!!! ! ( )! exp ( ) ( )( ) ( ) exp ( r )!!! - =!!!! p - r! p!!! -! x - m x - m y - m y - m y - m = exp! ( ) - r ( )( ) + ( ) -( - r )( ) p ( - r )! ( - r )!! -! x - m y - m!! r!!! - r = exp - p ( - r ) ( )!!!!!!!! x - m - r ( y - m ) = exp! -!! p ( - r )! ( - r )!!! the mean of f X ( x y) i m + r ( y - m ), with variance ( - r ). ( - ) Conider m = m =0 and = =, then the mean of f ( x y) i r y m and variance ( - r ) X 7
8 Auto-correlation Model for Shadow Fading Example: Shadow fading effect imulated with and without auto-correlation model Correlated hadow fading (with auto-correlation[]) Uncorrelated hadow fading 8
9 Cro-correlation Model for Shadow Fading A for the hadow fading effect among different radio link, the crocorrelation indicate the imilarity of the propagation environment. For example, the hadow fading effect for the two radio link are le correlated in the left figure then in right one. Longer common propagation path induce higher correlation BS BS BS BS MS MS 9
10 Cro-correlation Model for Shadow Fading Cro-Correlation Model for Shadow Fading[4] : θ: Angle-of-Arrival Difference (AAD) ρ: correlation coefficient q if q 60 r ( q) = if q > 60 o o 0
11 Cro-correlation Model for Shadow Fading Simulation Methodology:. Generate the uncorrelated random variable X=[x,x x N ] each x n i Normal ditributed with zero mean and tdσ n in db. Obtain the correlation coefficient matrix C and! r r N!! r r! N =! G!!!! r r!! N N! T G= CC C can be obtained by Choleky decompoition (note: it take high computation power). Then cro-correlated hadow fading effect Y=[y,y y N ] can be obtained by Y=CX
12 Reference [] Gudmundon, M., Correlation Model for Shadow Fading in Mobile Radio Sytem, Electronic Letter, pp.45-46, vol. 7, No 3, November 99. [] ETSI TR 0. v3..0, Selection procedure for the choice of radio tranmiion technologie of the UMTS, April 998. [3] I-Kang Fu, A Dynamic Simulation Platform for Heterogeneou Multiple Acce Sytem, Mater Thei, Department of Electrical Engineering, National Chung Cheng Univerity, Taiwan, R.O.C., July 00. [4] Thoma Klingenbrunn, Preben Mogenen Modelling Cro- Correlated Shadowing in Network Simulation, IEEE VTC,999, pp
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