Abstract. 1. Introduction. 2. Fading

Transcription

1 An Interative Simulation for Flat Fading P.Marihamy*, J.Senthilkumar and V.Vijayarangan ECE Dept., National Engineering College Kovilpatti , India. * Nizwa College of Tehnology, Sultanate of Oman {pmarihamy, senvimjag, Abstrat Behavior of the Fading an be analyzed through omputer simulation. In this paper, a omputer simulation has been developed newly using both MATLAB and Visual Basi programming languages. MATLAB is used to simulate the fading phenomenon, whereas Visual Basi is used to reate a visual user environment for interative simulation. Further, the use of Visual Basi failitates us to onvert the developed simulation program into an exeutable pakage. The exeutable pakage has an advantage of arrying out the simulation on any Windows Operating System based mahines without the requirement of MATLAB and Visual Basi.. Introdution Wireless mobile ommuniations have beome one of the most essential ommuniation failities of today. In mobile ommuniation, a priniple problem with the propagation environment is the rapid variation in reeived signal strength as the ommuniating parties move. Suh rapid variation in reeived signal strength is termed as fading []. The presene of fading affets the QoS of the system. For a system to work properly, a thorough investigation on fading harateristis is required prior to design and installation. This investigation is possible by means of field observation and omputer simulation. Simulation an be arried out using either traditional programming languages suh as C/C++ [] or speial programming languages suh as MATLAB [3]. MATLAB's ease of use relative to traditional programming languages has made it more attrative for use in aademi and industrial software developments. The main objetive of this paper is to develop a user-friendly interative simulation program and to run the simulation on any Windows Operating System based mahines without the requirement of the programming languages on whih simulation was developed. In this paper MATLAB has been onsidered for its ease of use to develop a program for fading simulation. It s built in GUI funtions also an be utilized to have user-friendly visual environment for interation. However, it doesn t have the faility to reate an exeutable pakage. Therefore, simulation annot be performed on the omputers whih are not loaded with MATLAB software. To avoid this diffiulty Visual Basi programming language has been onsidered along with the MATLAB. Visual Basi has a faility to reate an exeutable pakage by linking MATLAB files. This exeutable pakage makes the simulation run on any Windows Operating System based mahines without the requirement of MATLAB as well as Visual Basi languages. The paper is organized as follows: Setion briefly desribes the flat fading mehanism and its representation in terms of probability density funtions. A proedure to simulate flat fading using MATLAB has been explained in Setion 3. In Setion 4, the reation of visual user environment using Visual Basi for interation is desribed. A proedure to onvert the simulation program into a single exeutable pakage has been desribed in Setion 5. Finally, onlusions are given in Setion 6.. Fading In mobile environment, fading an be ategorized into large-sale fading and small-sale fading. Large-sale fading represents the average signal power attenuation or path loss due to motion over large areas, whereas small sale fading represents the short-term flutuation in the signal amplitude due to multipath. Small-

2 sale fading an be further lassified as flat or frequeny seletive []. A reeived signal is said to undergo flat fading, if the mobile radio hannel has a onstant gain and a linear phase response over a bandwidth larger than the bandwidth of the transmitted signal. Under these onditions, the reeived signal has amplitude flutuations due to the variations in the hannel gain over time due to multipath. However, the spetral harateristis of the transmitted signal remain intat at the reeiver. On the other hand, if the mobile radio hannel has a onstant gain and linear phase response over a bandwidth smaller than that of the transmitted signal, the transmitted signal is said to undergo frequeny seletive fading [4]. Main fous of this paper is to simulate the flat fading phenomenon. Major probabilisti models that haraterize the flat fading are: Rayleigh Statistial Model, Riian Statistial Model and Nakagami model.. Rayleigh Fading Model The mobile antenna reeives a number of refleted and sattered waves. If we assume that there is no diret path or line-of sight (LOS) omponent, the reeived signal s( due to unmodulated arrier an be expressed as []. N s( = a t os( ω t + φt ) t= () where N is the number of paths. The phase φ t is a random variable, whih depends on the varying path lengths. In the ase of an unmodulated arrier, the transmitted signal at frequeny is the transmitted signal frequeny and a t is the amplitude of the signal at the t th path. By inorporating the Doppler effet due to motion, the reeived signal s( an now be written as N s( = a t= t os( ω t + ω t + φ ) di i () where w d is the Doppler frequeny due to motion. Now, the signal an be expressed interms of inphase and quadrature omponents as, s( = I( osω t Q( sinω t (3) From the above equation, the envelope R of the reeived signal an be written as [ I( ] [ Q( ] R = + (4) When N is large, the inphase and quadrature omponents will be Gaussian. The envelope R varies in time aording to the Rayleigh distribution. The Rayleigh distribution funtion f(r) is given by f r r r) = exp, r σ σ ( 0 (5) where r is the envelope amplitude of the reeived signal, and σ is the predetetion mean power of the multipath signal.. Riian Fading Model The Riian distribution is observed when, in addition to the multipath omponents, there exists a diret path. In the presene of suh a path, the transmitted signal given in eqn. () an be written as [][3] s( N = t t= a os( ω t + ω t + φ ) + k os( ω t + ω (6) where the onstant k d is the strength of the diret omponent, ω is the Doppler shift d along the LOS path, and ω d t are the Doppler shifts along the indiret paths. The envelope in this ase has a Riian density funtion given by r r + k d rkd f ( r) = exp, 0 Io r (7) σ σ σ where Io( ) is the zeroth order modified Bessel funtion of the first kind. The umulative distribution of the Riian random variable is given as kd r F( r) = Q,, r 0 σ σ di i d d (8) where Q(, ) is the Marum s Q funtion. The Riian distribution is often desribed in terms of the Riian fator K, defined as the

3 3 ratio between the deterministi signal power (from the diret path) and the diffuse signal power (from the indiret paths). K is usually expressed in deibels as k K ( db) = 0log d 0 (9) σ In equation (9), if k d goes to zero (or if k d σ << r σ ), the diret path is eliminated and the envelope distribution beomes Rayleigh, with K(dB) = -..3 Nakagami-m Model It is possible to desribe both Rayleigh and Riian fading with the help of a single model using the Nakagami distribution [5]. The fading model for the reeived signal envelope, proposed by Nakagami, has the pdf given by m m m r f ( r) = Γ( m) Ω n mr exp Ω, r 0 (0) where G(m) is the Gamma funtion, and m is the shape fator (with the onstraint that m = ½) E { r } [ r E(r )] { } m = () E The parameter Ω ontrols the spread of the distribution and is given by Ω = E r () { } The orresponding umulative distribution funtion an be expressed as mr F ( r) = P, m Ω (3) where P(, ) is the inomplete Gamma funtion. In the speial ase m =, Nakagami redues to Rayleigh distribution. For m >, the flutuations of the signal strength is lower ompared to Rayleigh fading, and Nakagami tends to Riian. 3. MATLAB Simulation The multipath faded signal has been simulated using MATLAB. From the simulation, the relationship between the number of paths and statistis of the reeived signal an be studied. The reeived signal at a given instant of time for a stationary reeiver an be generated using the eqn.. Generating the signal using eqn. allows the inlusion of Doppler effet due to user s mobility. The path amplitudes are taken as Weibull-distributed random variables [3], whih an be generated using the funtion weibrnd from the Statistis Toolbox. The two-parameter Weibull distribution allows the variation of the mean and variane of the sattering amplitudes. The phases are taken to be uniform in between 0 and π and this is generated using the funtion unifrnd from the Statistis Toolbox. The inphase and quadrature omponents, of the simulated signal has been obtained using the ommand demod(,,, qam ). Then the envelope of the reeived signal is obtained using eqn.4. Numerial values for the veloity of the mobile, arrier frequeny and number of paths are entered as input for the simulation. Number of signal samples generated in a single iteration of simulation has been taken to be four times the arrier frequeny. The variations in the reeived signal strength due to Rayleigh fading is shown in Fig.. The generated samples are found to follow the Rayleigh distribution as expeted after about 40 iterations. This trend is shown in Fig.. Probability distribution urve of the simulated samples losely follows the theoretial Rayleigh distribution urve.

4 4 4. Visual Basi The Visual Basi Environment ats as a front end of this work. Better user interativeness has been added for Flat Fading studies. Animations for Rayleigh and Riian fading has also been inluded to give visual demonstration about the fading in a mobile environment. Fig. Rayleigh faded RF signal Fig. Rayleigh distribution funtion of the reeived signal. For the simulation of Riian distributed fading a diret path has to be onsidered. To inorporate the presene of diret path omponent the eqn.6 has been onsidered. A term without any random phase in the equation indiates the diret path omponent. Then the rest of simulation is similar to the ase of Rayleigh fading. Simulation an also be run with different veloities to study the effet of motion. To use the above Simulation programs with the Visual Basi environment, the following preparations are required: i) The program files and funtions are onverted into dynami link library (dll) files using COM builder tool in the MATLAB. ii) The above dll files and other supporting funtions suh as plotting graph are pakaged as a single file using the pakage omponent tool. This pakage omponent tool is available in the omponent menu of the COM builder. To get a Visual user environment visual forms are reated for Rayleigh and Riian fading. The forms an be ativated using the ommand Show. Fig.3 shows a form for Rayleigh fading. Text boxes are provided in the forms for entering the desired parameters. The values entered are onverted to double format using the ommand CDbl and manipulations are done on these values. In the Visual Basi the neessary events (e.g: Buttons to view Rayleigh distribution, Riian distribution et.,) are reated using the GUI faility. Toolbars and Menubars are also reated for user inter-ativeness. The menus are reated using Menu Editor. The event handling funtions are invoked using the ommand Call, along with funtion name and input parameters. Based on the input values, simulation results are obtained. Help files are also have been reated whih give some basi information about fading. As an example, a help window showing several types of fading is shown in Fig Exeutable Pakage Using the Pakage and Deployment Wizard in Visual Basi environment, all the developed files suh as dll file, pakage omponent, animation files and help files are enapsulated into a single self extrating exeutable pakage. This pakage an be loaded on any Windows Operating System based mahines and the simulation an be arried out. The steps that are required for the development of an exeutable pakage have been summarized below:

5 5. Write programs in MATLAB to simulate Fading phenomena.. Using the MATLAB COM builder tool onvert the above program files into dll file. Then pakage this dll file along with other supporting files using Pakage Component tool. 3. Create forms and events in Visual Basi and link the dll file with it. 4. Using Visual Basi s Pakage and Deployment Wizard faility, the files obtained in steps and 3 are ombined and onverted into a single exeution pakage. Fig.3 An interative form reated for Rayleigh fading using Visual Basi. 6. Conlusions MATLAB programming has been used to simulate flat fading beause of its ease of use. Further, for useful appliations these MATLAB program files have been linked with Visual Basi programming through dynami link library faility. The use of Visual Basi brings benefits in two ways: ) provides better Visual user environment to input the fading parameters interatively, and ) the developed programs an be onverted into an exeutable pakage. The exeutable pakage thus obtained has been tested suessfully on Windows operating system based mahines without MATLAB and Visual Basi softwares. Fig.4 A help window reated using Visual Basi Referenes [] T. S. Rappaport, Wireless Communi- ations - Priniples and Pratie, IEEE Press, In. New York and Prentie Hall, In., New Jersey, 996. [] Angeleri.E, Mazzei.L, Pegoretti.A, Rayleigh fading simulation on PCs, IEEE Region 0 Conferene on Computer and Communiation Systems, IEEE TENCON'90, pp.77-80, vol., 990. [3] Gayathri S. Prabhu and P. Mohana Shankar, Simulation of Flat Fading Using MATLAB for Classroom Instrution, IEEE Transation on Eduation, vol 45., February 00. [4] Dersh.U, Ruegg.R.J, Simulations of the time and frequeny seletive outdoor mobile radio hannel, IEEE Tran. on Vehiular Tehnology, Volume: 4, pp , Aug.993. [5] Beaulieu.N.C, Cheng.C, An effiient proedure for Nakagami-m fading simulation, IEEE Global Tele ommuniations Conferene, GLOBE COM '0, pp , Vol.6, 00.

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