Lecture 4: Frequency Reuse Concepts

Transcription

1 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts Distace betwee Co-Chael Cell Ceters Kowig the relatio betwee,, ad, we ca easily fid distace betwee the ceter poits of two co chael cells (cells with the same frequecy bad) i terms of ad. Cosider ay two co chael cells. We will take for simplicity a cell ad its co chael cell that is located to its top left locatio as show i the below figure. If we rotate this cofiguratio by 9 Clockwise, ad set to the origi to be the ceter poit of Cell 1, we get the followig: 1

2 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts To compute the distace, we eed to compute ad, or simply,, ad show i the above figure. Oce these are foud, the distace is computed easily usig Pythagoras Theorem. Let us defie the cell radius to be the distace from the ceter poit of the cell to ay of its corers as show i the figure below. Note that the edge legth of the cell is equal to cell radius because of the hexagoal shape, while the lie from the ceter to mid poit of ay edge is equal to. Clearly, X1 i i 3 (1)

3 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts j 3 X j cos( 6 ) () Therefore, X X + X 1 j 3 i+ (3) ad Y is 3j Y j si( 6 ) (4) So, the distace D becomes D i ( ) j 9 j i + 3ij + + 3i + 3ij + 3j 3 i + ij+ j 3j 9j 4 4 (5) We otice that the part i the paretheses i the last form of D is othig but N, which meas we ca rewrite it as D 3N (6) The quatity D 3N Q (7) is called the chael reuse ratio is a idicatio of how ofte frequecies are beig reused. Distace betwee a Cell Corer ad its Co-Chael Cell Ceters Note that this is exactly the same as fidig the distace betwee all corers of a cell ad its cochael cell ceter. Now that we have foud the distace betwee co chael cells ceters, we ca easily exted this to fid the distaces betwee all co chael cells ceters ad a specific corer of a 3

4 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts cell. This ca be doe by fidig the coordiates of all corers of the origial cells ad takig the coordiates of these corers i cosideratio whe computig the desired distaces. We have already foud coordiates of oe co chael cell to be j 3 j 3 i+, (8) Coordiates of Corer 1 of Origial Cell is (, ) (9) Coordiates of Corer of Origial Cell is Coordiates of Corer 3 of Origial Cell is,, Coordiates of Corer 4 of Origial Cell is (, ) (1) Coordiates of Corer 5 of Origial Cell is Coordiates of Corer 6 of Origial Cell is,, So, ow we ca fid all 6 distaces betwee the ceter of the co chael cell ad the 6 corers of the origial cell. (1) (11) (13) (14) Iterferece ad System Capacity There are differet types of iterferece that cellular calls suffer from. Amog these types are Co Chael Iterferece (iterferece that results from the trasmissio of sigals at the same frequecy of a particular chael trasmitted from a earby co chael cell). Also, there is Adjacet Chael Iterferece (iterferece that results from trasmittig a sigal with a earby frequecy but from the 4

5 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts same tower or aother mobile uit i the same cell. Because of the limited capabilities of aalog ad digital filters, it may be very difficult to remove adjacet chaels completely). Co-Chael Iterferece ad System Capacity Iterferece is measured i terms of received Sigal (Power) to received Iterferece (Power) atio or SI, which is sometimes expressed as S I. First ote that the power P received at some distace from atea d over the power P received at some other distace d is give by P P d d (15) which ca be writte i the form d P P d where is power received at some distace, is power received at some distace, ad is called path loss expoet. (16) Computatio of Co-Chael Iterferece i Differet Cofiguratios To compute the Forward chael SI, we use equatio (16) to compute the Sigal power ad agai use equatio (16) to compute the Iterferece power as follows S I P P of Sigal of All Iteferig Sigals d P Dist. of Mobile to Origial Tower d P d P Dist. of Mobile to Tower 1 Dist. of Mobile to Tower 6 (17) Clearly, P ad d have o effect o the SI ad they cacel out to give S I 1 Dist. of Mobile to Origial Tower Dist. of Mobile to Tower 1 Dist. of Mobile to Tower 6 (18) 5

6 EE 499: Wireless & Mobile Commuicatios (8) Lecture 4: Frequecy euse Cocepts The performace of a system is usually measured i terms of the miimum SI, which occurs at the corers of the cell providig service to the mobile statio. The distace i this worst case of servig tower to the mobile statio is while the distace from the co chael cell towers to the mobile statio are obtaied by fidig the Cartesia distaces of the co chael cell tower coordiates give i (8) ad the corers of the origial tower give i (9) (14). Numerical Evaluatio of Worst SI for Several Cofiguratios To fid umerical results of worst SI for several cofiguratios, a MS Excel sheet is developed for this reaso. Simple parameters such as (which has o real effect o the worst SI), i, j, ad. 6