Question 1. Typical Cellular System. Some geometry TELE4353. About cellular system. About cellular system (2)
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1 TELE4353 Moble a atellte Commucato ystems Tutoal 1 (week Questo 1 ove that fo a hexagoal geomety, the co-chael euse ato s gve by: Q (3 N Whee N + j + j 1/ 1 Typcal Cellula ystem j cells up cells ow About cellula system Each base stato s allocate a poto of total umbe of chaels avalable to the system. Neghbog cells ae assge ffeet goups of chaels so that tefeece betwee them s mmze. Hexagoal cells ca cove a ceta aea wth mmum umbe of cells (compae to squae a tagle. Cluste s the set of N cells whch collectvely use the ete fequeces avalable. 3 4 About cellula system ( Lage cluste sze meas that the ato betwee cell aus a the stace betwee co-chael cells s small. A mmum cluste sze (N s esable fo maxmzg the capacty. Fequecy euse facto s 1/N. ome geomety BC AB + AC AB. AC.cosα B A C 5
2 Ajacet cell stace R + R RR..cos(1 3R R 3 R 1o Co-chael cell stace ( ( j j + ( ( cos1 ( + j + j 3R + j + j 3N 3N R R N j 7 8 Questo A ceta aea s covee by a cellula system wth 84 cells a a cluste sze N. 8 voce chaels ae avalable fo the system. Uses ae ufomly stbute ove the aea covee by the system. Each use has o aveage calls pe hou a hols the call fo 1. mutes. Wth a blockg pobablty of.1. a eteme the maxmum cae taffc pe cell fo N4 a 7 b eteme the maxmum umbe of uses that ca be seve by the system fo N4 a 7. Elag A Elag s a measue of taffc testy, 1 Elag s the amout of taffc testy cae by a chael that s completely occupe. f a chael s occupe 3 mutes each hou the taffc testy s.5 Elag. A use taffc testy s the call equest ate multple by the holg tme. Au λh 9 1 Elag B table shotee fo GO.1 (fom p 79 a p 81 of the book Numbe of chaels Elag Pluggg the values fo N4 Total umbe of chaels s 8. Each cell has 7 chaels to use. Usg the Elag B table taffc cae by each cell s 5.1 Elag Each use has A u *1.m/m.4 Elag Each cell ca accommoate 5.1/ uses 84 cells system 84* uses 11 1
3 Pluggg the values fo N7 Total umbe of chaels s 8. Each cell has 4 chaels to use. Usg the Elag B table taffc cae by each cell s 9 Elag Each use has A u *1.m/m.4 Elag Each cell ca accommoate 9/.475 uses 84 cells system 84*759 uses Questo 3 f a tasmtte pouces 5 Watts of powe, expess the tasmt powe uts of a Bm b BW f 5 W s apple to a uty ga atea wth a 9 MHz cae fequecy, f the eceve powe Bm at a fee space stace of 1 m fom the atea. What s eceve powe at 1 km? Assume uty ga fo the eceve atea Fs fee space equato t t P ( ( 4π P : Tasmt powe t G : Tasmt atea ga t G : Receve atea ga PG G λ L λ : opeatg wavelegth L: ystem loss ot elate to popagato G λ 4π Ae c f λ Atea ga A e : atea apetue c: spee of lght f: Cae fequecy 15 1 Path loss a close stace Pt G G PL( B 1log 1log P 4 L ( ( f P P > > t λ ( π ( Bm: ( Bm 1log + log.1w Pluggg the values Pt ( mw Pt ( Bm 1log 1log ( 5 47Bm 1mW Pt ( W Pt ( BW 1log 1log( 5 17BW 1W PG 5*1*1* ( 1/3 t tgλ 3 ( 1 3.5*1 mw ( 4π L ( 4π 1 *1 3 ( ( P 1 Bm 1*log 3.5*1 4.5Bm ( Bm ( 1 Bm + log log 4.5Bm 4B 4.5Bm
4 Questo 4 f a sgal to tefeece ato of 15 B s eque fo satsfactoy fowa chael pefomace of a cellula system, what s a fequecy euse facto a cluste sze that shoul be use fo maxmum capacty f the path loss expoet s a 4, b 3. Assume that thee ae sx co-chael cells the fst te, a all of them ae the same stace fom the moble. Use sutable appoxmatos. Co-chael tefeece 19 gal to tefeece Pluggg the values (4 P P R ese powe: P tefeece: P 1 ( / R ( 3N 15B 31.3 ( 3N 4 ( / R ( 3N 31.3 N 4.59 N 7 shoul be use N B 1 Pluggg the values (3 ( 3N 3 15B 31.3 ( / R ( 3N 31.3 N 11.1 N 1 shoul be use N B Assgmet fo home (homewok! Repeat the same poblem whe 1 o sectoe ateas ae use stea of om ectoal ateas. 3 4
5 Questo 5 Assume a eceve s locate 1 km fom a 5 W tasmtte. The cae fequecy s 9 MHz, fee space popagato s assume, G t 1, a G, f (a the powe at the eceve, (b the magtue of E-fel at the eceve atea, (c the ms voltage apple to the eceve put assumg that the eceve atea has a puely eal mpeace of 5 Ω a s matche to the eceve. Gve Paametes 1 km, stace fom the tasmtte P t 5 W, Tasmtte powe G t 1, Tasmtte atea ga G, Receve atea ga f9 MHz λc/f.333 m, R at 5 Ω, Receve atea esstace 5 oluto to a The powe eceve at the stace 1 km s PG t tgλ ( (4π L (4π mw ( [ Bm] 1log 1.53Bm 1mW 7. 1 ( [ BW ] 1log 1W W W 91.53BW oluto to b The magtue of the eceve E fel s 4π Gλ G A e Ae λ 4π ( PG E( E( t t PGG t t λ ( 4π 1π 1π ( 4π P P A f e 1 ( 1 ( e /4.33 /4 P π P π π V E(.39 A G λ π π m 7 8 oluto to c The eceve powe s gve at V ( 4R at whee R at s the esstace of the matche eceve. The ope ccut ms voltage at the eceve put s 1 Vat ( 4Rat mV Questo A eceve a uba cellula ao system etects a 1 mw sgal at 1 m fom the tasmtte. oe to mtgate co-chael tefeece effects, t s eque that the sgal eceve at ay base stato eceve fom aothe base stato tasmtte whch opeates wth the same chael must be below 1 Bm. A measuemet team has eteme that the aveage path loss expoet the system s 3. eteme the majo aus of each cell f a 7-cell euse patte s use. What s the majo aus f a 4- cell euse patte s use? 9 3
6 Gve Paametes P ( 1mW Bm 1 m, Refeece stace P ( -1 Bm, 3, Path loss expoet N7, N4, Cluste sze A Example fo the 7-cell Cluste The eceve powe fom the cell opeatg wth the same chael has to be less tha 1 Bm < 1Bm R oluto to Q, cot. Applyg the fomula fo the eceve powe at a stace ( ( 1log 1 3log 1/3 3N R 154.4m 3N Fo N7 Fo N4 oluto to Q, cot R 47.13m R 1.93m
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