Fundamentals of Cellular Networks

Transcription

1 Fundmentls of ellulr Networks Dvid Tipper Assoite Professor Grdute Progrm in Teleommunitions nd Networking University of Pittsburgh Slides 4 Telom 2720 ellulr onept Proposed by ell Lbs 97 Geogrphi Servie divided into smller ells Neighboring ells do not use sme set of frequenies to prevent interferene Often pproximte overge re of ell by idelized hexgon Inrese system pity by frequeny reuse. Telom

2 ellulr Networks Propgtion models represent ell s irulr re Approximte ell overge with hexgon - llows esier nlysis Frequeny ssignment of F MHz for the system The multiple ess tehniques trnsltes F to T trffi hnnels luster of ells K group of djent ells whih use ll of the systems frequeny ssignment Telom ellulr onept Why not lrge rdio tower nd lrge servie re? Number of simultneous users would be very limited (to totl number of trffi hnnels T) Mobile hndset would hve greter power requirement ellulr onept - smll ells with frequeny reuse Advntges lower power hndsets Inreses system pity with frequeny reuse Drwbks: ost of ells Hndoffs between ells must be supported Need to trk user to route inoming ll/messge Telom

3 ellulr onept (ont) Let T totl number of duplex hnnels K ells size of ell luster (typilly 4, 7,2, 2) N T/K number of hnnels per ell For speifi geogrphi re, if lusters re replited M times, then totl number of hnnels system pity M x T hoie of K determines distne between ells using the sme frequenies termed o-hnnel ells K depends on how muh interferene n be tolerted by mobile sttions nd pth loss Telom ell Design - Reuse Pttern Exmple: ell luster size K 7, frequeny reuse ftor /7, ssume T 490 totl hnnels, N T/K 70 hnnels per ell G F A E G F D A E G F D A E D Assume T 490 totl hnnels, K 7, N 70 hnnels/ell lusters re replited M3 times System pity 3x totl hnnels Telom

4 luster Size From geometry of grid of hexgons only ertin vlues of K re possible if repliting luster with out gps 2 K i 2 + ij + j 2 where i nd j re non-negtive integers K 7 (i 2, j ) K 4 (i 2, j0) 2 4 K 2 (i2, j2) Telom ellulr onepts To find o-hnnel neighbors of ell, move i ells long ny hin of hexgons, turn 60 degrees ounterlokwise, nd move j ells (exmple: i2, j2, K2) K i 2 + ij + j 2 r ell rdius Are of hexgon 2.6 r 2 d distne to ohnnel ell Telom

5 ellulr onepts From hexgonl geometry d r 3K The quntity d/r is lled the o-hnnel reuse rtio d / r 3K K i 2 + ij + j 2 r ell rdius Are of hexgon 2.6 r 2 d distne to o-hnnel ell Telom Frequeny Reuse RSSI, dm -60 SITE A SITE -90 /I -20 Distne r Telom d

6 Frequeny Reuse Relte luster size to rrier to ohnnel interferene rtio /I t the edge of ell propgtion model of the form P r P t Ld -α L onstnt depending on frequeny, d distne in meters, α pth loss oeffiient, Then t edge of ell in enter of network the /I is given by I 6 j i P Lr t α P Ld t α 6 r d α A A A A A A A K 9 Telom 2720 Frequeny Reuse Solving for d/r results in d r / α Remember d / r 3 K, whih results in K 3 6 I 6 I 2 / α Exmple: onsider ellulr system with /I requirement of /I 8 d nd suburbn propgtion environment with α 4, determine the minimum luster size. 8 d > , K /3 x (6 x ) , Sine K must be n integer round up to nerest fesible luster size > K 7 Telom

7 Frequeny Reuse Note one n relte /I to K for vrious pth loss grdients I 6 r d α r db α log0 I d S r in d Remember I db d / r α log K 0 ( K ) luster size N Telom Frequeny Plnning Typil /I vlues used in prtie re 3-8 d. Digitl systems hve lower /I (3-5 d) One the frequeny reuse luster size nd frequeny llotion determined frequenies must be ssigned to ells Must mintin /I pttern between lusters. Within luster seek to minimize djent hnnel interferene Adjent hnnel interferene is interferene from frequeny djent in the spetrum f f 2 Telom

8 Frequeny Assignment Typil /I vlues used in prtie re 3-8 d. One the frequeny reuse luster size nd frequeny llotion determined frequenies must be ssigned to ells Must mintin /I pttern between lusters. Within luster seek to minimize djent hnnel interferene Adjent hnnel interferene is interferene from frequeny djent in the spetrum Exmple: You re operting ellulr network with 25KHz NMT trffi hnnels through 2. Lbeling the trffi hnnels s {f, f2, f3, f4, f5, f6, f7, f8, f9, f0, f, f2} Ple the trffi hnnels in the ells below suh tht frequeny reuse luster size of 4 is used nd djent hnnel interferene is minimized Telom Setoring Setoring used to improve the /I rtio mke luster size K smller Use diretionl ntenns rther thn omni-diretionl 20 setoring ell divided into 3 (20 o setoring) or 6 (60 o setoring) eqully sized setors Frequenies/trffi hnnels ssigned to ells must prtitioned into 3 or 6 disjoint sets Redues the number of o-hnnel ells using interferene Disdvntges: need intr-ell hndoff, inreses omplexity Telom

9 Setoring setoring o setoring redues number of interferers from 6 to 2 Telom Setored Frequeny Plnning Exmple: Allote frequenies for GSM opertor in U.S. PS - blok who uses 7 ell frequeny reuse pttern with 3 setors per ell Use Frequeny hrt vilble from F web site Groups frequenies into 2 tegories ells A-G nd setors -3 in eh ell Telom

10 Setored Frequeny Plnning Exmple: Allote frequenies for AMPS opertor in ellulr -blok who uses 7 ell frequeny reuse pttern with 3 setors per ell Use Frequeny hrt vilble from F web site Groups frequenies into 2 tegories ells -7 nd setors A- in eh ell Telom Trffi Engineering Given or N T/K trffi hnnels per ell wht is GoS or how mny users n be supported for speifi GoS Required grde of servie? Usully 2% bloking probbility during busy hour usy hour my be. busy hour t busiest ell 2. system busy hour 3. system verge over ll hours si nlysis lled Trffi Engineering or Trunking sme s iruit swithed telephony, use Erlng nd Erlng Models Telom

11 Trffi Engineering Estimte trffi distribution? Trffi intensity is mesured in Erlngs (mthemtiin AK Erlng) One Erlng ompletely oupied hnnel, e.g., rdio hnnel oupied for 30 min. per hour rries 0.5 Erlngs Trffi intensity per user A u A u verge ll request rte x verge holding time H Totl trffi intensity trffi intensity per user x number of users A u x n u Telom Trffi Engineering Telom

12 Erlng Model M/M// queue To estimte the performne of trunked system use the Erlng queueing model identil servers proess ustomers in prllel. ustomers rrive ording to Poisson proess ustomer servie times exponentilly distributed The system hs finite pity of size, ustomers rriving when ll servers busy re dropped loked lls lered model () Anlyze using Mrkov Proess of n(t) number of ustomers in the system t time t μ e ( Pb ) e P b Telom M/M// Let π i denote the stedy stte probbility of i ustomers in the system, then the stte trnsition digrm for n(t) is given by μ 0 μπ 2μ 3μ ( )μ μ π j 0 ( + jμ) π j π j + ( j + ) μπ j+ ( μ) π π j < j Flow blne equtions Solve determining π i in terms of π 0, then sum of probbilities Telom

13 M/M// Probbility of ustomer being bloked (,) π i (, ) π! n n! n 0 Vlid for M/G// queue (,) Erlng s formul, Erlng s bloking formul Erlng formul n be omputed from the reursive formul (, ) (, ) + (, ) Usully determined from tble or hrts Telom Trffi Engineering Erlng bloking probbilities Telom

14 Erlng hrts Telom Trffi Engineering Erlng tble Telom

15 Trffi Engineering Erlng Tble Telom M/M// Other performne metris n be relted to Erlng formul (,) The rried lod e ( (, )) Effetive throughput of the system Men server utiliztion Men number in the system ρ e ( (, )) L ( (, )) μ Averge dely in the system W μ Telom

16 Trffi Engineering Exmple onsider single nlog ell tower with 56 trffi hnnels, when ll hnnels re busy lls re bloked. lls rrive ording to Poisson proess t rte of ll per tive user n hour. During the busy hour 3/4 the users re tive. The ll holding time is exponentilly distributed with men of 20 seonds. () Wht is the mximum lod the ell n support while providing 2% ll bloking? From the Erlng tble with 56 hnnels nd 2% ll bloking the mximum lod 45.9 Erlngs (b) Wht is the mximum number of users supported by the ell during the busy hour? Lod per tive user ll x 20 se/ll x /3600 se 33.3 merlngs Number tive users 45.9/(0.0333) 377 Totl number users 4/3 number tive users 836 Determine the utiliztion of the ell tower ρ ρ α/ 45.9/ % Telom Erlng M/M/ Model identil servers proesses ustomers in prllel. ustomers rrive ording to Poisson proess ustomer servie times exponentilly distributed Infinite system pity. loked lls delyed model (D) Anlyze using Mrkov Proess of n(t) number of ustomers in the system t time t μ Telom

17 M/M/ The server utiliztion (ρ) ρ μ The trffi intensity () offered lod (Erlngs) μ The stbility requirement ρ < < With trffi intensity Erlngs, is the minimum number of servers requirement. Telom M/M/ Let π i denote the stedy stte probbility of i ustomers in the system, then the stte trnsition digrm for n(t) is given by μ 2μ 3μ ( )μ μ μ π j 0 0 μπ ( + jμ) π j π j + ( j + ) μπ j+ ( + μ) π j π j + μπ j+ j < j Flow lne equtions Telom

18 M/M/ π j kμ π j j < π j j μ π j Solve determining π i in terms of π 0, then sum of probbilities Telom M/M/ (5) π 0 n n! n 0 + ( )!( ) π π i i ; i < i! π 0 i i π i 0 ; i! Telom

19 Telom M/M/ (6) + 0 ) )!( (! ) )!( ( ), ( n n j j n π Probbility of ustomer being delyed (,) (,) Erlng s formul, Erlng s dely formul Erlngs seond formul In the telephone system, (,) represents bloked ll delyed (D). n ompute (, ) from Erlng vlue )), ( ( ), ( ), ( Telom M/M/ (7) μ μ ), ( ), ( + + q q q q q W W L W L L L Other performne mesures expressed in terms of (,)

20 M/M/ (8) Distribution of the witing time in the queue P μ ( ρ ) t { w t} (, ) e q The pth perentile of the time spent witing in the queue t p t p p ln (, ) μ ( ρ ) Note: p > - (,) Telom Trffi Engineering Exmple 2 A servie provider reeives unsuessful ll ttempts to wireless subsribers t rte of 5 ll per minute in given geogrphi servie re. The unsuessful lls re proessed by voie mil nd hve n verge men holding time of minute. When ll voie mil servers re busy ustomers re pled on hold until server beomes free. Determine the minimum number of servers to keep the perentge of ustomers pled on hold < or equl to % The offered lod is 5 ll per minute x minute/ll 5 Erlngs From the Erlng tbles 3 servers re needed. Determine the.995% of the dely in ess the voie servers With p.995, (,).0, 3, nd μ t p p ln (, ) μ ( ρ ) yields t p.0866 minute 5.2 ses Telom

21 Fix hnnel Assignment Sheme Mrket Study Number of Subsribers Per ell Demogrphis Assume lls/subs during Pek one hour with Averge holding time Erlngs/ell Assume GOS ( % ll bloking < 2 %) Apply: Erlng Number of hnnels per ell nd Number of hnnels per system Telom ell Spitting How n one inrese pity when hot spot ours? ell splitting One pproh insert low power miroell reuse frequenies A Must be reful to not violte ohnnel interferene requirements Expensive! Telom

22 Frequeny Reuse Prtitioning Split hnnels into two or more groups one with lower power nd smller reuse luster size to inrese pity. Requires hndoffs within ell. Must be reful to not violte ohnnel interferene requirements Frequeny reuse prtitioning Telom Summry ellulr onept Setoring Frequeny Plnning Trffi Engineering Frequeny Reuse Prtitioning Telom