2.3 A cellular service provider decides to use.a digital TDMA scheme which can tolerate a signal-to-interference ratio of 15 dB in the worst case. Find the opti- mal value of N for (a) omni-directional antennas, (bi 120° seetoring, and le) 60° sectoring. Should sectoring be used? If so, which case (60° or 120°) should be used? (Assume a path loss exponent of n = 4 and consider trunking effi- ciency). B35) Odet i, be Ke nunker of -chacatd, Parterfeing cs, Grocincterestian.( can)" Fa + 26. Assure N24, DISAB = 31.623 > 9-59 (6) Fer te? sect %=2, afin BOS 3193 > W245 © Fer 60° secterng, 7071, f Lu 23163 > W278) > 23 From (4). (6) and () We Can St they using [R0” Sector Can mrierse the copruly 4y 4 fact of U3, or 2.333. At caph wing 60" Sectrng can alse jreveere Ue Copeaity by he sant fostor. it wll arcrease the bracing ofeicny thucfore We cheese the 120° Sect ering2.5 ForaN =7 system witha Pr{Blocking| = | % and average cali length of 2 minutes, find the traffic capacity loss due to trunking for 57 channels when going from omni-directional antennas to 60° sectored antennas. (Assume that blocked calls are cleared and the average per user call rate is A = 1 per hour, & Ut Sane wha ued in eral 2-9, then 9 fre ame directional artery to G0" Seeteved ontennac, He rater of chewrals spor Sector = 4225 Ginn Prl bleeiog] r pm the Erlbeg B destribstio, 2 have Us totel offered tfc snleaelly por Seelor Att) Ebeg Fer steel fhaar, He 9 minute tal, Us ruber of calls hot Gach Seach sedter Con Kendle per hor ie Ye4-: 44-123 users un” Zoe > coll ply = bx 38 ustes, fron erupha9, => bs m tewhing offeeng = Glew N =7,G0S= 1%=001,H= Pminutes, C= 57 channals, Erlang 8 system, A= 1 cal/nour Lose in U? (compare U for omni-directional and V for 60 sectring 2224) > We need to find: for omakdirectional=? and for 60° sectoring |A.=AH= 1 callnour x (2/60) hour = 0.023 Erlang per user Fo Omol-ditectional anternas: the number of channels (C} = 57 channels From Erlang 8 table/diagram: Traffic capacty A= 44.22 Erlang The number of users that the system can handle: U= Ala, = 48.22/0.038 = 1325 users Fr 60° sectoring: the numberof chennels per sectors S7/6 =9 channels From Erang 8 table/digram: Traffic capacty A= 3.783 Eiang U3.783/0.033 users per sector 6 sectors» 678 usrs in all sectors User capactylons= (1 ~ BOE For seca). 99. (4 ~ $28). 190-494 decease2.6 Assume that a cell named “Radio Knob” has 57 channels, each with an effective radiated power of 32 watts and a cell radius of 10 km. The grade of service is established to be a probability of blocking of 5% (assuming blocked calls are cleared). Assume the average call length is 2 minutes, and each user averages 2 calls per hour. Further, assume the cell has just reached its maximum capac- ity and must be split into 4 new microcells to provide 4 times the capacity in the same area, (a) What is the current capacity of the “Radio Knob" cell? (b) What is the radius and transmit power of the new cells? (c) How many chan- nels are needed in each of the new cells to maintain frequency reuse stability in the system? (d) If traffic is uniformly distributed, what is the new traffic car- ried by each new cell? Will the probability of blocking in these new cells be below 0.1% after the split? sae “ane _ ctl dius = 10 brn, COS is 5, blocked calls eleared, H= 2 minutes, andy [Assume eal wil be spit ise eels) calls px our 5) Whats be currenteapaciy of te“Radio Kot” eel? Using the fanctions defined in problem 27 " A;70.067 Eniangs P=0s Probability of blocked catls C87 ‘Assume NT cell, AMPS 40 Tota! guess KapscyerooxGOS(K.CHIA) Solve iteratively foro uaffic Apscyat se Bangs AxlP.C) A, Number of user is U= usvi2921 or = T.uiert 1) What ists radius snd vansmi power of the sew cel? Siete sew eth ms cove hese of eld eth be as of te Beatie ofthe ol el Tener covery ete ea ee eu cre Ris R? (Bae which equals the area ofthe original cell Tomtinain the same SNR, the power atthe edge o Feit a the nev cells must equal the power atthe edge ofthe rR)" p, [S stall wher Ps andP; ate the powers of tke base sation in the old and new cells ‘espectivey, PR*: MP.W32 watts, chen Py=2 wattsEach new cell gets the cumber of c Sumber of channels ig the cll spliting proces enaplete ena cel once ©) Keathicisusitoray disaibuted, what isthe nev bk in tese new cells be Below 0.1% afer he gpl? SP EE™ GIN Wil te probaly of ar U=193 users per new eal RUA AsI2.467 Bangs GOS(2.87,57}=0 ‘The probability of blocking is tess than .1% Given: C=57 channels, P= 32 watt, R, = 10km, GOS = 5%, Erang B system,H = 2 minutes, A= 2 call/hour Cell wil be spit nto 4 cells. (a) User capacity (Uiof the orginal cell? A,= 22/60 0.067 Erlang From Erlang 6 table: A = 51.59 Erlang Number of users U = A/A,= 769 users (0)R,=2,Py=? Ares of orginal cell= 4x res ofrew cells Pa hi” R2=4x ERE > RP=LRE > Ry= ZR, =5km 12 Ry” > Pia= Pa (Ra/Ry)" > Py =P (1/2)" Assume n= 4 > Pz =Px(l/16) = 32/16 =2 watt {c} Microcalis have the same number of channels as the eriginal calls after cell splitting. While the total number of channels in the original areais increased. {(@) Traffic (A) carried by each new cell = 2, wll the GOS be < 0.19%? Users willbe distributed over & cells 192 x0.067 = 12.85 Erlang, Ths is the traffic that is being carried by each cell. From Eriang 8 table: For GOS= 0.1% and 57 channels, ‘A= 38.39 Erlang, this s the maximum amount of traffic that can be carried by each cell for GOS = 0.1% The current carried traffic Is only 12.86 Erlang, which Is less than the maximum traffic that can be handled by the cell. So, the probability of blocking willbe less than 0.1%.2.7. Exercises in trunking (queueing! theory: (a) What is the maximum system capacity (tofal and per channel) in Erlangs when providing a 2% blocking probability with 4 channels, with 20 chan- nels, with 40 channels? (b) How many users can be supported with 40 channels at 2% blocking? Assume H = 105, 4 = 1 cal/hour. (©) Using the traffic intensity per channel calculated in par: (a), find the grade of service in a lost call delayed system for the case of delays being greater than 20 seconds. Assume that H = 105 s, and determine the GOS for 4 channels, for 20 channels, for 40 channels. (@) Comparing part (a) and part (c), does a lost call delayed system with a 20 second queue perform better than a system that clears blocked calls? Fer C= 4 chaunls. frm ths Gig chert ta Aeaat £1 Erbngs = Apothosh = 36 Fr (= 40 Gannls Avcet = 31 Elegs Agprchest 6) Y= Ase sa 2 pop3 users US Gate ee (0) Fer C= 4 Chonsals, Aunt = 11 lugs. Az le5 stoondsfeall fe OS Cee lf» the Exbag C chart , we Kove Prl dey 20] 2 0-03 = Pel delg > 2a5ee} = Pol delog 20) exp -(C Hree) 2oeftt] = O03x expl-C41x84/e5 ] = oyFa C= 30 charms. Alea = /4 Glags , we have PL diby >0] F006 > Pel dibg > 2:00) = PoLdbeg>0}- expl- (cA) 2050/11) = bof x exp [- (Be-6)xd0/}95) = o.0/9 Fer C= #0 chonncls, Ate =3/ lergs, We have P, [dehy >0] = 0-0) => Pr delay 22052] = oa OPL-(40-4 1) tf] 0.018 (d) Frm Le) Wwe Gan Se that th Prvabilty Met a coll wll be delayed J te then dv Sted tn a lost call dhayed systen os Less Uy ag J® lh the difercnt Chonah pumbers. hes a Lot cell led. system Piper belle then @ Systm thag deps bloiked alls.28 A receiver in an urban cellular radio system detects a 1 mW signal at d = dy = | meter from the transmitter. In order to mitigate co-channel inter- ference effects, it is required that the signal received at any base station receiver from another base station transmitter which operates with the same channel must be below -100 dBm, A measurement team has determined that the average path loss exponent in the system is n = 3, Determine the major radius of each cell ifa T-cell reuse pattern is used. What is the major radius ifa 4-cell reuse pattern is used? Sle Fer 7 Coll reuse tatem, the snteefororee Sippel pore from ansitir treasomitler Behe Capy"= py (Bory fone Row the tram Prver in bese Stein, D vs te dsterce tthe center f Ue rarcut Co-chonrel cells ce tha wager redins. In thes eat, P= mld, vey O=IM, N23, thes we have . we hare Fer 4 cell vet pattern. W*4. Imi (. La yp fom, ° rye <-foodem => Y > 62¢9m100 dem, n=3 Given: dy= 1 m, Po = 1 mW, P, 2 For N=7 and N =4 The power received at co-channel cells, at distance D, must be below -100d8m 4y"0_ aR vay R= Po(Z) .E= VN > B= Po (4) OR P,(dBm) = Py(dBm) — 10n log (2), 2 = V3 > P.(4Bm) = Pp (dBm) — 107 log ( for N -100 = 0- 30 tog (4) > tog (“H4) = 333 VIR = 10°33 = 2154.43 > % 170.1 2.10 Show that if n = 4, a cell can be split into four smaller cells, each with half the radius and 1/16 of the transmitter power of the original cell. If extensive mea ‘surements show that the path loss exponent is 3, how should the transmitrer powek be changed in order to split a cell into four smaller cells? What impact, will this have on the cellular geometry? Explain your answer and provide drawings that show how the new cells would fit within the original macrocells. For simplicity use omni-directional antennas. Callis split into 4 smaller cells Area of original cell = 4x area of micro cells 33 SB aia 4x SRz > RI=TRE > R,=3R Pu Rpt = Py Ro” > Pra= Pay (Re/R)" D Pip =Py (1/2) Forn=4 Pi, = Py: (1/2)*= 1/16 Py Forn=3 Pro = Pry (1/2)? = 1/8 Pi2.19 The U.S. AMPS system is allocated 50 MHz of spectrum in the 800 MHz range, and provides 832 channels. Forty-two of those channels sre control channels. The forward channel frequency is exactly 45 MHz greater than the reverse channel frequency. (bd (a) Is the AMPS system simplex, half-duplex, or duplex? What is the bandwidth for each channei and how is it distributed between the base station and the subscriber? (b) Assume « base station transmits control information on channel 352, operating at 880.560 MHz, What is the transmission frequency of a sub- scriber unit transmitting on channel 352? (©) The A-side and B-side cellular carriers evenly split the AMPS channels. Find the number of voice channels and number of control channels for each carrier. (d) Let’s suppose you are chief engineer of a cellular carrier using 7-cell reuse. Propose a channel assignment strategy for a uniform distribution of users throughout your cellular system. Specifically, assume that each cell has 3 control channels (120° sectoring is employed) and specify the number of voice channels you would assign to each control channel in your system. (e) For en ideal hexagonal cellular layout which has identical cell sites, what in the distance between the centers of two nearest co-channel cells for 7- cell reuse? for 4-cell reuse? 327) (a) Tke AMPS Systm i daplen = Given (tel bucdwith Buegs = 50/4 Hp, Ceoreh f= 327 (ot. " This feodwadth of OoKte for te dapler cherccl 3 split nto foro Ct-meg Asarelsa fomed elaacel C from tht bose- cubserrber) onda reve feats Ofer the the bose ctetitn), each pth beudwidth of werd Cherstl exact ly 5 Milz hs phe he yen on the revere Stanel. For Fy = 888 s6ulie Frente = Fu 45 = 35-560 pitizW032, Clad nurbor oF etre docck (c) Grier Nan = 42, we tave Wold runder of yore chertcl J (d) See @rample 3-3 For Pe tell vous 2 M27. 02 BR bia = 48 => p= 55aR. bhere Ri ts reudisss of the cl (e or 4 cell reuse Wa%, Os Ge IB 2 #45 => p=2.20 Pretend your company won a license to build a US. cellular system (the appli- cation cost for the license was only $600!). Your license is to cover 140 square km. Assume a base station costs $500,000 and a MTSO costs $1,500,000. An extre $500,000 is needed to advertise and start the business. You have con- vinced the bank to loan you $6 million, with the idea that in four years you will have earned $10 million in gross billing revenues, and will have paid off the Joan. (a) How many base stations (ie. cell sites) will you be able to install for 86 million? (b) Assuming the earth is flat and subscribers are uniformly distributed on the ground, what assumption can you make about the coverage area of each of your cell sites? What is the major radius of each of your cells, assuming a hexagonal mosaic? {c) Assume that the average customer will pay $50 per month over a 4 year period. Assume that on the first day you turn your system on, you have a certain number of customers which remains fixed throughout the year. On the first day ofeach new year the number of customers using your system doubles and then remains fixed for the rest of that year. What is the mini- mum number of customers you must have on the first day of service in order to have earned $10 million in gross billing revenues by the end of the 4th year of operation? (@) For your answer in (c), how many users per square km are needed on the first day of service in order to reach the $10 million mark after the 4th year? TR] (a) Given Laan = $6x108, Gat of MP0. Cons =S15at08 Cot of 0 base Station, Cas= $5x0%, Got of adver teement . Cade $5 x0%, Wwe have, whe rasmbre of the base staiens re ore able onstall . ve Lenn Corvo- Coa _ O20 15 SHE _ 3 Cox xo CD Giren N= & Clls. Dotal Gorenge ots Ait = (4okn cocrape aren of each coll Aw * Gee BP 2.6 emt Sie Apsths 2627, te have Be [Beg = [BE = 25h(0) Far each spear, ach cositnee wil poy P=5oxjz= $506, Assens the munbur of custimars on the fired dey of Servite 1S M, the gis brthing Pons y the ed of the fossth yeor of Poatin Ge (Mt2m4 478M) P= (err p We pad G ESt0KI0' => (5p 2 loxo* = > roxte! _ “so * > M2 OES = ena S-} Hence The Ininimem prrember of costemer am the first deg oF Sorte w N12 (d) maker of users par Sgume Kn 2A = He HR usts/t