Impact of the Various Tiers of Interfering Cells on CDMA Systems

Transcription

1 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) Ipact f the Varius Tiers f Interfering Cells n CDMA Systes SAMAD S. KOLAHI Unitec New Zealand, Auckland NEW ZEALAND Abstract:- In this paper, using a siulatin and delling technique, the sensitivity f ther-cells interference factr and the prbability f blckage versus the additin f the varius tiers f neighburing cells has been studied. Situatins with tiers f neighburing cells are cnsidered and fr tw scenaris, when the bile chses as he cell the nearest base statin, and when it cpares tw base statins and chses the base statin with the strnger signal. It is cncluded that it is usually enugh t cnsider nly three tiers f neighburing cells t get a gd understanding f the perfrance issues f the CDMA he cell. The siulatin results cnfir that by chsing the better f tw base statins a significant reductin in ther-cells interference can be achieved cpared t chsing the clsest base statin. The ther-cells interference factr is fund and cpared with the upper bund results btained in earlier studies. Key Wrds:- CDMA, ther-cells interferences, nuber f tiers 1. INTRODUCTION Mbile cunicatins has enjyed rapid grwth during the last decade. As the aunt f bandwidth available reains the sae, capacity planning beces an iprtant issue in cellular systes. CDMA syste capacity decreases with the aunt f interference. In CDMA all calls interfere with ne anther as they all use the sae frequency range. Each base statin nt nly receives interference fr biles in the he cell (intra-cell interference) but als fr biles lcated in neighburing cells (inter-cell interference). Earlier researchers have lked at varius nuber f tiers f interfering cells (fr ne tier in [1,2] t tw tiers in [3] t five tiers in [4]) t investigate the perfrance f the CDMA systes. There is little in the literature t deterine hw any tiers f neighburing cells are t be included in the syste del t get a certain precisin in blcking prbability results. In this paper, the effect f the varius tiers n the CDMA syste is investigated. It is deterined that it is enugh t cnsider nly three tiers f neighburing cells in rder t get a gd understanding f the perfrance issues f a CDMA he cell. The rganizatin f this paper is as fllws. In the next sectin the syste del is discussed. The siulatin results are then presented. The last sectin presents cnclusins. 2. SYSTEM MODEL A cellular CDMA syste (a he cell and tiers f neighburing cells) is cnsidered with a base statin lcated at the center f each cell (Figure 1). Calls are cnsidered t suffer lg-nral shadwing (but nt Rayleigh fading [5]). All cells are assued t be hgeneus in every respect and users are assued t be unifrly distributed ver the cell area. The reverse link (bile t base statin) is investigated as it is the liiting link due t its inferir perfrance cpared t the frward link [6,7].

2 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) f ( t) ( λ1 + λ1 ) t ( λ1 + λ2 ) e (1) pririty is given t handff calls. λ 1 λ2 λλ 1 +λ λ n λ n Figure 1: A he cell and tw tiers f neighburing cells. The CDMA syste is delled as a M/M/ syste (Figure 2) [5,8,9,1]. Calls are assued t arrive in the syste with Pissn distributed prbability with ean arrival rate λ calls/secnd. Calls reain in the syste with a negative expnentially distributed call hlding tie with ean 1/µ secnds/call. When a call is accepted it reains in the syste during its call hlding tie. Call Arrivals 1 Servers Call Departures Figure 2 : Call arrivals, service, and departures fr M/M/ syste Handff request arrivals als fllw a Pissn distributin [9,11]. The su f tw Pissn prcess (with λ 1 and λ 2 ) is anther Pissn prcess with λλ 1 +λ 2 (Figure 3) [12]. We define the ttal arrival rate λ as the su f the nral call arrival rate λ 1 and handff traffic λ 2. The prbability density functin is given by: Figure 3: Additin f Pissn Prcesses is anther Pissn Prcess There is n liit n the nuber f calls accepted t the syste (sft capacity) as lng as they eet the required call quality. Any calls nt eeting this required quality are blcked fr entering the syste. 3. BLOCKING PROBABILITY CDMA capacity is interference liited. With greater interference, fewer calls can be accepted t the syste as the quality f calls decreases. In a CDMA syste, each base statin nt nly receives interference fr biles in the he cell (intra-cell interference) but als fr biles lcated in neighburing cells (inter cell interference). The interference received fr ther cells depends n the signal strength received fr the biles aking the calls. The prpagatin del used assues that attenuatin is prprtinal t the prduct f the th pwer f the distance (r) and a lgnral rand nuber (ξ) representing shadwing with ean zer and standard deviatin f σ ξ db, that is S /1 S 1 ξ t r (2) where S t and S are the transitted and received pwer respectively. The interference fr the jth bile in neighburing cell i is expressed as (figure 4):

3 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) ( I) r 1 ξ /1 ξ ξ /1 S. S( r / / 1 r ) 1 (3) ξ 1 r ξ ξ / 1 ( I / S ) ( r / r ) 1 (4) The ttal ther-cell interference I is the interference prduced by all users wh are pwer cntrlled by ther base statins. Assuing a CDMA syste with M uter cells and N users per cell, then the ttal ther user interferences-t-signal rati ( I / S ) is [5]: M N ( I / S ) I / S (5) i 1 j 1 On each call arrival, the ttal interference is deterined fr which the blcking cnditin can be checked. This invlves repeatedly generating fr each user a rand lcatin f r between and 1 and unifr rand variable θ between and 2π. The value f r can be calculated fr each neighburing cell s interfering calls. r E N b S / R S / R W / R I / W (( N 1) S + I + η )/ W ( N 1) + ( I / S) + / S (6) η where (I/S) is the rati f ther-cells interference t the received signal strength (S) at the he base statin, η is backgrund nise, W/R is the Prcessing Gain, W is available spread bandwidth, and R is data rate. Taking vice activity (α) int cnsideratin, E b N W / R α ( N 1) + α ( I / S ) + η / S (7) The CDMA syste can nw be siulated and E b /N calculated using (5) and (7) fr every call arrival. The ttal interference at the he base statin is deterined fr which the utage cnditin can be checked. If the required call quality f (E b /N ) is nt achieved, the call is blcked. The siulated blcking prbability is then btained fr a given Erlang traffic (λ/µ), by taking the rati f the nuber f blcking events t the ttal nuber f call arrivals (Figure 5). The accuracy f the abve del was tested in [14] where the results atched with the analytical results f [8]. d r The ther-cells interference factr (f) can be calculated as the rati f ther-cells interference t within-cell interference, He Cell Figure 4: Interfering call distance t he cell f I ( N 1) S I / S N 1 M N i 1 j 1 [( r / r ) 1 ( N 1) (8) ] ξ ξ / 1 Using equatins (4,5), the received pwer fr interfering cells at the he base statin is then calculated by cnsidering the path lss expnent and shadwing paraeter ξ -ξ. Fr each interfering call, a lgnral differential shadwing paraeter, ξ -ξ, is generated with ean zer and ttal standard deviatin σ T σ ξ 2 (If independent lgnral variables ξ and ξ have ean zer and variance f σ 2 ξ, ξ -ξ has ean zer and variance 2σ 2 ξ ). The transissin quality f a CDMA call in ters f the energy per bit ver ttal interference spectral density E b /N ay be calculated as [13]: Siulatin results were btained fr the tw scenaris when the he cell was chsen as: (a) the clsest cell (r <r ); and (b) the cell that prvides the strngest signal, in which case the bile will still chse the clsest cell as he cell if [1] ξ ξ / 1 ( r / ) 1 r 1 (9) whereas it will chse the neighburing cell if the RHS f equatin 9 is greater than ne. 4. RESULTS

4 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) The siulatin is perfred fr ne illin arrivals and n each arrival the rati f ther-cell interferences I t within-cell interference (N-1)S is deterined. These values are then averaged ver the siulatin perid. te that the value f S is nt required when calculating the rati in (8). The blcking prbability is btained by taking the rati f the nuber f blcked calls t the ttal nuber f call arrivals (Figure 5). The siulatin is started with ne tier (a he cell and 6 interfering cells) and ther-cells interference factr (f) and blcking prbability is calculated. Next the secnd tier is added (a he cell and 18 interfering cells) and the sae rati is calculated. The additins f tiers are cntinued until any further additin has insignificant effect (Table 1). Fr paraeter values f σ ξ 8dB (σ T 11.3), W/R125, E b /N 5.12 (7dB), α.375, S/η-1dB, and 4, and 21 Erlang f traffic per cell (λ/µ), the GS (Grade f Service) and the rati f ther-cell interference t within-cell interference are calculated and tabled. In Table 1, Clun A is the ther-cells interference factr (f) if the bile chses the clsest cell as the he cell. Clun B is the ther-cells interference factr when the bile cpares the signal fr the tw nearest cell sites and chses the better ne as its he cell. The clun %change is the percent change in the ther-cells interference factr results as anther tier is added. In the Table, 4 th tier eans tiers 1-4 inclusive. Table 1 results indicate that a significant iprveent is achieved if we use the better base statin f the tw nearest base statins (clun B) as a easure fr chsing the he cell cpared t chsing the clsest base statin (clun A) as he cell. The result clearly indicates that it wuld be enugh t take int cnsideratin the first three tiers and ignre the furth tier nwards. This culd be seen in % change clun f data. Fr ttal shadwing paraeters f 1dB and 12 db, the upper bund f paraeter f is fund in [15] t be 1.28 and Using equatin (8), the siulatin results indicate the ther-cells interference factr t be.52 and.68 respectively which is less than the upper bund values. It was fund that the average ther-cells interference factr was essentially independent f the traffic lad, a cnsequence f cnsidering an assued hgeneus syste with a large nuber f call arrivals. A %change GS B %change GS 1st tier nd tier rd tier th tier th tier th tier Table1: effect f varius tiers f cells n interference and blcking prbability fr 4. and σ ξ 8dB (σ T 11.3) 5. CONCLUSIONS The ipact f the neighburing cells n the perfrance f CDMA systes under perfect pwer cntrl was investigated. It was nted that it is enugh t cnsider nly three tiers f neighburing cells (and ignre the higher tiers) t get a gd understanding f the perfrance issues f the CDMA he cell. The siulatin results shwed that by chsing the better f tw base statins as he cell a significant reductin in ther-cells interference and blcking prbability culd be achieved cpared t chsing the clsest base statin. It is fund ut that the upper bunds results f the ther-cells interference factr btained analytically in a previus study is

5 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) significantly higher than the actual ther-cells interference factr deterined via siulatin. References: [1] Z. Lei, D.J. Gdan, and N.B. Mandaya, Lcatin-dependent ther-cell interference and its effect n the capacity f a cellular CDMA syste, IEEE Vehicular Technlgy Cnference, 1999, vl. 3, pp [2] S. Shin, K. Lee, and K. Li, Perfrance f the packet data transissin using the ther-cell interference factr in DS-CDMA dwnlink, Wireless Cunicatins and Netwrking Cnference, 22, vl. 1, pp [3] A. Chatvich, and B. Jabbari, Effect f nnunifr traffic lad n Erlang capacity f CDMA, IEEE Vehicular Technlgy Cnference, 49 (1), 1999, Pages [4] H. Stellakis, A. Girdan A. Aksu,and W. Biagini, Other cell interference and capacity f pwer cntrlled CDMA in wireless fixed access netwrks, The Ninth IEEE Internatinal Sypsiu n Persnal, Indr and Mbile Radi Cunicatins, 1998, Pages [5] J. S. Evans and D. Everitt, On the Teletraffic Capacity f CDMA Cellular Netwrks, IEEE Transactin n Vehicular Technlgy, vl 48(1), 1999, pp [6] J. S. Evans and D. Everitt, Analysis f Reverse Link Traffic Capacity fr Cellular Mbile Cunicatin Netwrks Eplying Cde Divisin Multiple Access, Australian Telecunicatin Netwrks and Applicatins Cnference, Melburne, Deceber 1994, pp [7] D. D Lee, D. H. Ki, Y. J. Chung; H. G. Ki, and K. C. Whang, Other-cell Interference with Pwer Cntrl in Macr/icr-cell CDMA netwrks, IEEE 46th Vehicular Technlgy Cnference, 1996., vl 2 (28), April-1 May 1996, pp [8] A. M. Viterbi and A. J. Viterbi, Erlang Capacity f a Pwer Cntrlled CDMA Syste, IEEE Jurnal n Selected Areas in Cunicatins, vl 11(6), 1993, pp [9] D. M. Lee, Perfrance Siulatin f Call Capacity fr Base Statin in CDMA Syste, IEEE 6 th Internatinal Cnference n Universal Persnal Cunicatins, Vl 2, 1997, pp [1] W. Lavery and D. Everitt, Analysis f The Uplink Teletraffic Behavir in CDMA Cellular Systes, in Prc. IEEE Vehicular Technlgy Cnference, Stckhl, Sweden, 1994, pp [11] R. P. Narrainen, Perfrance Analysis f Sft Handff in CDMA Cellular Netwrks, IEEE Transactin n Vehicular Technlgy, vl 5(6), 21, pp [12] P. T. Strait, Prbability and Statistics with Applicatins, chapter 8, secnd editin, Harcurt Brace Jvanvich Publishers, New Yrk, [13] K. S. Gilhusen, I. M. Jacbs, R. Padvani, A. J. Viterbi, et. al, On the Capacity f a Cellular CDMA Syste, IEEE Transactin n Vehicular Technlgy, vl 4(2), 1991, pp [14] S. S. Klahi, On Erlang Capacity f CDMA Systes, Mbile and Wireless Cunicatins, G. Oidyar, Ed., rvell: Kluwer Acadeic Publishers, 23, pp [15] A. J. Viterbi and A. M. Viterbi, Other-Cell Interference in Cellular Pwer-Cntrlled CDMA, IEEE Transactin n Cunicatins, 42 (2), pp , 1994.

6 Prceedings f the 4th WSEAS Int. Cnf. n Infratin Security, Cunicatins and Cputers, Tenerife, Spain, Deceber 16-18, 25 (pp ) Start Get first arrival tie with its call hlding tie Get a new call arrival tie with its call hlding tie, Calculate departure tie Call Deparure, NN-1 (Nn in the syste) lwest t arr > lwest t dep Call Arrival (narrnarr+1) Get r, ξ ξ Calculate r Calculate (I/S) Calculate E b /N Blck the Call (blckedblcked+1) Eb/N >7dB Accept the call t the syste (NN+1) Add the call, Cllect Syste Statistics narr (N)<5 Calculate Gs (blcked / narr) Set narr, blcked t zer (start new batch) KK+1 K<2 Stp Precisin required Achieved? Figure 5: Blcking prbability calculatins in the siulatin del.