On Erlang Capacity of CDMA Systems

Transcription

1 On Erlang Capacity f CDMA Systes Saad S. Klahi Meer, IEEE Unitec Institute f Technlgy, Auckland, New Zealand Astract: In this paper, the Erlang capacity f ile prtcls such as FDMA (Frequency Divisin Multiple Access), TDMA (Tie Divisin Multiple Access), and CDMA (Cde Divisin Multiple Access) systes are cpared assuing perfect pwer cntrl. Methds f calculating the traffic capacity f such systes are discussed. A siulatin and deling ethd is used and the results are cpared with previus analytical ethds. The siulatin result is clse t analytical result althugh a different apprach is adpted. CDMA can prvide up-t ties re traffic capacity than FDMA and 5.3 ties re traffic capacity than TDMA. Key wrds: CDMA, Capacity, Erlang 1. INTRODUCTION Mile cunicatins has enjyed cntinuus grwth in ters f nuer f ile phne users in the last several years. Traffic anageent f the netwrk is ecing re iprtant as the nuer f ile phnes increase. Tele-traffic engineering issues are vital in planning, design, and diensining f ile CDMA netwrks. Traffic engineering f FDMA and TDMA systes is a straightfrward atter as each user ccupies a slice f the andwidth r tie slt respectively. If each user ccupies 3KHz f andwidth, with frequency reuse f 7 and 3 sectrs per cell, the nuer f channels per sectr in 1.5 MHz is 19. Fr a TDMA syste, the syste uses the 3KHz and fr three calls, each taking turns in using the 3KHz range. The nuer f channels will e N 57 Channels/sectr. Using the Erlang- B frula (1), assuing lcking praility f., the traffic intensity is

2 calculated as A 1. 3 fr FDMA systes and A fr TDMA systes. Nte that the result iplies that althugh the nuer f channels is 3 ties greater in TDMA cpared t FDMA, it can carry 3.8 ties re traffic t that f FDMA. P lcking N ( A) k N ( A) / N! k / k! (1) The traffic engineering issue is nt straightfrward in CDMA as all calls use the sae andwidth (the whle andwidth spectru). The traffic capacity f the CDMA syste can e investigated y varying the traffic lads (arrivals versus departures t the syste) and deterining the praility f call lsses. The rganizatin f this paper is as fllws. In the next sectin the syste del is discussed. The lcking praility calculatins are intrduced in sectin 3. Siulatin and analytical results are reprted in sectin 4 and se cncluding rearks are given in sectin 5.. SYSTEM MODEL A cellular CDMA netwrk with 37 cells is cnsidered (a he cell and three tiers f neighring cells) with a ase statin lcated at the center f each cell. All cells are assued t e hgeneus in every respect. The reverse link (fr ile t cell site) is deled as it is the liiting link due t its inferir perfrance cpared t frward link [1]. The calls t the CDMA syste are deled as Pissn [] with ean arrival rate f calls/sectr/secnd and ean call hlding tie f 1/ secnds per call. In queuing ters, this is a M/M/ syste which is eing used fr CDMA systes deling. Once the ile call has een aditted, it stays in the syste during its call hlding tie which is deled as negative expnential with praility density functin: f t ( t) e () Traffic density (ffered traffic lad), /, represents the excess f the arrival rate versus departure rate. / is easured in Erlang.

3 On Erlang Capacity f CDMA Systes All calls are allwed int the syste (sft capacity) if they eet the required Quality f Service (QS). Any calls nt eeting this required quality are nt peritted t enter the syste ut are lcked. 3. CDMA BLOCKING PROBABILITY In CDMA all calls use the sae frequency range. These calls therefre interfere with ne anther. CDMA capacity decreases with the aunt f interference. Cnsider a CDMA he cell and its neighring cells, each cell site nt nly receives interference signal fr iles in the he cell (intra-cell interference) ut als fr iles lcated in neighring cells (inter cell interference). The pwer f signals received is the prduct f the transitted pwer, th pwer f the distance and a lgnral shadwing paraeter ( ) with ean zer and standard deviatin f. This shadwing paraeter varies with different terrains. Assuing S t and S are the transitted and received pwer respectively, we have: S S. 1 t r /1 (3) The interference fr the jth ile in neighring cell i is expressed as [4]: ( I) ij /1 r 1 S. (4) /1 1 r ( I / S) /1 ij ( r / r ) 1 (5) where S is the received signal strength at he ase statin, r is the distance t crrespnding he cell ase statin (figure 1), r is the distance t the neighring cell, and are lgnral (Gaussian in db) rand variale distriutin with zer ean and standard deviatin representing shadwing paraeter in neighring and he cell, and is path lss expnent.

4 Ttal ther cell interference I is interference prduced y all users wh are pwer cntrlled y ther ase 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: M N i1 j1 ( I / S) I / S (6) ij On each arrival f a new call, the ttal interference is deterined fr which the lckage cnditin can e checked. This invlves repeatedly generating r etween and 1 and unifr rand variale etween and. Using figure 1, r can e calculated fr each user as: r r d d r Cs (7) r d r R Figure 1. Interfering call distance t he cell Using equatins (5) and (6), the ttal received pwer fr interfering cells at the he ase statin is calculated y cnsidering the path lss expnent and shadwing paraeter -. If independent lgnral variales and have average zer and variance f, - has ean zer and variance. Fr each interfering call, a lgnral shadwing paraeter, -, is generated with ean zer and standard

5 On Erlang Capacity f CDMA Systes deviatin. The transissin quality f a CDMA call ay then e calculated in ters f the energy per it ver ttal interference [4] spectral density E / N. E S / R S / R W / R N I / W (( N 1) S I ) / W ( N 1) ( I / S) / S (8) ( I / S) is the rati f ther cells interference t the received signal strength (S) at he ase statin, N is the nuer f active users in the cell, is ackgrund nise, W/R is Prcessing Gain, W is availale spread andwidth, and R is data rate. Taking vice activity int cnsideratin, we have: E N W / R ( N 1) ( I / S) / S (9) On each call arrival E / N is deterined (6,9) t decide if the call is accepted t the syste r is lcked. The lcking praility can then e calculated fr a given traffic lad. 4. RESULTS 4.1 Siulatin Results The siulatin is perfred fr ne illin arrivals. On each arrival, the ttal interference at the he ase statin is deterined and fr this the lcking cnditin can e checked. If the required call quality f E / N 7dB, r BER<1-3, is nt achieved, the call is lcked. The lcking praility is then calculated fr a given Erlang traffic ( / ), y taking the rati f the ttal nuer f lcking events t the ttal nuer f call arrivals. Fr values f 8dB, W / R 15, E / N 5.1(7dB),.4, S / 1dB, and 4 and the lcking praility f %, and assuing perfect pwer cntrl, traffic intensity ( / ) is deterined y siulatin as 7 Erlangs which crrespnds t apprxiately 36 vice

6 channels per sectr per 1.5MHz. The 1.5MHz spectru utilizes nine 1.5MHz CDMA frequency lcks [5]. The nuer fr channels ust therefre e ultiplied y 9. Ttal nuer f channels supprted will e 34 which crrespnds t 39.7 Erlangs/sectr. 4. Analytical Results Using the analytical ethd [3] with perfect pwer cntrl, the traffic capacity can e calculated as: (1 )( W / R) F( B, p) (1 f )( E / ) N Erlangs/sectr (1) where ( E B / N )[ Q 1 ( P lcking ( W / R)(1 ) )] (11) and Q( z) z 1 e y dy (1) fr perfect pwer cntrl: B 4 F( B,) 1 (1 1 ) (13) B where is the ackgrund (theral) nise t ttal acceptale interference, p is the standard deviatin f pwer fluctuatins, f is the rati f ther cell interference t wn cell interference. Nuerically fr P lcking=., W/R=15, =.1, p =, f=.55, E / N 5.1(7dB) and =.4, we tain: Q -1 (P lcking)=.57, B=.19, F(B,)=.871, Erlangs/sectr. This analytical Erlang capacity f is slightly higher ut clse t the siulatin results f 39.7 Erlangs/sectr tained ave.

7 On Erlang Capacity f CDMA Systes Iperfectins in pwer cntrl schees can reduce this capacity y apprxiately % [3]. The siulated CDMA traffic capacity is therefre apprxiately 47.8 Erlangs. This is 47.8/1.3 = ties re than an analgue syste and 5.3 ties (47.8/46.8) re than the TDMA Erlang capacity calculated ave. These results are very clse t the results deterined analytically in [3] althugh a different apprach is adpted. 5. CONCLUSIONS The traffic capacity f a CDMA syste is analyzed using siulatin and deling tls and cpared t analytical ethds. The analytical results are slightly higher ut clse t siulatin results tained in this wrk. CDMA can prvide up t ties re traffic capacity than its predecessr FDMA systes and up t 5.3 ties re traffic capacity than TDMA systes fr the sae frequency range. 6. REFERENCES [1] J.S. Evans and D. Everitt, Analysis f Reverse Link Traffic Capacity fr Cellular Mile Cunicatin Netwrks Eplying Cde Divisin Multiple Access, Australian Telecunicatin Netwrks and Applicatins Cnference, Melurne, pp , [] J.S. Evans and D. Everitt, On the Teletraffic Capacity f CDMA Cellular Netwrks, IEEE Transactin n Vehicular Technlgy, vl 48(1), pp , [3] A.M. Viteri and A. J. Viteri, Erlang Capacity f a Pwer Cntrlled CDMA Syste, IEEE Jurnal n Selected Areas in Cunicatins, vl 11(6), pp , [4] K.S. Gilhusen, I.M. Jacs, R. Padvani, A. J. Viteri, et al, On the Capacity f a Cellular CDMA Syste, IEEE Transactin n Vehicular Technlgy, vl 4(), pp , [5] R. Padvni, Reverse Link Perfrance f IS-95 Based Cellular Systes, IEEE Persnal Cunicatins, third quarter, pp. 8-34, 1994.