Dstrbuted Channel Allocaton Algorthm wth Power Control Shaoj N Helsnk Unversty of Technology, Insttute of Rado Communcatons, Communcatons Laboratory, Otakaar 5, 0150 Espoo, Fnland. E-mal: n@tltu.hut.f ABSTRACT In ths paper, we ntegrate the channel assgnment and power assgnment nto a dstrbuted channel access algorthm. A cost-functon s ntroduced to provde some optonal channels accordng to ther cost for transmtted power level searchng. The smulaton results show that ths algorthm largely ncreases capacty compared wth the fxed channel allocaton (FCA). The proposed algorthm can adapt to the call saturated state of network and does not cause hgh ntracell handover access. It has a short average call setup tme even at hgh traffc loads. We suggest that the ntracell handover rate should be a factor n evaluaton of an algorthm s performance, because hgh handover access wll ntensvely ncrease the load of swtch and cause much hgher call droppng and blockng probabltes than those we expect. transmsson n downlnk and uplnk; c) a par of transmtter power for the BS and MS. The key ssue of such a rado resource allocaton s to allocate channels to calls as possble wthout resultng n droppng of on-gong calls. J. Zander [], G. J. Foschn [3] have developed some power control algorthms based on the dea of balancng the SIRs on all rado lnks, but the fnal SIR acheved by ths algorthm may be unsatsfactory for some of lnks. Some calls must be dropped n order to keep SIRs of other calls hgher than the predefned threshold value. Obvously, the channel assgnment s hghly correlatve wth the power control. The combnaton of DCA and power control n obtanng some substantal capacty gans has been reported [4], but nadvertent droppng of calls caused by orgnatng calls s not much treated. In addton, an exhausted searchng scheme let t mpractcal for call setup. In ths paper, a dstrbuted channel allocaton algorthm s proposed based on a cost functon. I. INTRODUCTION In recent years, as the number of subscrbers to the moble rado system has been growng rapdly, ncreasng the capacty of ths system,. e., the number of subscrbers per area (or volume) unt at some predefned level of servce qualty, s one of the key ssues of moble communcatons. The tradtonal channel allocaton method, the fxed channel allocaton (FCA), s not very effcent for utlzaton of avalable spectrum, and mpractcal n mcrocell communcaton systems, because the large number of cells, rregulartes n propagaton and traffc dstrbutons make pre-allocaton of channels almost mpossble. Dynamc channel allocaton (DCA) had long been pursued as the answer for copng wth tme and spatal varatons of traffc demand n communcaton networks. Any DCA algorthm would be classfed as a tmd DCA algorthm or as an aggressve DCA algorthm. For the aggressve DCA algorthm, assgnng a channel to a new call mght result n call-drop of on-gong calls. A DCA scheme mnmzng the call outage probablty, n order to mnmze the call drop probablty, has been proposed [1]. The power control can suppress the adjacent channel nterference (for non-orthogonal channels), the cochannel nterference (for orthogonal channels), and mnmze power consumpton to extend termnal battery lfe. Undoubtedly, the power control can rase the network capacty. To establsh a new rado lnk the system has to assgn: a) an access base staton (BS); b) a par of channels for sgnal II. DYNAMIC CHANNEL AND POWER ASSIGNMENT ALGORITHM A. Cost of Channel Assgnment The control of channel access and power control may be combned nto a channel management polcy. Accordng to smulaton by G. J. Foschn and Z. Mljanc [4] nadvertent droppng of calls caused by orgnatng calls can occur so often that all unsuccessful (blocked or dropped) calls are unntentonally dropped calls and not blocked calls. In addton, an exhausted searchng and too frequent ntracell handover access (average 0% as much as the new call access n ther scheme) wll decrease the system capacty and make t dffcult to mplement nto real network. A fully dstrbuted scheme wll reduce the complexty of system, but such knd of algorthm s always very aggressve. Properly selectng a channel and transmtted power wll reduce the aggressveness and reduce the call drop probablty. Snce uplnk and downlnk channels are assumed not to nterfere each other; n prncple, there s no bg dfference between downlnk and uplnk n channel allocaton, we only consder the downlnk stuaton n followng. COST FUNCTION When a new call s accepted nto the network, t mght cause qualty deteroraton of on-gong calls. The cost of a call admsson depends on the assgned channel l for ths 0-7803-3871-5/97/$10.00 1997 IEEE 406
call, the dstance D between cell centers of co-channel users of channel l, the locaton (r, θ ) of all cochannel users, and the transmtted power set P P ( n), of all cochannel users. The cost functon wll be: C = C( P, r, θ, l, D ), n. (1) However, the power control s n the sense of local optmzaton of nterference probablty n the aspect of the transmtted power, the transmtted power s not consdered as a factor of the cost functon C n ths paper. E[10 ξ/10 ] between dfferent cells, and only consderng the varable D n (4), we can assume the average nterference to a cochannel user n type nterferng cells s almost twce as much as that n type 3 nterferng cells. That means that, f assgnng a new user n the host cell, the cost to the cochannel user n type nterferng cells s almost twce as much as that n type 3 nterferng cells. r ϕ MS d h MS j cell k D r j 3 3 cell h Fgure. Downlnk nterference. Fgure 1 Smulaton network. -host cell, For any cell, normally, only two ters of cells are consdered as ts nterferng cells. If a cochannel user s assgned n the host cell, for the second ter of nterferng cells (Fg. 1), the co-channel nterference to cells of type 3 (q = D/R = 3 ) s dfferent from that to cells of type (q = D/R = 3). As shown n Fg., the downlnk cochannel nterference power of moble n cell k from a moble j n cell h s: I = P d α ξ j j h 10 /10, () where d = ( h D + r Dr cos ϕ ) 1/ ; P j s the transmtted power of moble j; ξ s the slow fadng varable wth lognormal dstrbuton. If assumed that the moble users are unformly dstrbuted wthn a cell, the average nterference power wth respect to the whole cell area n cell s: I = I f ( A) da A j α = R P E j 0 π R 0 - nterferng cells. ξ/ 10 [ 10 ] R d α 1 π R rdrdϕ. (3) By numerc calculaton, for α = 4, the average nterference for D/R = 3 and D/R = 3 s respectvely: C α ξ I = R Pj E[ 10 / 10 ], (4) π 01363. D / R = 3 where C = for. 0. 0736 D / R = 3 From (4), t can be seen that the average nterference wth the dstance D = 3R s approxmately twce as much as that n the dstance D = 3 R. If gnorng the dfference of We use the average nterference as a clue to construct a cost functon for channel allocaton. For cell x, denote F(x) as the avalable channel set n cell x, H(k) as the occuped channel set n nterferng cell k, I 1 (x) as the set of the frstter of nterferng cells, I (x) as the set of the second-ter of type nterferng cells, and I 3 (x) as the set of the secondter of type 3 nterferng cells (Fg. 1). We defne the cost to the nterferng cell k { I 1 (x), I (x), I 3 (x) }, due to allocatng channel l F(x) n cell x, as Cx ( k, l) = 0 f l H( k) c f l H( k) and k I1( x), (5) f l H( k) and k I( x) 1 f l H( k) and k I ( x) where the constant c s defned as a large value n order to avod assgnng a cochannel user n the frst-ter of nterferng cells as possble. The overall cost functon to ts nterferng cells for channel l s Cx ( l) = Cx ( k, l). (6) k { I 1 ( x), I ( x), I 3 ( x)} From (6), we can calculate the cost of each avalable channel n cell x. The cost of a channel roughly descrbes ts effects on the on-gong calls, f ths channel s allocated. We wll use the cost to decde the prorty of a channel. The lower the cost of a channel, the hgher the prorty of the channel for allocaton. B. Power Assgnment All channels used n the system are assumed to be orthogonal channels and only co-channel nterference s consdered. The call s establshed wth the base staton from whch the call receves the strongest sgnal. Assume that channel p s assgned to a call n cell. For the downlnk, let coeffcent g k (>0) denote the lnk gan on the path from cell to cell k. If the transmtter power of base staton (BS) n cell s T (>0), then the receved power n cell s g T. Suppose that the same channel s reused n cell 3 0-7803-3871-5/97/$10.00 1997 IEEE 407
k wth the transmsson power T k, then g k T k becomes the amount of co-channel nterference from cell k. The sgnal to nterference rato (SIR) s: SIR = N g T g T T g V k k + k =1 = 1,,..., N, = γ, (7) where N s the number of co-channel users n a system and V s the addtve nose level. If there exsts a power vector T = [T 1, T,..., T N ] t, such that γ γ for = 1,,..., N (where γ s threshold value of SIR), the allocaton of channel p s achevable. Fndng or achevng an optmal power vector T s the task of the power control. We use followng dstrbuted power control algorthm to search for a locally optmal power for the new call: and T(0) = T mn, T (k+1) = mn{ η (k) T (k), T max }, (8) where η ( k) = γ γ ( k) ; T(0) and T(k) denote the ntal and the k-th dscrete tme transmtted power vector respectvely; T mn and T max are the mnmum and maxmum transmtted power respectvely. Ths power control algorthm s also used to mantan the qualty of on-gong calls. C. Channel Allocaton Algorthm Quckly makng decsons on the access channel and transmtted power are key ssues of qualty of servce (QoS). We ntegrate the channel assgnment and power assgnment nto a dstrbuted channel access algorthm. To reduce the call drop rate and to shorten the call set-up tme, all avalable (free) channels are evaluated by each base staton, and some optonal channels are provded accordng to ther prortes for transmtted power level searchng. The cost functon n equaton (6) s used to decde the prorty of a channel. The lower the cost of a channel, the hgher the prorty of the channel. The hghest prorty of a channel has the hghest prorty for call set-up probaton. The calculaton of channel cost s based on the local nformaton about current state of channel occupancy n the cell s vcnty (two ters of cells). Every cell has a lst of the prorty for all avalable (free) channels. The prorty of avalable channels n each base staton s updated (real tme) after a call s accepted or termnated (drop or departure) n ts nterferng cells. The proposed algorthm s operated n the followng way: For any cell, two ters of cells are consdered as nterferng cells (Fg. 1). The channel state nformaton (allocatng or releasng) of each cell s locally exchanged to ts nterferng cells. Every cell mantans a prorty lst of ts avalable channels accordng to ther cost. The lower the cost of a channel, the hgher the prorty of ths channel. The prorty lst s updated (real tme) after a call s accepted or termnated n ts nterferng cells. In order to avod as possble assgnng a cochannel user n the frst ter of nterferng cells, we choose the constant c n (5) as 13. To reduce the aggressveness of the algorthm, f the cost of a channel s hgh than 3 (not more than one cochannel user n the frst-ter cells), the channel s marked n order not to allow ts use for call set-up. When a call arrves n a cell, the hghest prorty (lowest cost) channel s chosen for call set-up probaton. The power control algorthm n Eq. (8) s used to check f ths channel can be assgned to the new call. That s, a plot sgnal s transmtted wth the power controlled by Eq. (8). At the same tme, the receved power of the plot sgnal and nterference are measured to check f ths channel can be accepted for servce. If the SIR s hgher than the predefned value, the channel s used for servce wth ths transmtted power. If the maxmum power s requested, or the teratons of power level adjustment s larger than the allowed value (chosen as 10 here), but the SIR s stll lower than the predefned value, swtch to another channel wth the next hghest prorty for probng, and so on. Actually, an exhaustve searchng scheme s not allowed n real system. Hence, we prescrbe that f four channels have been probed, but the SIR requrement s stll not satsfed, the call s blocked. If a call s n servce, the power control algorthm n Eq. (8) s used to mantan ts qualty. Each base montors ts own served calls at some amount of tme nterval. We assume that all base statons are synchronsed. When a call s SIR falls below the target value, the power control procedure s requested. However, f the maxmum transmtted power s requested or the teratons of power level adjustment are larger than the allowed value, but the SIR s stll below a specfed value, the handover procedure s requested. The call set-up procedure wll begn to search for a channel for handover. If a channel s found, the call s moved to ths channel. Otherwse, the call s dropped. III. SIMULATION MODELS The performance of ths algorthm s nvestgated by smulatons. In these smulatons, the network model s a two-dmensonal regular hexagonal grd wth 81 cells (9 9) (Fg. 1). In order to avod the boundary effect, the left-most and the rght-most columns are neghbours wth each other, and so are the top and the bottom rows. Thus, the results are representatve of an nfnte system, and therefore may be appled to a large network. Around a host cell, only two ters' cells (6 cells n the frst ter and 1 cells n the second ter) are consdered to be nterferng cells. The channel model s assumed as an average pathloss wth an nverse fourth power (α = 4) dstance dependency, and lognormal slow fadng wth zero mean value and a σ= 8 db standard devaton. There are 36 orthogonal channels avalable n the system. The cell radus s 5 km. The maxmum and mnmum transmtted powers are 0 and 0.0 0-7803-3871-5/97/$10.00 1997 IEEE 408
Watts respectvely (30 db range). Assume all channels n all cells have a -10 dbm nose level at the recevers. The threshold value of SIR for assgnng a channel to a new call and the target value of ongong calls both are chosen as γ = 1 db. The threshold value for call droppng s 10 db. Omndrectonal antennas are assumed to be used n the system. The call arrval n each cell s an ndependent Posson process wth unform arrval rate. The duraton of each call s exponentally dstrbuted wth a mean of 10s. Locatons of calls are randomly generated wthn each cell. IV. SIMULATION RESULTS The purpose of ths algorthm s manly to maxmze the number of mobles that can be assgned nto a network and mnmze the call drop rate of on-gong calls. In addton, the effcency of the algorthm s also consdered. If an algorthm acheves lower block probablty by causng ntensve random ntracell call handover, t s stll questonable. Because of the lmtaton of the system processng capacty (ncludng computng, measurng capacty, ect.) n real network, such an algorthm would create hgher probabltes of call block and drop than those from smulatons. To evaluate the system performance, two extra parameters, R h, the ntracell handover rate, and R uh, the unperformed-handover rate, are defned as: R h = number of requests of ntracell handover access number of admtted calls number of unperformed handover calls n successful calls R uh = total number of successful calls The physcal meanng of R h s the average number of ntracell handover accesses caused by admttng a new call. In followng smulatons, the number of call arrvals vares from 175,000 to 18,000 dependng on the traffc load. The SIR of each served call s measured once per second. If the SIR of an on-gong call s deterorated lower than the target value 1 db, the power control procedure s called. If the maxmum transmtted power s requested or the teratons of power level adjustment have been 10, but the SIR s stll below 10 db, the handover procedure s requested. If there s not a qualfyng channel for handover, the call s dropped. The blockng and droppng probabltes for dfferent traffc load (unform) are shown n Fg. 3. The blockng probabltes of fxed channel allocaton (FCA) wth reused sze of three (N = 3) are also shown. We fnd that at the load of approxmately 9.4 Erlangs our scheme performs wth 1% blockng and 1.% droppng probabltes whle FCA shows about 9.7% blockng probablty. The system capacty has acheved qute good mprovement compared wth FCA. The DCA used ths cost-functon n (6) has shown [5] outperformed the frst avalable (FA) and the mnmum SIR (MSIR) DCA schemes (no handover and power control). It has lower droppng and unsuccessful call (blockng and droppng) probabltes. Therefore, ths cost-functon based, DCA algorthm s not so aggressve. The results of handover rate wll gve more support to ths statement. Probabltes of blockng and droppng 10 0 10-1 10 - Total channels = 36 FCA blockng probablty(n=3) Blockng probablty Droppng probablty 10-3 9 10 11 1 13 14 15 Traffc load (Erlangs/cell) Fgure 3. Probabltes of blockng and droppng wth unform traffc loads. Rate 10 0 Intracell handover rate Unperformed-handover rate 10-1 9 10 11 1 13 14 15 Traffc load (Erlangs/cell) Fgure 4. The ntracell-handover rate and unperformed handover rate wth unform traffc loads. The ntracell handover rate s shown n Fg. 4. It vares from 34.3% to 44.1%. The results are very nterestng that the handover rate ntally ncreases wth traffc load ncrement, but for traffc loads over 11 Erlangs t decreases wth the traffc load ncrement. The reason mght be that: the droppng and blockng probabltes ncrease wth the traffc load ncrement; for hgh traffc load, whle the calls n network reach a value, the system controls the call admsson and only those not so aggressve calls are allowed nto network (Fg. 3 shows that there s a crosspont between the curves of the blockng probablty and the droppng probablty). The unperformed handover rate (Fg. 4) gves more evdence for ths explanaton. The unperformed handover rate vares slghtly from 87.5% to 91.4%. It ntally decreases wth ncreasng the traffc load, but for traffc loads over 11 Erlangs t ncreases wth ncreasng the traffc load. Therefore, ths channel allocaton algorthm can adapt to the call saturated state of network and does not cause a seres of call handover. In order to evaluate the speed of call setup, we smulate how many allocated channels (allocated to new calls or handover calls) are from channels wth the hghest prorty (called number 1) and the second hghest prorty (called 0-7803-3871-5/97/$10.00 1997 IEEE 409
number ). Fgure 5 shows the percentage of allocated channels n the locaton of the prorty lst wth dfferent traffc loads. More than 98% allocated channels are from the hghest and next hghest prorty channels. That means that 98% allocated channels, have undergone the set-up probng wth one or two channels after those channels are found to satsfy the SIR requrement. The number of allocated channels from the hghest prorty channels slghtly ncreases at hgh traffc loads. Ths algorthm s desgned to search channels for call set-up from the frst four hghest prorty channels whose cost s not larger than a specfed value, but most of them are from the frst two hghest prorty channels. Hence, ths algorthm performs wth a short call setup tme and at hgh traffc loads the average tme s slghtly shorter than that at low traffc loads. Percentage of allocated channels n the locaton of the prorty lst 100.0% 80.0% 60.0% 40.0% 0.0% 0.0% Number Number 1 4.7% 5.3% 5.0% 4.7% 4.% 3.6% 3.4% 93.3% 93.% 94.7% 95.9% 9.8% 93.9% 95.6% 9 10 11 1 13 14 15 Traffc load (Erlangs/cell) Fgure 5. Percentage of allocated channels n the locaton of the prorty lsts. Number 1 s denoted the hghest prorty channels and number s denoted the next hghest prorty channels. Comparng the performance of our algorthm wth the algorthm whch does not have any prorty channels for call setup probaton and just randomly chooses any free channels. If the chosen channel does not satsfy the SIR requrement, another free channel s randomly chosen to perform the same procedure untl the SIR requrement s satsfed or the call s blocked [4]. Because of the long smulaton tme, we only smulate the latter case at 15 Erlangs traffc load. Even though the latter algorthm has 0.5% blockng probablty and 4.% dropng probablty, the ntracell handover rate s 696% and the unperformed handover rate s 66.3%. That means that average 6.96 ntracell handover accesses are caused by an admtted call; almost 34% successful calls are supported by ntensve handover. In addton, only 7.8% and 10.% allocated channels, have undergone set-up probng wth one and two channels respectvely after those channels are found to satsfy the SIR requrement. Because of the lmted processng capacty n practcal system, such huge ntracell handover mght not be acceptable and must cause much hgher call block and drop probabltes than those from smulated results. Hence, the ntracell handover rate should be a factor to evaluate the performance of an algorthm. In addton, the latter algorthm has a longer call setup tme. V. CONCLUSIONS In ths paper, we have presented a dstrbuted channel access algorthm combnng the channel assgnment and power assgnment. A cost-functon, has been ntroduced to provde some optonal channels accordng to ther cost for transmtted power level searchng. The smulaton results show that ths algorthm largely ncreases the capacty compared wth the fxed channel allocaton (FCA). We fnd that at the load of approxmately 9.4 Erlangs our scheme performs wth 1% call block and 1.% call drop probabltes whle FCA (N=3) gves about 9.7% call block probablty. The proposed algorthm can adapt to the call saturated state of network and does not cause hgh ntracell handover rate. The handover rate vares from 34.3% to 44.1%, and the unperformed handover rate vares slghtly from 87.5% to 91.4%. For traffc loads over 11 Erlangs, the handover rate decreases, and the unperformed handover rate ncreases wth ncreasng the traffc load. Ths algorthm performs wth a short call setup tme and at the hgh traffc load the average tme s even slghtly shorter. 98% allocated calls are set up on the hghest and next hghest prorty channels. Fnally, we suggest that the ntracell handover rate should be a factor n evaluaton of the performance of an algorthm, because too hgh ntracell handover access wll ntensvely ncrease the load of swtch and cause hgher call drop and block probabltes than those we expect. ACKNOWLEDGEMENTS I am very grateful for Prof. Sven-Gustav Häggman to revew and comment the manuscrpt. The project s fnancally supported by Noka Research Centre, Telecom Fnland, Technology Development Centre of Fnland and Helsnk Telephone Company. REFERENCES: [1] Shaoj N and Sven-Gustav Häggman, Dynamc Channel Allocaton Based on SIR Estmaton, n Proc. nd Internatonal Workshop on Mult- Dmensonal Moble Communcaton, Seoul, July 96, pp. 177-181. [] J. Zander, Performance of Optmum Transmtter Power Control n Cellular Rado Systems, IEEE Trans. Veh. Technol., Feb. 199, pp. 57-6. [3] G. J. Foschn and Z. Mljanc, A Smple Dstrbuted Autonomous Power Control Algorthm and ts Convergence, IEEE Trans. Veh. Technol., vol. 4, no. 4, Nov. 1993, pp. 641-646. [4] G. J. Foschn and Z. Mljanc, Dstrbuted Autonomous Wreless Channel Assgnment Algorthm wth Power Control, IEEE Trans. Veh. Technol., vol. 44, no. 3, Aug. 1995, pp. 40-49. [5] Shaoj N, A Cost-Functon Based Dstrbuted Dynamc Channel Allocaton Algorthm, submtted to the 3rd Asa-Pacfc Conference on Communcatons, Sydney, Australa, 1997. 0-7803-3871-5/97/$10.00 1997 IEEE 410