On capacity of OFDMA-based IEEE WiMAX including Adaptive Modulation and Coding (AMC) and inter-cell interference

Transcription

1 1 On capacty of OFDMA-based IEEE WMAX ncludng Adaptve Modulaton and Codng (AMC) and nter-cell nterference Chad Tarhn, Tjan Chahed GET/Insttut Natonal des Télécommuncatons - UMR CNRS rue C. Fourer Evry CEDEX - France {chad.tarhn, tjan.chahed}@nt-evry.fr Abstract We study n ths paper the capacty of the downlnk of OFDMA-based IEEE WMAX system n the presence of two types of traffc, streamng and elastc. We focus n partcular on the mpact of Adaptve Modulaton and Codng (AMC) as well as nter-cell nterference resultng from dfferent frequency reuse schemes. Several performance measures, namely blockng rates, mean transfer tme and the mean number of collsons between two OFDMA WMAX cells, are then derved and quantfed. We show that reuse parttonng results n a lower blockng probablty for streamng flows n the nner regon but a much hgher one for elastc flows n the outer regon; the overall cell throughput ncreases meanng that the decrease n the number of collsons mproves the overall throughput. I. INTRODUCTION WMAX systems are based on versons d and e of the IEEE standard whch defnes a physcal (PHY) and medum access control (MAC) layers for broadband wreless access systems operatng at frequences below 11GHz. The frst of these standards, publshed n 2004, addresses fxed servces whle the second, publshed n 2005, s ntended for moble servces. The IEEE e specfcatons defne three dfferent PHY layers: sngle-carrer transmsson, Orthogonal Frequency- Dvson Multplexng (OFDM), and OFD Multple Access (OFDMA). The multple access technque used n the frst two of these PHY specfcatons s pure TDMA, whle the thrd technque uses both the tme and frequency dmensons for resource allocaton. From these three PHY technologes, OFDMA has been selected by WMAX Forum [1] as the basc technology for portable and moble applcatons. Compared to TDMA, OFDMA leads to a sgnfcant cell range extenson. Ths s due to the fact that the transmt power of the moble staton s concentrated n a small porton of the channel bandwdth whch ncreases the Sgnal-to-Nose Rato (SNR) at the recever. Another nterestng feature of OFDMA s that t eases the deployment of networks wth a frequency reuse factor of 1, thus elmnatng the need for frequency plannng. In wreless communcaton systems, random fluctuatons prevent the contnuous use of hghly bandwdth-effcent modulaton, and therefore Adaptve Modulaton and Codng (AMC) has become a standard approach n recently developed wreless standards, ncludng WMAX. The dea behnd AMC s to dynamcally adapt the modulaton and codng scheme to the channel condtons so as to acheve the hghest spectral effcency at all tmes [2]. Adaptve modulaton changes the codng scheme and/or modulaton method dependng on channel-state nformaton - choosng t n such a way that t squeezes the most out of what the channel can transmt. In OFDMA, modulaton and/or codng can be chosen dfferently for each sub-carrer, and t can also change wth tme. Indeed, n the IEEE standard, coherent modulaton schemes are used startng from low effcency modulatons (BPSK wth codng rate 1/2) to very hgh effcency ones (64-QAM wth codng rate 3/4) dependng on the SNR. It has been shown that systems usng adaptve modulaton perform better than systems whose modulaton and codng are fxed [3]. Adaptve modulaton ncreases data transmsson throughput and the system relablty by usng dfferent constellaton sze on dfferent sub-carrers. In a cellular OFDMA system, adjacent cells usng subcarrers of exactly the same frequency and tme can cause nterference to one another unless nter-cell nterference mtgaton technques are appled. Ths nterference takes the form of collsons, the number of whch ncreases as moble statons get closer to the edge of the cell. To combat ths, a reuse parttonng [4] scheme can be appled and controls the reuse factor n dfferent parts of the cell. In the lterature, several works consdered the capacty of broadband wreless OFDMA-based WMAX systems. In Reference [10] for nstance, work has been done on one regon only wthout takng AMC nto account. In Reference [11], focus was mostly on nterference n a mult-cell settng wthout reuse parttonng. In ths work, we focus on the capacty of OFDMA-based WMAX systems consderng both ntra-cell AMC and nter-cell collsons n the presence of two types of traffc, constant-bt-rate streamng flows, such as voce, and elastc data ones whch are governed by TCP at the transport layer, wth and wthout reuse parttonng. II. PHYSICAL LAYER IN WIMAX A. OFDMA sub-carrer allocatons OFDMA s a multple access technque whch dvdes the total Fast Fourer Transform (FFT) space nto a number of sub-channels (set of sub-carrers that are assgned for data exchange) whereas the tme resource s dvded nto tme slots

2 (.e. n WMAX OFDMA PHY [3], the mnmum frequencytme unt of sub-channelzaton s one slot, whch s equvalent to 48 sub-carrers) and a frame s constructed by a number of slots. Let N denote the total number of sub-carrers of all types, plots, guard and data, (and whch s equal to the sze of the FFT) and let N denote the total number of data subcarrers after reservng the plot and guard sub-carrers whch we dvde nto L groups, each wth K = N /L data subcarrers. In OFDMA-based WMAX system, resource allocaton s done n tme-frequency doman: a call may share a sub-channel wth other users. Ths s llustrated n Fgure 1 where users 2, 3, 4 and 5 occupy each one sub-channel half of the tme whle user 1 occupes one sub-channel all the tme. Wth OFDMA, the user devce could choose sub-channels based on geographcal locaton wth the potental of elmnatng the mpact of deep fades. Frequency Fg. 1. K 2 1 User 4 User 2 Tme User 5 User 5 User 3 User 4 User 3 fram e Slot User 2 Subchannel Tme-frequency resource allocaton n OFDMA WMax system B. AMC and cell decomposton In ths work, and wthout loss of generalty, we study AMC n the presence of path loss only whch we characterze by a certan value ξ; hgh effcency modulaton s used for users where ξ ξ, correspondng to a large SNR 1. Ths results n the dvson of the cell nto r regons, =1...r (see Fgure 2), whch we assume to be concentrc crcles of radus R for smplcty, but mght be of dfferent topology f we take nto account other phenomena, such as fast-fadng. In each regon, users have the same modulaton scheme and experence thus a correspondng bt rate whch decreases as users get further from the base staton. To calculate the area covered by each modulaton scheme, we must determne the maxmal dstance R between Base Staton (BS) and users usng a correspondng modulaton. Ths dstance s determned usng the maxmal SNR a user should receve wthout data loss. Dfferent values of receved SNR for dfferent modulaton/codng schemes have been calculated n Reference [6] and are shown n Table I (frst three columns). We shall now use them to calculate R. 1 Please note that, for the tme beng, only the SNR matters, and not SINR, the Sgnal to Interference plus Nose rato, as we now nvestgate the case of one cell n solaton. Later n the text, the multple-cell settng wll arse along wth underlyng nterference and SINR. Fg. 2. 2R 3R 4R BS 1R 1S 64-QAM 16-QAM QPSK BPSK Cell decomposton nto regons 2S S S 3 4 The path loss for the free space model s gven by [8]: λ PL [db] = 10log[G E G R ( 4πR ) 2 ] = 10logG E 10logG R +20log( 4πR λ ) (1) where G E s the emtter antenna gan, G R s the recever antenna gan, R s the dstance between the emtter and the recever and λ s the wavelength. Ths path loss s also equal to: PL [db] = P E [dbm] SNR[dB] N[dBm] (2) where P E s the emtted power and N s the thermal nose (n unts of decbels) whch s equal to: N[dBm] =10log(τTW) (3) τ = watt/k Hz s the Boltzmann constant, T s the temperature n Kelvn (T = 290) and W s the transmsson bandwdth n Hz. Usng the above equatons, we can calculate the relatonshp between the dstance and the SNR as follows: R = λ 10 PE [dbm]+10log(ge )[db]+10log(gr)[db] SNR[dB] N[dBm] 20 4π (4) The area of each regon S s gven by: S = π (R 2 R 2 1) where R 0 =0. For the sake of llustraton, let us consder the followng example based on the lcensed band for WMAX to outdoor use n France whch starts at a frequency of 3.4GHz and whch has system bandwdth equal to 20MHz. At ths bandwdth, the thermal nose s equal to dBm. Accordng to the maxmum allowed Effectve Isotropc Radated Power (EIRP) of 1W, where the emtters are assumed to have an emsson power P E of 1W for users. We consder the case of antennas n BS and user equpment wthout gan. In Fgure 3, we represent the dstance assgned to SNR for swtchng ponts. The proporton of each surface area per PHY assumpton s determned and shown n n Table I.

3 BPSK 1/2 QPSK 3/4 16 QAM 1/2 16 QAM 3/4 64 QAM 2/3 64 QAM 3/4 on the bass of Processor Sharng (PS) [9]. The number of sub-channels L e allocated to an elastc call n regon S s thus gven by: L e = L r =1 Ls ns r (6) =1 ne Recever SNR[dB] x ndcates the largest nteger that s less than or equal to x. n s and ne are the number of streamng and elastc flows n regon S. Fg cell radus [m] Receved SNR functon of the dstance Modulaton Codng rate Recever SNR(dB) Surface [%] BPSK 1/ / QAM 1/ / QAM 2/ / TABLE I IEEE PHY ASSUMPTIONS C. Throughput of the cell s,e The nstantaneous physcal bt rate R of streamng or elastc users n regon S s gven by: R s,e = Ls,e K C log 2 (M) (1 BLER) T s S c (5) = L s,e K B E (1 BLER) where L s,e s the number of sub-channels to be assgned to streamng/elastc users n regon S, K s the number of data sub-carrers assgned to each sub-channel, C s the codng rate of the M-ary modulaton, T s s the OFDMA symbol duraton gven by: T s = T b + T g wth T b the useful symbol perod (n unts of mcroseconds) N gven by W n and T g the guard perod equal to G T b, W s the bandwdth (MHz), n s the samplng factor, G s the rato of cyclc prefx (CP) to useful tme, S c s the sector coeffcent (S c s equal to 1 n FUSC and 3 n PUSC 3 sectors), B s the baud rate (symbols/sec), E s the effcency of the modulaton (bts/symbol) n each regon S and BLER s the perceved Block Error Rate 2. Now, streamng flows have constant-bt rates, and so they are assgned a gven number of sub-channels L s per regon. As of (TCP-based) elastc calls, snce they tolerate reducton n ther throughput, they wll smply share the left over capacty 2 Note that for each value of SINR, we can determne a couple of values (E,BLER) and these values are determned by lnk level curves E = f(sinr) and BLER = g(sinr) III. MARKOVIAN MODELING We assume that streamng calls arrve to regon S accordng to a Posson process wth ntensty λ s and use L s subchannels for an exponentally dstrbuted tme wth mean 1/µ s ndependent of the share of the resources they get. We also assume that elastc flows arrve to the system accordng to a Posson process wth ntensty λ e and assume for tractablty that ther servce rate s exponentally dstrbuted wth mean µ e = Re E[Z] where E[Z] s the mean fle sze 3. A. Transton matrx Let us focus now on one cell. We can model our system as a Contnuous Tme Markov Chan (CTMC) by takng nto account the proposed prortes for the ntegraton of streamng and elastc flows as well as the way they share resources. The state s characterzed by the followng row vector: n := (n s 1,n s 2,..., n s r,n e 1,n e 2,..., n e r) where n s and n e, for = 1...r, represent the number of streamng and elastc calls n regon S, respectvely. The state space of the system s gven by: S := { r n N 2r (L s n s + L e n e ) L} (7) =1 where L s and Le denote the number of sub-channels allocated to streamng and elastc calls n regon S respectvely and L s the maxmum number of sub-channels n the cell. We now determne the steady-state probablty vector Π= {π( n ) n S }. Note that the correspondng system s non homogeneous as the departure rate of elastc calls depends on the overall number of calls n the system whereas streamng calls do not. The soluton of the steady-state dstrbuton s obtaned by solvng the set of lnearly ndependent equatons gven by: Π Q =0 n S π( (8) n )=1 To construct the transton matrx Q, we must consder all possble transtons between neghborng states. Let q( n n ) denote the transton probablty from state n to neghborng states n. Note that when we accept a new call n regon S, 1 r the state s noted by n s,e and when a call + 3 In fact, the total length of an elastc flow n unts of packets s found to follow a log normal dstrbuton, accordng to the measurement-based modellng [7]

4 termnates the servce the next state s n s,e. We thus have the followng transton rates: q( n n s )=λ s + q( n n s )=n s µs q( n n e )=λ e (9) + q( n n e )= ne µe ( n ) E[Z] and the values q( n n ) must be obtaned as the sum of all terms n each lne n matrx Q s equal to zero for 1 r. B. Performance measures Based on the steady-state probabltes of our CMTC, we now determne the performance measures relatve to our model. 1) Blockng probablty: The call blockng probabltes of both types of flows, B s and Be n regon S, are obtaned by summng up the steady state probablty of saturaton states: B s,e = π( n ) (10) n S s,e where S s,e s the subset of states n S for whch any new call of class- s blocked when arrvng to the system due to lack of resources. Formally, S s,e := { r n S (L s kn s k + L e kn e k)+l s,e >L} k=1 2) Mean transfer tme: The mean transfer tme of class- elastc flows can be calculated from the Lttle s formula by: n T e = λ e (1 Be ) (11) where n e s the mean number of elastc flows n regon S. IV. REUSE PARTITIONING IN OFDMA WIMAX A. Reuse parttonng Frequency reuse s the technque of ncreasng data capacty wthout compromsng range. In the smplest case, the avalable channel s subdvded nto groups, and the channel frequences n each group are assgned to a cell wth adjacent cells operatng at dfferent frequency sub-channels n order to maxmze spectral effcency. When a frequency reuse of one s used all cells operate on the whole frequency band. In a frequency reuse 3 scheme, each cell s allocated a thrd of the frequency band, and a 3-cell pattern s used. The frst method suffers from the degradaton n the qualty of connecton due to CoChannel Interference (CCI), whle n the second method capacty s also reduced as a cell can only use a thrd of the total frequency band. To combat ths, and to mprove the spectral effcency of cellular systems, a reuse parttonng scheme [4] can be appled. Ths means that a dynamcal repartton of the bandwdth s appled between dfferent nterferng and non-nterferng regons n the cell. In ths secton, we apply ths reuse parttonng concept to OFDMA WMAX (see Fgure 4) and derve next the mpact of ths reuse parttonng on the number of collsons n the cell n avodng nterference at the cell edges. of L1I and L1E Fg. 4. Cell 1 Cell 2 L1I L1E collson zone (a) of L2I and L2E L 2 I L 2 E of L1I Cell 1 Cell 2 L1I L1E of L1E collson zone (b) L 2 I L 2 E of L2I of L2E Cell plannng (a) wthout and (b) wth frequency reuse parttonng B. Collsons There are several approaches as how to dstrbute avalable sub-carrers to sub-channels. The smplest one conssts of pckng randomly sub-carrers from avalable ones such that any avalable sub-carrer has the same probablty to get allocated to an arrvng user. We refer to ths method as random allocaton of sub-carrers whch does not requre any coordnaton between cells. Other allocaton algorthms, such as based on frequency selectvty, are possble. We however restrct our focus n ths work to random ones so as to hghlght best the generc performance of OFDMA based systems. In the case of two cells, the followng lemma establshes the mean number of collsons when the number of occuped sub-carrers s (L K1) and (L K2) n cell 1 and cell 2 respectvely. Lemma 1: The mean number of collsons n L subchannels s gven by: E[C K1,K2] = L E [C K1,K2] (12) where E [C K1,K2] s the mean number of collsons n one group of sub-carrers and s n turn gven by: c max E [C K1,K2] = c Pr(c K1,K2) (13) c=c mn Pr(c K1,K2) beng the probablty of havng c collsons n ths group and s equal to: ) K1 c ( N/L )( N/L c n1c=0 c n1c K2 c ( N/L )( N/L c c n1c cmax c=c mn K1 c n1c=0 K2 c ) (14) c s the number of colldng sub-carrers. It belongs to {c mn : c max } wth and c mn = max(0,k1+k2 N/L) c max = mn(k1,k2,n/l) and n1c s the number of non-colldng sub-carrers n cell 1; n1c {0:K1 c}.

5 Proof: Let K denote the number of occuped subcarrers n each group of N/L sub-carrers n cell. Recall that c s the number of collsons n each group; t ranges between above-mentoned c mn and c max. The probablty of havng c collsons n ths group of subcarrers s equal to the rato between the number of possble allocatons such that the number of colldng sub-carrers s c to the total number of possble allocatons. Collsons are possble n the group of (N/L) sub-carrers, whch mples that we have ( ) N/L c possble combnatons for collsons n the collson zone of cell 1 and ( ) N/L c n1c possble combnatons for non-colldng sub-carrers n the same cell. Knowng that cell 1 has chosen a gven set of K1 sub-carrers, the number of possble combnatons for the non-colldng subcarrers n cell 2 s equal to: ( ) N/L c n1c K2 c. The number of possble allocatons such that we have c colldng sub-carrers s then the product of ( )( N/L N/L c ) c n1c K2 c over all possble combnatons of non-colldng sub-carrers. Now, the total number of possble allocatons s then the summaton over all possble combnatons : cmax ( N/L )( N/L c ) c=c mn c n1c K2 c. The probablty of havng c collsons s then gven by Eqn. (14). The expected number of collsons n one group s then obtaned by Eqn. (13). Based on the collsons n each of the L groups, the total number of collsons C n the total channel (bandwdth) s gven by: C = L =1 c. These collsons beng ndependent and the groups dentcal, we obtan the mean number of collsons n Eqn. (12). Lemma 2: The mean number of collsons n the system s equal to [11]: E[C] = K1,K2 =1 2 ( Π (K ))E[C K1,K2] (15) where E[C K1,K2] s gven from Equaton (12) and Π (K ) = n S π( n )Pr(K n ) s the probablty of havng LK sub-carrers n cell. V. NUMERICAL RESULTS We now present some numercal results obtaned by the smulaton of our flow model when appled to an OFDMA system wth an FFT sze of 1024 sub-carrers and consderng wthout loss of generalty 2 regons wth AMC respectvely 16-QAM 3/4 (E 1 =3bt/symbol) and (E 2 =1bts/symbol). These parameters of effcency corresponds to the transmsson modes wth convolutonally coded modulaton [12]. Moreover, let L =5; L s 1 = L s 2 =1; λ s =0.01; λe =0.01; µ s =0.02; BLER =0; E[Z] = 500Kb. Based on Equaton (5) and usng a baud value B = 2666symbol/sec and K = 48, R1 s = 128Kbps, R2 s = 384Kbps. We frst start wth the case of a sngle cell where the number of sub-carrers s the same n the outer and nner regons,.e., wthout reuse parttonng. Fgures 5 and 6 show the blockng probablty for, respectvely, streamng and elastc flows as a functon of an ncreasng arrval rate of streamng flows. And ths for the two Blockng probablty of streamng flows Fg. 5. Blockng probablty of elastc flows Fg x Blockng probablty for streamng flows n two regons Blockng probablty for elastc flows n two regons regons, the nner one (labeled 16-QAM 3/4) and the outer one (labeled ). We observe n terms of blockng that we have only one class for streamng flows n the nner and outer regon. Data flows however are elastc and share capacty among themselves n a far manner on the bass of processor sharng. Ths makes them obtan the same blockng rate. They however obtan dfferent mean transfer tmes n each regon correspondng to the bt rate they acheve theren, as shown n Fgure 7. We next turn to the case when reuse parttonng s enabled. Wth respect to Fgure 4, the number of sub-channels n the nner regon L1I remans unchanged whereas ther number n the outer regon s decreased, L1E =4. Ths decrease n the number of sub-channels n the outer regon leads to new blockng probabltes for both types of traffc as shown n Fgures 8 and 9 for, respectvely, streamng and elastc flows as a functon of an ncreasng arrval rate of streamng flows for the two regons, nner and outer. For streamng flows, the blockng probablty n the nner regon decreases as flows n ths regon have now access to all sub-channels whereas flows n the outer regon do not. The latter have thus hgher blockng. For data flows however, both

6 Mean transfer tme for elastc calls (s) Blockng probablty of elastc flows Fg. 7. Mean transfer tme for elastc flows n two regons Fg. 9. Blockng probablty for elastc flows wth reuse parttonng x Blockng probablty of streamng flows Overall cell throughput Wthout reuse parttonng Wth reuse parttonng Fg Blockng probablty for streamng flows wth reuse parttonng 2 Fg Overall cell throughput blockng rates, nner and outer, ncrease wth respect to the case wth no frequency reuse, as more streamng flows are now accepted; wth a hgher ncrease n the outer rng as less sub-channels are now avalable. Now, the mean number of collsons n the system s equal to 10 2 wthout reuse parttonng and half that when reuse parttonng s enabled. And so, one would expect a hgher overall throughput for the cell. Ths s the case, as shown n Fgure 10, and whch means that the decrease n the number of collsons when reuse parttonng s enabled mproves the overall throughput. VI. CONCLUSION In ths paper, we consdered the calculaton of capacty of the downlnk of OFDMA-based IEEE WMAX systems, focusng on the effect of AMC as well as reuse parttonng and underlyng collsons n the case of more than one cell. And ths, for two types of flows, constant-bt-rate streamng and elastc data. Our next step shall be on QoS ssues, especally for streamng traffc whch suffers from degraded performance as users get away from the base staton n the case of moblty. REFERENCES [1] [2] A. Molsch, Wreless Communcatons, IEEE Press, [3] H. Yaghoob, Scalalable OFDMA Physcal Layer n IEEE WrelessMAN, Intel Technology Journal, pp , August [4] M.Johansson, Dynamc Reuse Parttonng Wthn Cells Based on Local Channel and Arrval Rate Fluctuatons, Techncal Report, Uppsala Unversty, Sweden, [5] IEEE , Part 16: Ar Interface for Fxed and Moble Broadband Wreless Access Systems, IEEE Standard for local and Metropoltan Area Networks, February [6] IEEE , Part 16: Ar Interface for Fxed Broadband Wreless Access Systems, IEEE Standard for local and Metropoltan Area Networks, October [7] A. B. Downey, The structural cause of fle sze dstrbutons, ACM SIGMETRICS Performance Eval. Rev., vol. 29, pp , June [8] G. L. Stuber, Prncples of Moble Communcaton, 2nd ed. Norwell, MA:Kluwer, [9] N. Benameur, S. Ben Fredj, F. Delcogne, S. Oueslat-Boulaha and J.W. Roberts, Integrated Admsson Control for Streamng and Elastc Traffc, QofIS 2001, Combra, September [10] C. Tarhn, T. Chahed, System capacty n OFDMA-based WMAX, ICSNC 2006, Taht, November [11] S-E. Elayoub, B. Foureste and X. Auffret, On the capacty of OFDMA systems, ICC 2006, Istanbul, June [12] Q.Lu, S.Zhou, G.B.Gannaks, Queung wth Adaptve Modulaton and Codng over wreless lnks: Cross-Layer analyss and desgn, IEEE transactons on wreless communcatons, vol.4, NO.3, May 2005.