Downloae from orbittuk on: Oct 2, 218 Erlang Capacity of Multi-class TDMA Systems with Aaptive Moulation an Coing Wang, Hua; Iversen, Villy Bæk Publishe in: Proceeings of IEEE ICC 28 Link to article, DOI: 1119/ICC283 Publication ate: 28 Document Version Publisher's PDF, also known as Version of recor Link back to DTU Orbit Citation APA: Wang, H, & Iversen, V B 28 Erlang Capacity of Multi-class TDMA Systems with Aaptive Moulation an Coing In Proceeings of IEEE ICC 28 pp 115-119 IEEE DOI: 1119/ICC283 General rights Copyright an moral rights for the publications mae accessible in the public portal are retaine by the authors an/or other copyright owners an it is a conition of accessing publications that users recognise an abie by the legal requirements associate with these rights Users may ownloa an print one copy of any publication from the public portal for the purpose of private stuy or research You may not further istribute the material or use it for any profit-making activity or commercial gain You may freely istribute the URL ientifying the publication in the public portal If you believe that this ocument breaches copyright please contact us proviing etails, an we will remove access to the work immeiately an investigate your claim
This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 28 proceeings Erlang Capacity of Multi-class TDMA Systems with Aaptive Moulation an Coing Hua Wang an Villy B Iversen Department of Communications, Optics & Materials Technical University of Denmark, Lyngby, Denmark Email: huw, vbi@comtuk Abstract Erlang capacity is traitionally efine as the maximum value of offere traffic among ifferent service classes that the system can support when the blocking probabilities at the call amission control CAC level o not excee certain threshols That is vali when a fixe amount of banwith is allocate to each user in each frame uring the whole service time However, with the introuction of aaptive moulation an coing AMC scheme employe at the physical layer, outage might occur ue to the fact that the allocation of banwith is ynamic base on the time-varying wireless channel conitions In this paper, we evaluate the Erlang capacity of a TDMA system with AMC supporting voice an ata traffics, by taking both the blocking an the outage probabilities into account The analytical moels for calculating the blocking an the outage probabilities are evelope separately, an a joint algorithm for etermining the Erlang capacity of the system is propose with some numerical examples I INTRODUCTION Future generation wireless communication systems are evolving to provie a wie range of services, incluing voice, ata an multi-meia applications, with ifferent quality of service QoS requirements, such as elay an throughput The economical usefulness of a system is effectively measure by the Erlang capacity, which is generally efine as the maximum traffic loa that the system can support with a certain blocking probability requirement Many moels have been propose at separate layers, such as the Rayleigh, Rician an Nakagami faing moels at the physical layer [5][7], an queuing moels at the ata link layer [4] In traitional channelize multiple access systems, eg, TDMA an FDMA, each user is assigne a fixe amount of banwith uring the whole service time, an the Erlang capacity can be easily obtaine by using the well-known Erlang-B formula However, traitional queuing moels o not consier the time-varying nature of wireless channels ue to multipath faing an Doppler shift Unlike wire networks, even if large banwith is allocate to a certain wireless connection, the QoS requirements may not be satisfie when the channel experiences eep faes In orer to enhance the spectrum efficiency while maintaining a target packet error rate PER over wireless links, aaptive moulation an coing AMC scheme has been wiely aopte to match the transmission rate to time-varying channel conitions With AMC, the allocation of banwith to each user is no longer eterministic ie, a fixe amount of banwith, but in a ynamic behavior Therefore, the calculation of the Erlang capacity shoul take both the call amission control CAC moule at the ata link layer as well as the AMC moule at the physical layer into consierations An analytical moel to investigate the performance of transmissions over wireless links is evelope in [1], where a finite-length queuing is couple with AMC However, the author only concentrates on a single-user case Reference [2] calculates the Erlang capacity of WiMAX systems with fixe moulation scheme, where two traffic streams, streaming an elastic flows, are consiere In this paper, we investigate the Erlang capacity of multi-user multi-class TDMA Systems uner the joint effect of CAC an AMC, by coupling the analysis of the blocking probability an the outage probability We first present analytical moels to calculate the blocking an the outage probabilities respectively Base on that, a joint algorithm to etermine the Erlang capacity of the system is propose The Erlang capacity in this paper is efine as the maximum traffic loa among ifferent service classes that the system can support when both the blocking an the outage probabilities o not excee certain threshols The rest of the paper is organize as follows In Section II, we introuce the system moel an the call amission control policy In Section III, analytical moels for calculating the blocking an the outage probability with AMC are presente together with the joint algorithm Numerical results are shown in Section IV Finally, a conclusion is rawn in Section V II SYSTEM MODEL We consier an infrastructure-base wireless access network, where connections are establishe between base station BS an mobile stations MSs Two types of services, voice service an ata service, are supporte by the system Voice service is not tolerant to packet elay, thus requires a constant bit rate Data service is more elastic in terms of being able to vary the transmission rate accoring to the channel conitions, but also requires a minimum throughput At the physical layer, the ata is transmitte frame by frame, where each frame is comprise of a fixe number of time slots, each of which contains a fixe number of symbols In the ownlink, the transmission to ifferent users is scheule on a time-ivision multiplexing TDM fashion, while time-ivision multiple access TDMA is applie in the uplink Aaptive moulation an coing scheme is employe at the physical layer, where multiple transmission moes are available, with each moe representing a pair of specific moulation format 978-1-4244-275-9/8/$25 28 IEEE 115 Authorize license use limite to: Danmarks Tekniske Informationscenter Downloae on November 6, 29 at 1:27 from IEEE Xplore Restrictions apply
This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 28 proceeings an a forwar error correcting FEC coe The transmission moe is etermine by the instantaneous signal-to-noise ratio SNR We assume that the channel is frequency flat, an remains constant within a frame, but may vary from frame to frame Furthermore, we assume that the BS has perfect knowlege of channel state information CSI of each user Base on these assumptions, the AMC scheme ajusts its transmission moe on a frame-by-frame basis Voice an ata users arrive at the cell in a ranom orer The CAC moule ecies whether an incoming call shoul be amitte or not To prioritize voice service, CAC reserves a fixe amount of banwith eicate for voice users, an allows both voice an ata users to compete for the remaining banwiths Let K enote the total number of time slots in a frame for ata transmissions, of which K time slots are reserve for voice users only Let n v,n enote the number of amitte voice users an ata users in the cell, respectively Each voice user is allocate time slots per frame on average to ensure a constant bit rate, an each ata user is allocate at least time slots per frame on average to guarantee a minimum throughput The remaining time slots can be allocate to ata users on eman to increase their throughput Uner the above conitions, the state space of the system is given by: subject to: S := n v,n N N 1 n v n K n K K III ANALYSIS MODELS In this section, we first evelop an analytical moel base on multi-imensional loss systems [4] to calculate the state space an the blocking probability of each traffic stream Then, given the istribution of the number of voice an ata users amitte in the system, the outage probability cause by AMC can be erive by analyzing the stochastic moel of ifferent transmission moes Finally, a joint algorithm for etermining the Erlang capacity of the system is propose A Analysis of Blocking Probability We use the BPP Binomial, Poisson & Pascal traffic moel in our analysis [4] This moel is insensitive to the service time istributions, thus is very robust for applications Each traffic stream i is characterize by the offere traffic A i,the peakeness Z i an the number of channels c i neee for establishing one connection The offere traffic A i is usually efine as the average number of call attempts per mean holing time Peakeness Z i is the variance/mean ratio of the state probabilities when the system capacity is infinite, an it characterizes the arrival process For Z i =1,wehavea Poisson arrival process, whereas for Z i < 1, we have a finite number of users an more smooth traffic Engset case For Z i > 1, it correspons to a more bursty Pascal arrival process In this paper, we assume that voice users arrive following the Engset case with a limite number of S sources Each source switches between the states of ile an busy, which are both exponentially istribute with intensity v an µ v, respectively Thus the arrival process of voice users is a state epenent stochastic process with arrival intensity λ v i =S i v, where i is the number of busy voice users at a given point of time The offere traffic of voice users is equal to v vµ v A v = S an the peakeness is equal to Z v =1 A v /S Data users arrive accoring to a Poisson process with arrival intensity λ, offere traffic A, an peakeness Z =1 The call-level characteristics of multi-class voice/ata TDMA systems with the CAC policy escribe in Section II can be moele by a two-imensional Continuous Time Markov Chain CTMC shown in Figure 1, where state i, j represents the number of time slots occupie by voice users an ata users, respectively As it is a reversible Markov process an has prouct form, the numerical evaluation can be one by using the convolution algorithm [4] 2 n 2 j i, j blocking for stream 1 blocking for stream 2 i n 1 n 1 ij =n Fig 1 Structure of the state transition iagram for two-imensional traffic processes with class limitations When calculating the equilibrium probabilities, state i, j can be expresse by state i, j 1 an recursively by state i,, i 1,, an finally by, [4] The probability of having a voice users an b ata users in the system can be represente as: qn v = a P n v = a = i Ω v qn v = i a Ω v 2 qn = b P n = b = i Ω qn = i b Ω 3 where Ω v an Ω are the sets of possible number of voice an ata users in each service class, x enotes the largest integer not exceeing x Ω v :=, 1,, K Ω :=, 1,, K K 4 qn v an qn are the relative state probabilities, calculate as follows: p v a K K p j if a K qn v = a = p v a K a p j if a> K K bc qn = b =p b p v j 5 116 Authorize license use limite to: Danmarks Tekniske Informationscenter Downloae on November 6, 29 at 1:27 from IEEE Xplore Restrictions apply
This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 28 proceeings P v block = P block = K cv i= K K i= 1 K cv i= K cv λ v i p vi K K p j λ p i p v K i c K K i= λ v i p vi p K i cv K cv λ v i= K cv 1 i p vi K i p j λ p K K K K K c p v j λ p i K i p v j 8 9 where p v an p are the state probabilities of each traffic stream as if it is alone in the system: p v i = S S i i α i 1 α j Ωv S j α j 1 α if i Ω S j v 6 p v = else where α =1 Z v p i = p = A i i! if i Ω A j j Ω j! else Base on the state probabilities, the close-form of the call blocking probability of each traffic stream can be obtaine by using the convolution algorithm, shown in Eqn 8 & 9 B Analysis of Outage Probability In AMC scheme, the moulation moe an coing rate is chosen epening on the time-varying channel conitions As a consequence, the number of time slots allocate to each user is varying on a frame by frame basis Outage is efine to occur when the total number of time slots require by the amitte users excees the total available time slots 1 AMC: For flat faing channels, we aopt the general Nakagami-m moel to escribe the receive signal-to-noise ratio SNR statistically, which is a ranom variable with Gamma probability ensity function [1]: p = mm m 1 m Γm exp m 7 1 where := E[] is the average receive SNR, Γm := t m 1 exp tt is the Gamma function an m is the Nakagami faing parameter m 1/2 The esign objective of AMC is to maximize the ata rate by ajusting the transmission parameters accoring to channel conitions, while maintaining a prescribe packet error rate PER P Let N enote the total number of transmission moes available N =5in this paper Assuming constant power transmission, we partition the entire SNR range into N 1 non-overlapping consecutive intervals with bounaries enote as n N1 n=1 Specifically, moe n is chosen when [ n, n1 Therefore, moe n will be chosen with probability: n1 P r n = n Γ = m, mn p Γ Γm m, mn1 11 where Γm, x := x tm 1 exp tt is the complementary incomplete Gamma function The close-form of the average PER corresponing to moe n is obtaine as [1]: PER n = 1 n1 a n exp g n p 12 P r n n where a n, g n are the moe epenent parameters shown in Table I The algorithm for etermining the threshol n N1 n=1 with the prescribe PER P is escribe in etails in [1] Moe 1 Moe 2 Moe 3 Moe 4 Moe 5 Moulation BPSK QPSK QPSK 16QAM 64QAM Coing rate 1/2 1/2 3/4 3/4 3/4 R n bits/sym 5 1 15 3 45 a n 2747229 92512 676181 533987 35358 g n 79932 34998 16883 3756 9 pnb 15331 1942 39722 12488 159784 TABLE I TRANSMISSION MODES WITH CONVOLUTIONALLY CODED MODULATION [1] 2 Outage Probability: Assume that there are G v voice users an G ata users amitte in the system, respectively Each user has an ON/OFF activity moel, represente by a ranom variable ξ, with probability P ξ v =1=α v for voice users, an P ξ =1=α for ata users We further assume that voice users require a constant bit rate of R v bits per frame, an ata users require a minimum throughput of R bits per frame Hence, the total amount of require banwith in terms of time slots per frame is given by: G v G Z = ξ v,i N v,i ξ,j N,j 13 i=1 j=1 where ξ v,i an ξ,j are the activity factors for the i th voice user an the j th ata user, respectively G v an G are ranom variables representing the number of voice an ata users amitte in the system N v,i an N,j enote the number of time slots require by the i th voice user an the j th ata user 117 Authorize license use limite to: Danmarks Tekniske Informationscenter Downloae on November 6, 29 at 1:27 from IEEE Xplore Restrictions apply
This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 28 proceeings respectively, epening on the current channel conitions R v N v,i N v, N v :=, n =,,N sr n R 14 N,j N, N :=, n =,,N sr n where s is the fixe number of symbols per time slot, R n enotes the number of bits carrie per symbol in transmission moe n shown in Table I, an x enotes the smallest integer larger than x N v,i an N,j are ranom variables with probability mass function: P N v,i = R v =Pr n n =,,N sr n P N,j = R 15 =Pr m m =,,N sr m Since Z is a sum of ranom variables, we can approximate Z to be a Gaussian ranom variable by applying the central limit theorem Therefore, the outage probability of the system can be approximate by: K E[Z] P outage =P r Z>K Q 16 VarZ It is assume that N v,i, N,j, ξ v,i an ξ,j are inepenent an ientically istribute ranom variables Furthermore, ξ v,i, ξ,j, N v,i an N,j are inepenent of each other G v an G follow probability mass function shown in Eqn 2 & 3, respectively The mean an variance of Z are given by: E[Z] =E E[Z G v,g ] 17 = E[G v ]E[ξ v ]E[N v ]E[G ]E[ξ ]E[N ] Var[Z] =E V [Z G v,g ] V E[Z G v,g ] = E[G v ] E[ξv]E[N 2 v 2 ] E 2 [ξ v ]E 2 [N v ] E[G ] E[ξ]E[N 2 2 ] E 2 [ξ ]E 2 [N ] V [G v ]E 2 [ξ v ]E 2 [N v ]V [G ]E 2 [ξ ]E 2 [N ] 18 C Calculation of Erlang Capacity The Erlang capacity in this paper is efine as the maximum value of offere traffic in each traffic stream A v, A that the system can support when the blocking probability an the outage probability o not excee certain threshols From the analytical moels evelope in the previous two subsections, we note that the blocking probability is etermine by the traffic loas A v, A an the average number of time slots occupie per connection,, which epen on the outage probability On the other han, the outage probability is etermine by the istributions of the number of voice an ata users G v, G, which epen on the blocking probability Therefore, the analytical moels of the blocking an the outage probabilities are tightly couple In this subsection, we propose a joint algorithm to calculate the Erlang capacity of multi-class TDMA systems with AMC Change A v, A Y v Calculate Pblock, Pblock, Gv, G Fig 2 Initialize cv, c, A, A Calculate v P outage Poutage meets requirement? Y v Recor P block, P Change the offere traffic? N block Extract Erlang Capacity Region N A v, A Increase cv, c Decrease cv, c Y Poutage > Preq Flow chart of the propose joint algorithm The joint calculation algorithm consists of iterations of two steps In the first step, given the traffic loas of voice users an ata users A v, A, the blocking probabilities are obtaine such that the outage probability requirement P outage is satisfie Specifically, the propose algorithm first sets the initial values of = E[N v ] an = E[N ], which are the average number of time slots neee for establishing one connection of voice an ata services, respectively, an calculates the user istributions, the blocking probabilities, an the outage probability by using Exp 2, 3, 8, 9 & 16 Then it checks whether P outage meets its requirement or not at the current values of an The values of an are increase if P outage is larger than the threshol, an are ecrease otherwise Unless P outage meets its requirement, an are further increase or ecrease Once P outage is satisfie, the blocking probabilities are recore uner given traffic loas Then the values of A v, A are moifie an the above proceure is repeate After we got the blocking probabilities uner various traffic loas, the algorithm procees to the secon step, where the Erlang capacity region is obtaine by extracting the maximum values of A v, A that meet both requirements of blocking an outage probabilities The flow chart of the joint algorithm is shown in Fig 2 IV NUMERICAL RESULTS In this section, we present some numerical results base on the analytical moels evelope in Section III The system parameters are liste in Table II We set the target outage probability to be 2%, which is usually consiere to be an acceptable QoS requirement Fig 3 shows the outage probability versus ifferent traffic loas of voice an ata services in Erlangs We can see N 118 Authorize license use limite to: Danmarks Tekniske Informationscenter Downloae on November 6, 29 at 1:27 from IEEE Xplore Restrictions apply
This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 28 proceeings Parameter Banwith Frame uration Value 1 MHz 1 ms Number of time slots in the ownlink, K 8 Number of symbols per time slot, s 4 Reserve time slots for voice users, K 1 Nakagami faing parameter, m 1 Average SNR, Target PER, P Constant bit rate for voice users, R v Minimum bit rate for ata users, R 15 B 1 4 64 bits/frame 128 bits/frame Voice activity factor, ξ v 4 Data activity factor, ξ 6 Peakeness of voice traffic, Z v 5 Peakeness of ata traffic, Z 1 TABLE II SYSTEM PARAMETERS USED FOR THE NUMERICAL EVALUATION from the figure that our propose algorithm can well keep the outage probability aroun the preefine threshol uner various traffic loas This is achieve by properly ajusting the values of,, which in tern changes the istribution of the number of voice an ata users in the system A two imensional Erlang capacity region at 2% blocking probability is shown in Fig 4 over ifferent outage probabilities an over ifferent bit rates of ata users We can see in all scenarios that the increase of ata traffic will severely reuce the capacity for voice users, an this phenomenon becomes more obvious when the bit rate of ata users increases from 128 bits/frame to 256 bits/frame This is generally because ata traffic usually has higher bit rate an activity factor, thus results in the loss of voice Erlang capacity more sharply Furthermore, we also observe that by changing the threshol of the outage probability from 2% to 6%, the Erlang capacity region of the system can only be marginally increase V CONCLUSION Aaptive moulation an coing AMC has been wiely use to match transmission parameters to time-varying channel conitions In this paper, we have investigate the performance of a TDMA system that carries both voice an ata traffics with AMC in terms of the Erlang capacity We have evelope analytical moels to calculate the blocking an the outage probabilities As the outage probability epens on the istribution of the number of users in the system, which is tightly couple with the blocking probability, we propose a joint algorithm to etermine the Erlang capacity that the system can support when both the blocking an the outage probabilities are within certain threshols Numerical results have shown that the voice traffic capacity is severely affecte by the ata traffic Moreover, we have also observe that the Erlang capacity region of the system can only be marginally increase by loosing the target outage probability outage prob 3 25 2 15 1 5 5 45 voice traffic Erlangs 4 35 1 15 2 ata traffic Erlangs Fig 3 Outage probability versus ifferent traffic loas, with a target outage probability P outage =2% offere traffic of voice users Erlangs 8 7 6 5 4 3 2 1 ata=256 bits/frame ata=192 bits/frame outage=2, ata=128 bits/f outage=6, ata=128 bits/f outage=2, ata=192 bits/f outage=6, ata=192 bits/f outage=2, ata=256 bits/f outage=6, ata=256 bits/f ata=128 bits/frame 5 1 15 2 25 3 35 offere traffic of ata users Erlangs Fig 4 Two imensional Erlang capcity region of the system, with a target blocking probability P blocking =2% REFERENCES [1] Qingwen L, Shengli Z, an Georgious B: Queuing With Aaptive Moulation an Coing Over Wireless Links: Cross-Layer Analysis an Design, IEEE Transactions on Wireless Communications, Vol4 Issue3, pp 1142 1153, 25 [2] Tarhini, C, an Chahe, T: System capacity in OFDMA-base WiMAX, International Conference on Systems an Networks Communication, ICSNC 6, Vol4 Issue3, pp 7 74, 26 [3] Ding Ling, an Lehnert James S: Erlang Capacity of a Voice/Data Cellular CDMA Uplink System Using Prioritize Amission Control an Aaptive Power Control, International Journal of Wireless Information Networks, Vol8 Issue1, pp 1 14, 21 [4] Villy B Iversen: Teletraffic Engineering Hanbook, COM epartment, Technical University of Denmark 25 336 pp [5] Sarkar, TK, Zhong J, Kyungjung K, Meouri, A, an Salazar-Palma, M: A survey of various propagation moels for mobile communication, IEEE Antennas an Propagation Magazine, Vol45 Issue3, pp 51 82, 23 [6] Viterbi, AM, an Viterbi, AJ: Erlang capacity of a power controlle CDMA system, IEEE Journal on Selecte Areas in Communications, Vol11 Issue6, pp 892 9, 1993 [7] Hong Shen W, an Moayeri N: Finite-state Markov channel - a useful moel for raio communication channels, IEEE Transactions on Vehicular Technology, Vol44 Issue1, pp 163 171, 1995 25 119 Authorize license use limite to: Danmarks Tekniske Informationscenter Downloae on November 6, 29 at 1:27 from IEEE Xplore Restrictions apply