IEE THIET February 2005

8/7/2019 IEE THIET February 2005

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Performance analysis of dynamic packet assignmentin cellular systems with OFDMA

R. Jayaparvathy, S. Anand and S. Srikanth

Abstract: The authors present a performance analysis of orthogonal frequency division multipleaccess (OFDMA) based cellular systems with dynamic packet assignment (DPA). Mostapproaches in the current literature for analysing wireless data networks do not take into accountthe interference conditions on the radio channel. An analytical model based on a two-dimensionalcontinuous-time Markov chain (CTMC), that takes into account the interference conditions on theOFDM subcarriers in addition to the traffic conditions, is proposed. The authors deriveexpressions for the mean delay and the average system throughput on the uplink and the downlinkin OFDMA based cellular systems with data traffic.

1 Introduction

High spectral efficiency and flexible data-rate access are themain focus of future wireless systems. Third generation (3G)wireless systems such as wideband code division multipleaccess (WCDMA) use interference averaging techniques andprovide bit rates of 50384kbit/s in macrocellular systemsand 2 Mbit/s in microcellular systems [1]. Interferenceavoidance techniques provide better spectrum efficiencycompared with interference averaging techniques [2]. In [3],Chuang and Sollenberger showed that fourth-generation(4G) wireless systems can provide data transmission ratesof 25 Mbit/s in macrocellular environments, and up to10Mbit/s in microcellular environments by deployingdynamic channel assignment (DCA) based on interference

avoidance, combined with orthogonal frequency-divisionmultiplexing (OFDM). In [4], Erikkson proposed andevaluated dynamic radio resource management schemes fornonreal-time packet-mode communication over an OFDMbased downlink in terms of spectrum efficiency, fairness andcomputational efficiency. In [5], Cimini et al. proposed theconcept of packetised DCA or dynamic packet assignment(DPA), which involves fast measurements on all subcarriersin parallel. In [6], Chuang and Sollenberger proposed asystem with DPA, that makes fast channel measurementsusing the multicarrier nature of OFDM. A variation ofOFDM called orthogonal frequency-division multiple access(OFDMA) has been proposed for the IEEE 802.16a wirelessmetropolitan area networks (WMAN) in the 211GHzband [7, 8]. It is possible to obtain physical-layer rates of upto 75 Mbit/s in the IEEE 802.16 WMAN for fixed broad-band wireless access [9] using OFDM or OFDMA.

Analytical models have been developed in [1013] tostudy the performance of multiple-access systems. In [10],Rubin and Tsai obtained message-delay distribution, using

a discrete-time priority queueing approach in a system with

two classes of traffic. In [11], Khan and Peyravi comparedthe effects of five bursty distributions on buffer size andend-to-end delay in cellular data networks. In [12], Prakashand Veeravalli present analytical techniques for cellularwireless packet data systems with incremental redundancy.The authors presented a time-scale separation approach toevaluate the mean delay and per-user throughput. Themodels in [1012] do not take the interference conditionsinto account. In [13], Anand et al., presented an analysis toevaluate the blocking probability in channelised cellularsystems with DCA; the analysis took into account voice-only traffic. However, next-generation cellular systems willtypically use both voice and data traffic [14].

In this paper, we present a performance analysis of DPA

in OFDMA-based cellular systems with data traffic. Inparticular, our analysis is applicable for fixed broadbandwireless access (FBWA) systems like the IEEE 802.16d [9],i.e. the analysis can be used to evaluate the capacity of IEEE802.16 WMAN. We consider a cellular OFDMA systemwhere each user requires a block of OFDM subcarriers fortransmission. We derive expressions for the mean data trafficdelay and the average system throughput on the uplink(mobile-to-base station link) [15] and the downlink (base-station-to-mobile link). Our analysis takes into account theinterference conditions on the OFDM subcarriers. Wemodel each cell as a buffer of infinite size. The state of thebuffer as seen by newly arriving data traffic in a cell ismodelled by a two tuple of non-negative integers

m

;k

,where m represents the sum of the number of data burstscurrently being transmitted and the number of buffered databursts, and k represents the number of subcarriers thatcannot be used by newly arriving data traffic due toviolation of interference constraints. We model the statespace of the two tuples m; k as a continuous-time Markovchain (CTMC), and solve the CTMC to obtain the meandelay and the average system throughput. We illustrate theaccuracy of our analysis by comparison with simulations.

2 System model

Consider a cellular system with 61 circular cells as shown in

Fig. 1. Although a hexagonal model for cells is commonlyused, we model the cells to be circles for analyticalsimplicity. It is of interest to develop an analytical model

S. Anand is with Samsung India Software Operations, Bangalore, India

S. Srikanth is with the AU-KBC Research Centre, Chennai, India

r IEE, 2005

IEE Proceedings online no. 20041020

doi:10.1049/ip-com:20041020

Paper first received 14th November 2003 and in revised form 28th June 2004

R. Jayaparvathy was with the AU-KBC Research Centre and is now with theCoimbatore Institute of Technology, Coimbatore, India

IEE Proc.-Commun., Vol. 152, No. 1, February 2005 45


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to compute the mean delay and the average systemthroughput on the uplink and the downlink. We considerdata-only traffic in our analysis. Data traffic consists ofactive data bursts and idle periods as shown in Fig. 2. Inpractice a data burst is a data packet of variable length, forexample an IP packet with zero idle time between a finite setof consecutive packets. Each active data burst requires ablock of OFDM subcarriers for transmission. Allocation ofa block of subcarriers (typically five to ten subcarriers) toeach data burst enables large data-rates in 802.16 systems [9]and in 4G systems [3]. The blocks and block sizes arechosen such that the physical-layer propagation character-istics of each block are independent and identicallydistributed (IID). Analysis of a system with varying blocksizes and varying requirements of number of blocks peractive burst is complex. Therefore to simplify the analysiswe assume that all blocks consist of equal number ofsubcarriers and it is necessary to allocate a block ofsubcarriers to each active data burst. This is valid becausethe service stations or the user nodes in the IEEE 802.16dsystem are usually of the grant per service station (GPSS)

type [8], for which it is reasonable to assume that all usersrequire equal resources on an average [9].

The analysis we present is valid irrespective of the size ofthe block. Therefore we present the analysis for a block sizeof one subcarrier per block. We consider systems like theIEEE 802.16d WMAN in which the traffic on the uplinkand on the downlink is expected to be symmetric [8].Therefore the block sizes are considered to be the same bothon the uplink and on the downlink. Our analysis isindependent of the block size. Henceforth, throughout thepaper, we use the term subcarrier to represent a block ofsubcarriers.

Subcarriers are allocated to the active data bursts andreleased during the idle periods. We consider OFDMA

because it is suitable for high data-rate transmissions andprovides flexibility in multiple-access and channel qualitymeasurements [3]. Also, DPA is specifically designed for an

OFDM system since it is possible to measure theinterference on all subcarriers in parallel using the multi-carrier nature of OFDM [16]. Hence, though the analysis isvalid for any FDMA system in general, it is particularlyapplicable to OFDMA-based cellular systems.

The subcarrier allocation strategy to the data bursts is asfollows.

On the uplink, when a data burst arrives at a user in cell i,the base station of cell imeasures the interference on all thesubcarriers. A subcarrier c is called a feasible subcarrier for

the data burst in cell i if the interference measured onsubcarrier c by the base station of cell i is below a specifiedthreshold E. The data burst is transmitted on a feasiblesubcarrier, if available. If there are no feasible subcarriersavailable, the data burst is buffered. The buffered databursts are transmitted on a first-come first-serve (FCFS)basis if a subcarrier becomes feasible following thedeparture of a data burst from the system.

On the downlink, when a data burst arrives for a user incell i, the user in cell i measures the interference on all thesubcarriers. A subcarrier c is called a feasible subcarrier forthe data burst if the interference measured on subcarrier cby the user in cell i is below a specified threshold, E. The

base station transmits the data burst to the user on afeasible subcarrier, if available. If there are no feasiblesubcarriers available, the data burst is buffered. Thebuffered data bursts are transmitted to users on an FCFSbasis if a subcarrier becomes feasible following a departurefrom the system.

This subcarrier allocation strategy is a decentralised ordistributed mechanism, whereas the system for DPAproposed in [3] considered a partially centralised algorithmfor subcarrier allocation where the interference conditionswere measured not only for the newly arriving user but alsofor estimation of the interference caused to the existing users

in the system if the newly arriving user is admitted. Weconsider the distributed system as it results in lowercommunication complexity. Therefore in the systemproposed in [3] data bursts do not undergo retransmission,whereas in the system we consider, both on the uplink aswell as on the downlink it is possible that a data burstcurrently under transmission can be corrupted due toviolation of interference constraints during the period oftransmission due to admitting a newly arriving data burst inanother cell. This is further explained as follows.

On the uplink, consider a data burst being transmitted onsubcarrier c in the ith cell. Let there be a newly arriving databurst in cell j j 6 i, which is also transmitted on subcarrierc. If the additional interference caused by the newly arrivingdata burst in cell jat the base station of cell iis such that itresults in the interference measured on subcarrier c by thebase station of cell igoing above the threshold, E, it results inthe data burst on subcarrier c in cell i getting corrupted.

On the downlink, consider a data burst being transmittedon subcarrier c to a user in the ith cell. Let there be a newlyarriving data burst in cell j j 6 i, which is also transmittedon subcarrier c. If the additional interference caused by thenewly arriving data burst in cell jat the user in cell iis suchthat it results in the interference measured on subcarrier c bythe user in cell igoing above the threshold E, it results in thedata burst on subcarrier c in cell i getting corrupted.

Both on the uplink and the downlink the corrupteddata bursts are retransmitted after a random time. The

1

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2829

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4748

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5253

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61

Fig. 1 Cellular system with 61 circular cellsCells 27: first tier of interferers to cell 1

Cells 819: second tier of interferers to cell 1

Cells 2037: third tier of interferers to cell 1

Cells 3861: fourth tier of interferers to cell 1

active

data burst

T1 T2 T3 T4 T5 T6

time, t

idle

period

idle

period

Fig. 2 Data traffic with active bursts and idle periods

46 IEE Proc.-Commun., Vol. 152, No. 1, February 2005


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retransmitted data bursts are treated as newly arriving databursts. Data bursts that are buffered due to nonavailabilityof subcarriers suffer a delay. The delay increases due toretransmissions. The mean delay is defined as the mean timespent by a data burst in the buffer, which includes timespent in the buffer by all the transmissions (i.e. first-timetransmission and all retransmissions) of the data burst.

The assignment of a subcarrier to a data burst among thefeasible subcarriers can be based on strategies like the bestsubcarrier allocation, i.e. the feasible subcarrier with theleast interference, or random subcarrier allocation, i.e. anyof the feasible subcarriers at random. Simulation studies in[17] show that the mean data burst delay and the averagesystem throughput performance of cellular systems withDPA are similar for both the best and random subcarrierallocation schemes. We consider the random subcarrierallocation scheme for analytical simplicity. We make thefollowing assumptions to carry out the performanceanalysis.

There are N 61 cells. All cells are of equal radius R,with the base stations situated at the centres of each cell.

There are n subcarriers available for allocation in theentire system.

The data burst arrival process in each cell is a Poissonprocess with mean arrival rate l. The data burst holdingtimes are exponentially distributed with mean 1/m seconds.

The positions of users in any cell are uniformlydistributed over the area of the cell. The positions ofdifferent users are independent of each other.

No two data bursts in the same cell are allocated thesame subcarrier, i.e. in any cell there is atmost one databurst transmitted on every subcarrier.

The signal undergoes Rayleigh fading, log-normalshadowing and attenuation due to the distance betweenthe users and the base stations. The path loss exponent istaken to be four.

The signal propagation characteristics are independentand identically distributed for all the subcarriers.

The users are assumed to have no mobility.

These assumptions are made on both the uplink and thedownlink.

3 Performance analysis

Consider the cellular system shown in Fig. 1. To obtain themean data burst delay and the average system throughputfor the system it is necessary to model the interference

conditions on the uplink and the downlink. It is alsonecessary to take into account the arrival rates and holdingtimes of the data bursts.

3.1 UplinkLet a user in cell itransmit a data burst on subcarrier c. LetSi be the set of all cells other than cell i that have a databurst transmitted on the same subcarrier c and hence causeinterference to cell i. Let Di Sij j be the number ofinterferers to cell i on subcarrier c. To simplify the analysiswe assume that a base station experiences significantinterference only from the users in the immediate neigh-bouring cells (i.e. the first tier of neighbouring cells).Therefore in Fig. 1 S1

f2; 3; 4; 5; 6; 7

g, i.e. 0

Di

6.

Let x be the probability that a subcarrier c is not feasiblefor a data burst in cell i. A subcarrier c is not feasible in cell idue to one of the following two reasons. There is no other

data burst being transmitted on subcarrier c in cell ibut theinterference on subcarrier c measured by the base station ofcell i is above the threshold E, or the data burst in cell i istransmitted on subcarrier c and gets corrupted and henceretransmitted. Let Pth(Di) be the probability that asubcarrier is not feasible for a data burst in cell i due toDi interferers causing the interference measured at the basestation of cell i to go above E, and let Prt(Di) be theprobability of data burst retransmission due to Diinterferers. Then x is given by

x 1 pX6Di1

PthDibDi pX6Di1

PrtDibDi 1

where p is the probability of there being a data burst in cell itransmitted on subcarrier c, and bDi is the probability mass

function ofDi which is given by

bDi 6Di

pDi1 p6Di

0

0 Di 6otherwise

(2

The value of x obtained from (1) is used in Section 3.4 in(4)(12) to evaluate the mean delay and the average systemthroughput.

3.2 DownlinkLet a user in cell ireceive a data burst on subcarrier c. Theuser in cell i receives interference from the base stations ofcells that have a data burst also being transmitted insubcarrier c. As on the uplink, we make the assumption thata user receives significant interference only from the basestations of the first tier of neighbouring cells. Defining Siand Di as previously (i.e. Section 3.1), the expression for xgiven in (1) is also valid on the downlink. However, on thedownlink, Pth(Di) is redefined as the probability of theinterference measured by a user in cell i from Dineighbouring base stations being above the threshold E.

3.3 Markov chain modelBoth on the uplink as well as on the downlink each cell ismodelled as a buffer of infinite size. A newly arriving databurst sees m1 subcarriers being used by other data bursts incell i, m2 data bursts buffered in cell i, and ksubcarriers notbeing feasible due to interference constraints. We model thestate seen by a newly arriving data burst in cell i as a two-tuple of nonnegative integers m; k, where m m1 m2: Itis observed that m kon for a subcarrier to be availablefor allocation to a newly arriving data burst. The state spaceof two-tuples m; k is modelled as a two-dimensionalcontinuous-time Markov chain (CTMC), with transitionrates as shown in Fig. 3. Transitions in the CTMC alsooccur from the states (m, k) to

m

1; k

1

due to

retransmissions of data bursts. We neglect these transitionsto simplify the analysis. However, we account for data burst

retransmissions by modifying the arrival rates to be l0 l=1 PR; where PR is the data burst retransmissionprobability, given by

PR X6Di1

PrtDibDi 3

in which PrtDi is as defined in Section 3.1 and bDi is asgiven in (2). The CTMC in Fig. 3 has transition rates of theform m0a and k0b, where m0; k0 2 f1; 2; ; ng: Theanalysis to obtain the values of a and b is complex. It isshown in (4)(12) that the mean delay and the system

throughput depend on the ratio b/a, and not on the actualvalues ofa and b. Hence to compute b/a we model the stateof a subcarrier seen by a newly arriving data burst as a two-



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state CTMC as shown in Fig. 4, in which the probability ofa subcarrier being feasible is 1 x; and that of a subcarriernot being feasible is x, where x is obtained from (1).

The structure of the CTMC shown in Fig. 3 is valid forboth the uplink and the downlink and therefore the analysiswe present in the following Section is valid for both.However, we point out that the values of the transition ratesa and b are different for the uplink and the downlink.Therefore the values of the mean delay and the averagesystem throughput are expected to differ on the uplink anddownlink.

3.4 Mean delay and average systemthroughputIt can be shown that the CTMC in Fig. 3 is positive

recurrent if and only if rr9l0=mon: When the CTMC ispositive recurrent the steady-state probability for theoccupancy of state (m, k), p

m; k

can be obtained as

pm; k

1

AB

rrm

m!

n

k

b

a

km n; k n

1

nmnAB

rrm

n!

n

k

b

a

km4n; k n

0 otherwise

8>>>>>>>>>:

4where A and B are normalisation terms given by

A rrn1

n!n rr Xnm0

rrm

m!5

and

B 1 ba

n6

The details are given in the Appendix. From the two-stateCTMC in Fig. 4, b/a can be obtained as

ba

x1 x 7

The probability of a subcarrier being allocated to a databurst p is given by

pXnm0

Xnmk0

minm; n kn

pm; k 8

The value of p obtained from (8) is used in (1) and (2) tocompute b/a, which in turn is used in (4)(6) to computepm; k: From (1), (2), (4), (7) and (8) it is observed that pand pm; k are to be computed iteratively. The meannumber of buffered data bursts Nb is given by

Nb Xmk!n m k npm; k 9The mean delay "DD is obtained using Littles theorem [18] as

"DD Nbl0

10The average system throughput Z is given by

Z 1 PR 1 PbX

mkn

m

npm; k 11

where PR is obtained from (3), and Pb is the probability of adata burst being buffered, which is given by

Pb Xmk!n

pm; k 12

To evaluate (4)(12) it is necessary to evaluate x, and hencePth(Di) and Prt(Di). We present the analysis to obtain Pth(Di)and Prt(Di) in Section 3.5.

3.5 Evaluation of Pth(Di) and Prt(Di)

3.5.1 Uplink: On any subcarrier c, the interferencereceived by the base station of cell i from the users in Di

neighbouring cells Iui (Di) is given by

Iui Di

Xj2sisij jDi

D4Bi; Pj10cij=10Uij 13

where Uij represents the Rayleigh fading loss from the userin cell j to the base station of cell i, D(Bi,Pj) is the distancebetween the base station of cell i(located at Bi), and the user

0,0 1,0 2,0 n2,0

n2,1

n1,0

n1,1

n+1,0

0,1 2,1 n,1

n ,0

0,2 1,2 n,2 n+1,2

0,n1

0,n 1,n

1,n1

.

.

.

b na b na

(n1)b 2a (n1)b 2a (n1)b 2a

nb a nb nb a nb a nb a

2a 2a

..............

.................

.............

1,1

2,2

2

2

2

(n1) n n

(n1) (n1) (n1)

(n2) (n2) (n2)

......................................................................................................................

.......................................................................................................................

.....................................................................................................................

.........

.........

.........n+1,1

...........

..........

(n1)b 2a

nb aa

(n1)b(n1)b(n1)b

nb a

2a

n2,2 n1,2

.......

Fig. 3 Markov chain model for state seen by a newly arriving data burst

a

b

subcarrier

not

feasible

subcarrier

feasible

Fig. 4 Two-state CTMC model to evaluate b/a



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in cell j (located at Pj), and 10cij=10 represents the log-

normal shadow loss from the user in cell j to the base

station of cell i. In (13), cijBN0;s2. Pth (Di) and Prt (Di)are given by

PthDi Pr Iui Di4En o

14and

PrtDi Pr Iui Di4E Iui Di 1 E

n o15

respectively. Therefore to evaluate Pth (Di) and Prt (Di) it isnecessary to evaluate the cumulative distribution functionofIi

(u) (Di). Conditioned on the positions of the users and theRayleigh fading loss, each term in the summation of (13) is

log-normal of the form 10Oij=10, where Oij $Nmij;s2and mij is given by

mij 40 log10DBi; Pj 10 log10 U 16In (16), Uis an exponentially distributed random variablewith unit mean. Using the approach described by Fenton in

[19], Iui Di can be approximated to be a log-normally

distributed random variable of the form 10ODi =10, whereODi

$N

mDi ; s

2Di

and s2Di and mDi can be obtained as

s2Di 1

w2ln 1

ew2s2 1

j2si e

2wmij

j2si ewmij

224

35 17

and

mDi ws2Di s2

2 1

wln

Xj2si

ewmij" #

18

In (17) and (18), w91n 10=10, and mij is obtained from(16). Averaging over the Rayleigh fading loss and theposition of the user, PthDi is given by

PthDi 1

pR2 DiZ ZQ EdB mDisDi

eUti01 ti0

Di

dri01dyi0

1 dri0

Di

dyi0Di

dU

19

where EdB 10 log10 E; and

Qx ZN

x

1ffiffiffiffiffiffi2p

py2=2

dy

From (19) it is noted that the computation of Pth (Di)involves 2Di+2 integrations, which results in 14 integrationswhen Di 6. To simplify the numerical computations weassume that the interferers are IID. This assumption is valid

due to the symmetry of the system. The expressions for s2Diand m

Diare then given by

s2Di 1

w2ln 1

ew2s2 1

Di

24

35 20

and

mDi mij ws2Di s2

2 1

wln Di 21

Pth (Di) is then given by

PthDi 1pR2

DiZ Z ZQ

EdB mDisDi

eUrdrdydU

22From (22) it is observed that only four integrations have tobe performed to evaluate Pth (Di), irrespective of the value of

the number of interferers Di. To determine Prt (Di) in (15) itis necessary to evaluate the joint probability

PJ Pr Iui Di4E; Iui Di 1 En o

23and the marginal probability

PM Pr Iui Di 1 En o

24PM in (24) is evaluated using the method similar to the oneused to evaluate Pth (Di). In [20], Anand et al., computed an

expression similar to PJ in (23) for CDMA systems by usingFentons approximation and ln 1 x % x for xj jo1: Weadopt the approach in [20] to evaluate PJand hence Prt (Di).The retransmission probability PR is obtained from (3). Thevalues of Prt (Di) obtained fro (15) and Pth (Di) obtainedfrom (22) are used to evaluate x in (1), which in turn is usedin (4)(12) to evaluate the mean data burst delay and theaverage system throughput on the uplink.

3.5.2 Downlink: On any subcarrier c the interferencereceived by a user in cell i from the base stations of Di

neighbouring cells Idi (Di) is given by

Idi

Di

Xj2sisij jDiD4

Pi; Bj

10cji=10Uji

25

where Uji represents the Rayleigh fading loss from the basestation of cell jto the user in cell i, D (Pi,Bj) is the distancebetween the user in cell ilocated at Pi, and the base station

of cell j located at Bj, and 10cji=10 represents the log-

normal shadow loss from the base station of cell j to the

user in cell i. In (13) cji $N0;s2:Pth (Di) and Prt (Di) are given by

PthDi Pr Idi Di4En o

26and

PrtDi Pr Idi Di4E Idi Di 1 En o 27respectively. Equation (26) is evaluated as we evaluated (14)in Section 3.5.1. Thus on the downlink Pth (Di) is obtained

from (22) by replacing s2Di and mDi by

s2Di 1

w2ln 1

ew2s2 1

j2si e

2wmji

j2si ewmji

224

35 28

and

mDi ws2Di s2

2 1

wln

Xj2siewmji

" #29

In (28) and (29) mji is given by

mji 40log10 D Pi;Bj 10log10U 30

The expression for PrtDi in (27) is evaluated by once againadopting the approach in [20]. The values of PthDi andPrtDi thus obtained are used to evaluate x in (1), which inturn is used in (4)(12) to compute the mean data burstdelay and the average system throughput on the downlink.

4 Results and discussion

We use the following values for the computations: N 61cells, n

150 subcarriers, 1/m

125 ms, E

13 dB,

s 8 dB, and R 1. The data burst arrival rate l is variedto obtain a load r9l=m in the range 1 to 40 Erlangs percell. The IEEE 802.16d standard for WMAN specifies a



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maximum of 2048-point FFT (i.e. 2048 subcarriers) for theOFDMA-based system [8]. However, typical OFDMAbased WMAN systems deploy a 1024-point FFT [7] ofwhich about 768 subcarriers are used for data traffic and theremaining for pilot signals. Hence we consider about 150blocks with about 5 to 6 subcarriers per block. Asmentioned in Section 2, our analysis is independent ofblock size and hence we perform the analysis for 150subcarriers.

The performance of dynamic channel allocation (DCA)is also provided for comparison. DCA refers to allocationof subcarriers to data traffic both to the active data bursts aswell as during the idle periods. The DCA traffic model is acircuit-switched version of DPA. Although this model is notused in wireless data networks we provide the comparisonto emphasise the advantage of DPA and that of OFDMAin cellular systems as DPA is feasible only over systems withOFDM or OFDMA which is deployed only in cellularsystems like the IEEE 802.16 or in 4G cellular systems. Thearrival rate and holding time for the DCA computations areobtained as follows. Consider the representation of datatraffic with active data bursts and idle periods as shown inFig. 2. Usually active bursts form 25% of the data traffic i.e.in Fig. 2 (T2

T1+T4

T3+T6

T5)/(T6

T1)E0.25. For

data traffic comprising of an average of 100 active databursts, the mean call holding time to perform the DCAcomputations 1/mdca is given by 1/mdca 100/(m*0.25) 50 sifm 125 ms. The arrival rate for DCA computationsldca isgiven by ldca l=100:

Figures 5 and 6 present the mean delay performance as afunction of the data traffic per cell on the uplink and thedownlink, respectively. The analytical results match closelywith the simulations, thus validating our analyticalapproach. The Erlang capacity of the system is defined asthe maximum carried traffic (in Erlangs) to obtain aspecified mean delay performance. From Fig. 5, the Erlangcapacity to obtain a mean delay of 1 ms is about 32.5Erlangs with DPA and 7 Erlangs with DCA. This results inan improvement of the Erlang capacity on the uplink byabout a factor of 4.5 with DPA, as compared with DCA.This improvement in the Erlang capacity with DPA isbecause in DPA, the subcarrier is released during the idleperiods of data traffic, and hence can be allocated to theactive data burst corresponding to the data traffic foranother user in the cell, thereby reducing the delay, whereasin DCA the subcarrier is held both by the active data burstsas well as during the idle periods. In other words, the

resources are better utilised when subcarriers are allocatedto the active data bursts alone and released during the idleperiods.

This can be quantitatively explained as follows. Consideran arrival rate of 1 call per second in DCA. As mentioned

earlier, m1dca 50 s thus leading to a load ofr 50 Erlangs.For the same data traffic, if DPA is used, this correspondsto an arrival rate of 100 bursts per second and for

m1dpa 125 ms it results in a load ofr 12.5 Erlangs. Thusfor the considered traffic statistics, DPA loads the systemless than DCA by a factor of about 1/4. Hence a gain ofabout four times can be obtained in the system capacity byusing DPA as against DCA. However, the actual value ofthe gain in capacity need not be exactly four since the activebursts are randomly distributed within the data session.

Similarly, from Fig. 6 it is observed that the Erlangcapacity to obtain a mean delay of 1 ms is about 34 Erlangswith DPA, and about 12 Erlangs with DCA. This results inan improvement of the Erlang capacity on the downlink byabout a factor of three with DPA, as compared with DCA.The absolute value of the mean data burst delay is smalleron the downlink than on the uplink (e.g. a mean delay of1ms occurs at r 34 Erlangs with DPA and r 12 Erlangswith DCA on the downlink, and at r 32.5 Erlangs withDPA and r 7 Erlangs with DCA on the uplink). Thereason for the reduction in the mean data burst delay on thedownlink is as follows. On the downlink, interference iscaused to a user from six neighbouring base stations. A useris always nearer to three of the six neighbouring basestations and far away from the other three base stations.

Therefore only three of the six neighbouring base stationscontribute significantly to the interference measured by auser. However, on the uplink the interference caused to abase station is due to users present in the six neighbouringcells and the average interference caused is equivalent to theinterference caused when all the six users are positioned atthe centres of their respective cells. Thus significantinterference is caused by users present in all the sixneighbouring cells. Therefore the average interference at auser on the downlink is lower than the average interferenceat a base station on the uplink. Hence, the buffering andretransmission probabilities on the downlink are lower thanthose on the uplink. This leads to lower mean delay on thedownlink. Since the absolute values of mean delays on the

uplink and the downlink are different with both DPA andDCA, the factor of improvement in the Erlang capacities isalso different.

5 10 15 20 25 30 35

106

104

102

100

102

data traffic per cell, Erlangs

meandelay,s

DPAanalysisDPAsimulationDCA

Fig. 5 Mean data burst delay: uplink, N 61 cells, n 150subcarriers

10 15 20 25 30 35 40106

105

104

103

102

101

100


meandelay,s


Fig. 6 Mean data burst delay: downlink, N 61 cells, n 150subcarriers



7/8

Figures 7 and 8 present the average system throughputperformance for varying data traffic on the uplink and thedownlink, respectively. The throughput remains the samewith both DCA as well as DPA. This is because throughputis the effective utilisation of the subcarrier, and DPArepresents the effective utilisation periods (i.e. active bursts)of DCA.

5 Conclusions

We have presented a performance analysis of OFDMA-based cellular systems with DPA. We derived expressionsfor the mean delay and the average system throughput onthe uplink and the downlink. Our analysis took intoaccount the interference conditions on the OFDM sub-carriers in addition to the traffic load conditions, and wasshown to be accurate. We also compared the performanceof DPA with that of DCA and showed that higher Erlangcapacities are possible with DPA as compared with DCA.This result is useful because it was already shown in [2] thatinterference avoidance techniques of DCA could result incapacities higher than that of CDMA, which in turnprovided larger capacities compared with circuit-switched

systems like GSM and GPRS. Hence the advantage inusing DPA makes DPA a very attractive mechanism toprovide high data-rates over wireless channels.

An extension of our approach to incorporate varyingblock sizes and varying requirements per active data burst isa topic for further investigation. Our analytical approachcan also be extended to study the performance of OFDM-based wireless adhoc networks.

6 References

1 Ojanpera, T., and Prasad, R.: An overview of air interface multipleaccess for IMT-2000/UMTS, IEEE Commun. Mag., 1998, 36, (9), pp.8295

2 Pottie, G.J.: System design choices in personal communications,IEEE Pers. Commun., 1995, 2, (5), pp. 5067

3 Chuang, J., and Sollenberger, N.: Beyond 3G: Wideband wirelessdata access based on OFDM and dynamic packet assignment, IEEECommun. Mag., 2000, pp. 7887

4 Erikkson, M.: Dynamic single-frequency networks, IEEE J. Sel.Areas Commun., 2001, 19, (10), pp. 19051914

5 Cimini, L.J. Jr., Chuang, J.C.I., and Sollenberger, N.R.: Advancedcellular internet service, IEEE Commun. Mag., 1998, pp. 150159

6 Chuang, J.C.I., and Sollenberger, N.R.: Spectrum resource allocationfor wireless packet access with application to advanced cellularinternet service, IEEE J. Sel. Areas Commun., 1998, 16, (6), pp. 820829

7 IEEE P802.16a/D3-2001: Draft amendment to IEEE standard forlocal and metropolitan area networks Part 16: Air interface for fixedwireless access systems Medium access control modifications andadditional physical-layer specifications for 211 GHz March 2002

8 Eklund, C., Marks, R.B., Stanwood, K.L., and Wang, S.: IEEE

standard 802.16: A technical overview of wireless MAN air interfacefor broadband wireless access, IEEE Commun. Mag., 2002, pp. 98107

9 IEEE P802.16-Revd/D3-2004: Draft amendment to IEEE standardfor local and metropolitan area networks Part 16: Air interface forfixed wireless access systems Medium access control modificationsand additional physical-layer specifications for 211 GHz January2004.

10 Rubin, I., and Tsai, Z.H.: Message delay analysis of multiclasspriority TDMA, FDMA and discrete time queueing systems, IEEETrans. Inf. Theory, 1989, 35, (3), pp. 637647

11 Khan, K., and Peyravi, H.: Delay and queue size analysis of TDMAsystems with general traffic. Presented at 6th Int. Symp. on Modeling,Analysis and Simulation of Computer and TelecommunicationSystems, July 1998

12 Prakash, R., and Veeravalli, V.V.: Wireless packet data systems withincremental redundancy Uplink analysis. Presented at Conf. onInformation Science and Systems, Princeton University, March 2002

13 Anand, S., Sridharan, A., and Sivarajan, K.N.: Performance analysis

of channelised cellular systems with dynamic channel allocation,IEEE Trans. Veh. Technol, 2003, 52, (4), pp. 847859

14 Gummalla, A.V., and Limb, J.O.: Wireless medium access controlprotocols, IEEE Commun. Surveys and Tutorials, Second Quarter2000

15 Jayaparvathy, R., Anand, S., and Srikanth, S.: Dynamic packetassignment in OFDM-based cellular systems performance analysis.Presented at IEEE Conf. APCC 2003, Sep 2003

16 Qiu, X., Chawla, K., Chuang, J., and Sollenberger, N.R.: Network-assisted resource management for wireless data networks, IEEE J.Sel. Areas Commun., 2001, 19, (7), pp. 12221234

17 Sridhar, M., and Namrata, D.: Performance of uplink MAC layer in4 G cellular networks. B.E. Project Report, AU-KBC ResearchCentre, Madras, India

18 Bertsekas, D., and Gallager, R.: Data networks (Prentice Hall ofIndia, 2000)

19 Fenton, L.F.: The sum of log-normal probability distributions inscatter transmission systems, IRE Trans. Commun. Syst., 1960, CS-8

20 Anand, S., Chockalingam, A., and Sivarajan, K.N.: Outage andcapacity analysis of cellular CDMA with admission control.Presented at IEEE Conf. WCNC 2002, March 2002

7 Appendix: Derivation of pm;k in (4)The differentialdifference equations of the CTMC in Fig. 3is given by

p00; 0 t a p0; 1 t mp1; 0 t nb l0p0; 0 t 31

p00; n t b p0; n 1 t mp1; n t na l0p0; n t 32

0 5 10 15 20 25 30 35103

102

101

100


averagesystemthroughput


Fig. 7 Average system throughput: uplink, N 61 cells, n 150subcarriers

0 5 10 15 20 25 30 35103

102

101

100


averagesystemthroughput

DPAanalysisDPAsimulation

DCA

Fig. 8 Average system throughput: downlink, N 61 cells,n 150 subcarriers



8/8

p0m; 0 t apm; 1 t m 1mpm 1; 0 tl0pm 1; 0 tnb l0 mmpm; 0 t 1 mon

33p00; k t k 1ap0; k 1 t mp1; k tn k 1 bp0; k 1 t

n

k

b

l0

ka

p

0; k

t

1

kon

34

p0m; k t l0pm 1; k t k 1apm; k 1 tm 1 mpm 1; k t 1 monn k 1 bp m; k 1 t n k b l0 ka mmj p m; k t 1 kon

35p0m; n t l0pm 1; n t m 1mp m 1; n tbpm; n 1 t l0 na mmpm; n t 1 mon

36p0m; 0 t apm; 1 t nmpm 1; 0 tl0pm 1; 0 tnb l0 nmp m; 0 t 1 mon 37p0m; k t l0pm 1; k t k 1apm; k 1 tnmpm 1 nmpm 1; k t n mo1n k 1 bp m; k 1 t n k b l0 ka nm p m; k t 1 kon 38

and

p0

m; n

t

l0pm 1; n t nmpm 1; n tbpm; n 1 tl0 na nmpm; n t n mo1 39

To prove (4) we proceed as follows. Let the steady-stateprobability of the system being in state m; k be p m; k.At steady state, i.e. as t-N, pm; kt pm; k, andp0m; kt 0. Therefore at steady state the probabilitypm; k can be obtained from (31)(36) aspm; k

pm; k 1 n k 1k

b

a

0 m n; 0 k n

pm 1; k rrm

0 m n; 0 k n

8>>>:

40where rr9l0=m. Similarly from (37)(39), p(m,k) can bewritten as

pim; k

pm; k 1 n k 1

k

b

a

nomo1; 0 k n

pm 1; k rrn

nomo1; 0 k n

8>>>: 41

From (40) and (41) we obtain

pm; k

p0; 0 rr

m

m!

n

k

b

a

k0 m n; 0 k n

pn; 0 rrn

mn nk

b

a

knomo1; 0 k n

0 otherwise

8>>>>>>>>>>>: 42

i.e.

pm; k

p0; 0 rrm

m!

n

k

b

a

k0 m n; 0 k n

p0; 0 rrm

n!nmnn

k

b

a

knomo1; 0 k n

0 otherwise

8>>>>>>>>>>>:

43Since P1m0 P

nk

0p

m; k

1

p0; 0Xnk0

n

k

b

a

k Xnm0

rrm

m! 1

n!

X1mn1

rrm

nmn

" #

1 44i.e.

p0; 0 1 ba

n Xnm0

rrm

m! rr

n1

n!

X1mn1

rr

n

mn1" #

1 45The summation in the LHS of (45) exists if and only if^rro

n; which is also a necessary and sufficient condition forthe stability of the system. Therefore when rron;p0; 0 isobtained as

p 0; 0 1AB

46where

A rrn1

n!n rr Xnm0

rrm

m!47

and

B

1

b

a

n

48

From (43) and (46)

pm; k

1

AB

rrm

m!

n

k

b

a

k0 m n; 0 k n

1

nmnAB

rrm

n!

n

k

b

a

knomo1; 0 k n

0 otherwise

8>>>>>>>>>>>:

49


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