A Subcarrier Allocation Algorithm for OFDMAusing Buffer and Channel State Information

Parimal Parag Srikrishna Bhashyam and R. AravindDepartment of Electrical Engineering Department of Electrical Engineering

Texas A&M University Indian Institute of Technology MadrasCollege Station 77843, USA. Chennai 600036, India.

parimal@neo.tamu.edu {skrishna, aravind}@ee.iitm.ac.in

Abstract We propose a new subcarrier allocation algo-rithm for Orthogonal Frequency Division Multiple Access(OFDMA) that gives fair allocation of capacity to multipleusers with different channel and traffic characteristics. Thisis achieved by utilizing buffer state information and mea-sured traffic statistics in addition to channel state feedback.Multiuser diversity gains are achieved in the proposed al-gorithm by scheduling across both time (buffering) and fre-quency (subcarriers). Simulation results are shown to illus-trate (a) improved capacity allocation and throughput, and(b) larger admissible traffic when compared to the existingalgorithms.

Keywords - OFDMA; Scheduling; Subcarriers; Buffering;Throughput; Delay; Fairness.

I. Introduction

Joint subcarrier and power allocation in OFDMA is acomplex problem [1]. Usually, the problem is simplified byseparating subcarrier allocation and power allocation [2],[3]. Subcarrier allocation provides more gain than powerallocation [3], [4]. In this paper, we focus on subcarrier al-location. Maximum capacity is provided by the Max-Ratesubcarrier allocation algorithm (MR-SAA) which allocateseach subcarrier to the user with the best channel condi-tions [5], [6]. However, it is not fair. The Rhee-Cioffi sub-carrier allocation algorithm (RC-SAA) [2] achieves propor-tional fairness amongst the users. However, the overallcapacity achieved is much lower. The capacity achievedby these subcarrier allocation algorithms that are solelybased on channel conditions does not necessarily translateinto throughput when the input traffic is bursty. Further-more, [7] shows that proportionally-fair scheduling can leadto unstable queues even for low arrival rates since it doesnot utilize the buffer state.Buffering of bursty traffic can take advantage of mul-

tiuser diversity across time and improve throughput per-formance by trading delay for throughput [8]. Recently,subcarrier allocation in the presence of buffer and chan-nel information has been studied in [10], [9]. In [9], thenumber of subcarriers for each user is determined prior tochoosing the specific subcarrier allocation scheme. In [10],improved delay performance is achieved by using the meanwaiting times in the sub-carrier allocation algorithm. TheModified-Largest Weighted Delay First (M-LWDF) rule [8]for time slot allocation in dynamic TDMA is a throughput

optimal rule1. We propose a subcarrier allocation algo-rithm (SAA) which extends the M-LWDF idea to scheduleusers on each subcarrier of an OFDMA system during everytime slot. Results are shown to illustrate that the proposedSAA: (a) allocates capacity fairly amongst the users, and(b) supports traffic load very close to the maximum capac-ity (achieved by the MR-SAA). The proposed SAA choosesthe user for each subcarrier based on a combination of thefollowing: (a) current channel conditions, (b) current bufferstate (delay), and (c) the measured ratio of arrival rate tothroughput for each user.The paper is organised as follows. We describe the sys-

tem model in section II. We propose our subcarrier allo-cation algorithm in section III. Simulation specifications,results, and discussions follow in section IV. Conclusionsare drawn in section V.

II. System Model

Fig. 1 shows the system model. A downlink OFDMAsystem with N users and K carriers is considered. Therandomly arriving incoming packets are buffered in a first-in-first-out (FIFO) queue with the buffer size for each userdetermined by the absolute delay bound for the correspond-ing user [11]. We transmit bits at the maximum rate forreliable communication over the channel in any time slot,the outage (number of bits dropped) is only due to bufferoverflow. if the buffer overflows. A single user is scheduledon each sub-carrier. Therefore, the problem of subcarrierallocation is essentially to choose an user for each subcar-rier. We define the set of all carriers as A = {1, 2, . . . ,K}.Let n(t) be the set of carriers assigned to user n in symbolperiod t. Since each OFDM carrier can be assigned onlyto one user, we have for all t

n(t)

m(t) = m = n, andN

n=1

n(t) = A. (1)

The wireless multipath fading channel is assumed con-stant over one OFDM symbol transmission and noise isassumed to be i.i.d. and AWGN with variance 2 for allcarriers and all users. The received OFDM symbol Yn,k(t)can be written in terms of the frequency-domain channel

1It renders the queues at the base-station stable if any other rulecan do so [8].

6220-7803-9152-7/05/$20.00 2005 IEEE

gain Hn,k(t), the noise at the receiver n,k(t) for user nand the transmitted symbol Xk(t) on carrier k in tth sym-bol period, as:

Yn,k(t) = Hn,k(t)Xk(t) + n,k(t), n {1, 2, . . . N}, k n(t).The normalized channel gains seen by kth carrier of user

n in symbol period t is n,k(t) = (|Hn,k(t)|2/2). We as-sume that the transmitter has knowledge of the channelsof all the users. Since channel conditions are time-varying,this information is assumed to be updated periodically withthe help of feedback channels.

...

a1(t)

a2(t)

aN (t)

X1(t)

X2(t)

XK(t)

...

Bufferinformationof N users

Combined carrierbit and powerallocation

from N usersinformationChannel

Carrier

&

bit

allocationTransmitter

OFDM

buffer

buffer

buffer

L2

modulator 1

modulator 2

adaptive

adaptive

adaptiveL1

modulator KLN

Fig. 1. Orthogonal Frequency Division Multiple Access

For power allocation, we use water-pouring [12]. Thepower allocated to subcarrier k in time slot t is given by

Pk(t) = ((t) (1/n,k(t)))+, (2)where (x)+ = max(x, 0) and (t) is chosen to satisfy theabsolute power constraint

Kk=1 Pk(t) = P . Therefore, the

maximum achievable rate for reliable communication in atime-slot t for a user n by any SAA is

n(t) =

kn(t)n,k(t), (3)

where n,k(t) = log2 (1 + n,k(t)Pk(t)) (4)

is the maximum rate that can be reliably supported on thecarrier k for that user.We denote the buffer length for user n by Ln. In each

OFDM symbol period t, one packet of random size arrivesper user. The number of bits in the packet for nth user isan(t), distributed uniformly in [0,Mn].A FIFO queue is implemented where Qn(t) shows the

buffer state of user n at time slot t in terms of pn,i(t),which denotes the enqueued bits of user n that arrived inthe (t i)th time slot. The absolute delay bound Dn is themaximum number of symbol periods a bit can be in thequeue, after which it is dropped. The buffer size is takenas Ln = MnDn to ensure the delay bound Dn for user n[11]. The queue, in terms of pn,i(t) and Dn, is given by

Qn(t) =[pn,Dn(t) pn,Dn1(t) . . . pn,1(t)

].(5)

Bits are transmitted with priority order from left to right.The total number of bits in the queue qn(t) and the delay ofthe Head-of-Line (HoL) packet Wn(t) for user n in symbolperiod t are given by

qn(t) =Dni=1

pn,i(t) (6)

Wn(t) = max{j : pn,j(t) = 0}, (7)

The problem of resource allocation for a limited totalavailable power P is divided into subcarrier allocation, i.e.,finding a set of carriers n(t) assigned to user n and powerallocation, i.e., finding Pk(t), k A over the total set ofcarriers A. The total throughput dn(t) for any user n ina time slot t is the minimum of the achievable rate n(t)and the total number of packets in the buffer qn(t);

dn(t) = min(qn(t), n(t)). (8)

III. Subcarrier Allocation Algorithm

Subcarrier allocation is the assignment of a disjoint setof carriers n(t) to each user n (for n = 1, 2, . . . , N) intime slot t. It can be seen from (8) that maximizing thesupportable rate n(t) for a user n in any time slot t doesnot maximize the throughput dn(t). This underlines theimportance of using buffer state information Qn(t) in sub-carrier allocation.Ideas used in time-slot allocation in dynamic TDMA can

be extended to subcarrier allocation in OFDMA. In dy-namic TDMA, buffers are used to achieve fairness overtime. In OFDMA, we have freedom of allowing multipleusers to share the channel simultaneously during each timeslot. Therefore, we can schedule both across time slots andsubcarriers (frequency).Resource allocation algorithms in [2], [3] schedule users

across subcarriers to achieve fairness during every symbolperiod. These algorithms do not schedule across time slots.We incorporate buffers for a multiuser OFDMA system andpropose a subcarrier allocation algorithm that utilizes thebuffer and channel state information and measured trafficstatistics available at transmitter. We achieve higher mul-tiuser diversity gain by scheduling both across time andacross the subcarriers.The Modified-Largest Weighted Delay First (M-

LWDF) [8] rule for time slot allocation in dynamic TDMAschedules the user with largest weighted delay, where theweight is proportional to the supportable rate of a user non the channel in that time slot t. It is a throughput optimalrule. so We propose a subcarrier allocation algorithm thatextends the M-LWDF idea for scheduling users on eachsubcarrier in every time slot. We also use a weighted delaymeasure for subcarrier allocation. However, the weight isproportional to the normalized channel gain and not thesupportable rate used in the M-LWDF rule for time slotallocation.It has been shown in [3], [4] that power allocation does

not offer substantial gains at high SNRs. Therefore, if weassume that every subcarrier gets equal power, then wecan consider the subcarriers as parallel channels. Since weknow MLWDF rule is throughput optimal for each indi-vidual channel, we can select best user for each subcarrierusing a rule similar to it. Once the subcarriers have beenallocated we do water-pouring to maximize the capacityregion in every time-slot. Other power allocation meth-ods given in [3] and [13] can also be combined with oursubcarrier allocation algorithm.Let an(t) and dn(t) denote mean windowed arrival and

mean windowed throughput respectively for user n, aver-

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aged over a sliding-window Tw. Given the normalizedchannel gains n,k(t), kth carrier of user n in symbol pe-riod t, an(t), dn(t) and buffer state Qn(t), we determinethe subcarrier set n(t) allocated to user n by the follow-ing algorithm.

1. Initialize: n(t) = , n = 1, 2, . . . , N2. For each subcarrier k = 1 to K(a) Select a user for subcarrier k:

j = argmaxi

[ai(t)di(t)

i,k(t)Wi(t)]

i = 1, 2, . . . , N. (9)

(b) Allocate subcarrier k to user j: j(t) = j(t){k}.

This algorithm equalizes between queue and channel con-ditions when subcarriers are allocated to users. Insteadof allocating carriers solely based on channel conditions,this algorithm also considers measured traffic statistics andbuffer state. If a user has a bad channel persistently and/orif it is a high rate user (relatively more bits to transmit perslot), it will be preferred over others with better channelconditions but relatively less bits to send. Since the avail-able capacity is allocated to the users who require it most,the throughput and delay performance are very good (asshown in the simulation results in Section IV).

IV. Simulation Results and Discussions

A 9 user, 64 subcarrier OFDMA system is consideredfor a 6-tap multipath fading channel with an exponentiallydecaying multipath profile. The channel for each user isassumed to be independent and identically distributed inevery OFDM symbol. We have simulated two importantcases, (a) users with i.i.d. channels, (channel variance beingidentically 1 for all users) and (b) users with scaled channelprofiles, i.e. all the subcarriers are assumed to be fadingindependently with variances for different users multipliedwith [.75 .5 .5 1 1 .5 .75 1 1] respectively. Simulation resultscan also be obtained when the channels are correlated. The9 users have linearly increasing rates in the ratio 1 : 2 : . . . :9 with an uniform arrival distribution. The total poweravailable at the base-station is fixed.The capacity allocated to nth user (limT 1T n(t)), is

the average maximum achievable rate over all the subcar-riers for reliable communication under the given resourceallocation policy. Fig. 2 shows the capacity allocated toeach user by the following algorithms: MR-SAA, RC-SAA,the SAA in [10] and the proposed SAA for case (a). Therequired capacity for each user (equal to the average arrivalrate) is also plotted for reference. The total traffic load ischosen to be 22.5 units (bits/OFDM symbol). Since theusers have i.i.d. channels, the MR-SAA allocates approx-imately the same capacity to each user. The MR-SAAachieves the maximum overall capacity (sum of the capac-ity allocated to all users) of 26.2, but the capacity is notallocated to the users who require it. The RC-SAA al-gorithm can allocate capacity proportional to the arrivalrates. However, the total capacity achieved by the RC-SAA ( 14) is not enough to support the required rate.

The SAA proposed in [10] is simulated as (correspondingto = 2 in [10])

j = argmaxi

[Qi(t)[ai(t)]

2 log2

{1 +

P

Ki,k(t)

}], (10)

assuming equal power allocation initially to obtain the val-ues of the achievable transmission rate in each subcarrierfor each user at time t.

Fig. 3 shows the capacity allocated to each user byabove-mentioned SAAs for case (b). MR-SAA allocatesmaximum capacity to the best channel users. Therefore,even when the overall capacity is maximum, it is not al-located according to the users requirements. RC-SAAattempts to take arrivals into account, however achievesmuch less overall capacity, since it doesnt take into ac-count buffer state. The proposed SAA and SAA in [10]take buffer and channel state into account in addition toarrivals and achieve higher diversity gains.

1 2 3 4 5 6 7 8 90

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

USER INDEX

ALL

OC

AT

ED

CA

PA

CIT

Y

REQUIRED CAPACITY

MAXRATE CAPACITY

RHEECIOFFI CAPACITY

CAPACITY IN [10]

PROPOSED ALGORITHM CAPACITY

Fig. 2. Allocated capacity and the required capacity for heteroge-neous rate users with i.i.d channels (Case (a))

1 2 3 4 5 6 7 8 90

1

2

3

4

5

6

USER INDEX

ALL

OC

AT

ED

CA

PA

CIT

Y

REQUIRED CAPACITY

MAXRATE CAPACITY

RHEECIOFFI CAPACITY

CAPACITY IN [10]

PROPOSED ALGORITHM CAPACITY

Fig. 3. Allocated capacity and the required capacity for heteroge-neous rate users with scaled channel profiles (Case (b))

Fig. 4 plots the outage as a percentage of total arrivedbits for the maximum outage user as a function of the to-

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tal traffic for case (a). It is evident that the proposedSAA can support significantly higher traffic ( 25) thanthe RC-SAA ( 15) while maintaining stable queues. Infact, the proposed SAA can support traffic upto 91% of themaximum achievable capacity of 26.2 without any outage,i.e., dropped traffic. The MR-SAA can support traffic onlyupto 26.2 (5/9) = 14.55. SAA in [10] supports a totaltraffic of 20 approximately. We can also infer for case (b),the maximum traffic supported by different SAAs with-out any outage from Fig. 5. The proposed SAA supportshigher maximum traffic ( 22) compared to that achievedby SAA in [10] ( 16).

18 20 22 24 26 280

5

10

15

20

25

30

35

40

45

50

TOTAL TRAFFIC LOAD

MA

XIM

UM

OU

TA

GE

AM

ON

G A

LL U

SE

RS

(IN

%) MAXRATE SAA

RHEECIOFFI SAA

SAA IN [10]

PROPOSED SAA

Fig. 4. Maximum outage among all users (in %) vs. Traffic forheterogeneous rate users with i.i.d. channels (Case (a))

18 20 22 24 26 280

10

20

30

40

50

60

70

80

90

100

TOTAL TRAFFIC LOAD

MA

XIM

UM

OU

TA

GE

AM

ON

G A

LL U

SE

RS

(IN

%) MAXRATE SAA

RHEECIOFFI SAA

SAA IN [10]

PROPOSED SAA

Fig. 5. Maximum outage among all users (in %) vs. Traffic forheterogeneous rate users with scaled channel profiles (Case (b))

The proposed SAA uses the HoL packet delay instead ofthe average queue delay used in [10] and provides a betterallocation of capacity. The Greedy Reassignment policy in[10] is not used in the simulation. The Greedy Reassign-ment policy can be used to improve our proposed SAA aswell as the SAA in [10]. In summary, the proposed SAAis able to allocate capacity to the users based on their re-quirements and keep the queues stable. Furthermore, the

proposed SAA uses measured arrival rates and does notneed prior knowledge of the actual arrival rates.

V. Conclusion

Buffering bursty traffic can provide a good delay-throughput trade-off and improve the overall throughputof the system. Therefore, subcarrier allocation based onqueue and channel information can perform significantlybetter than MR-SAA and RC-SAA which do not use queueinformation. A good SAA should be close to the MR-SAA in total (sum) capacity while being as fair as possible.The proposed algorithm performs better than the existingsubcarrier allocation algorithms like [2], [10] in terms ofthroughput improvement and fair capacity allocation. Theproposed SAA: (a) allocates capacity fairly amongst theusers, and (b) supports traffic load very close to the maxi-mum capacity.

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