distributed uplink scheduling and rate control in cdma2000 using adaptive antenna arrays

Int. J. Electron. Commun. (AEÜ) 63 (2009) 841–852

www.elsevier.de/aeue

Distributed uplink scheduling and rate control in cdma2000 using adaptiveantenna arrays

Elias Yaacoub∗, Zaher Dawy, Ali El-Hajj, Karim Y. Kabalan

Electrical and Computer Engineering Department, American University of Beirut, P.O. Box 11-0236, Beirut, Lebanon

Received 25 February 2008; accepted 3 July 2008

Abstract

Distributed uplink scheduling and rate control in CDMA networks are considered in the case of adaptive antenna arrayspresent at the base station. The system model with omnidirectional antennas is generalized to the case where adaptive antennaarrays are deployed. Rate control in a probabilistic manner is investigated. Long-term control by the base station through tokenbucket constraints is incorporated in the system. Monte Carlo simulation results show considerable improvement when adap-tive antenna arrays are used. Optimization of the rate transition probabilities is treated in the special case of on–off scheduling.� 2008 Elsevier GmbH. All rights reserved.

Keywords: Antenna arrays; Distributed uplink scheduling; Rate control; Token bucket; cdma2000

1. Introduction

cdma2000 1xEV-DO Release 0, or IS-856, is a 3G cellularsystem designed to provide spectrally efficient packet dataservices for wide-area wireless internet access [1]. 1xEV-DO achieves a substantial gain in uplink throughput overtraditional cdma2000 systems since it employs advancedtechnologies such as hybrid-ARQ, adaptive modulation andcoding, multiuserdiversity, and adaptive server selection [2].1xEV-DO Release 0 is the first cellular CDMA system thatemploys closed-loop interference control on the uplink viarise-over-thermal (RoT) feedback [3]. This improves thespectral efficiency by allowing the network to operate athigher RoT while maintaining system stability. The increasein demand for delay-sensitive applications with symmetricdata rate requirements such as wireless gaming, video tele-phony, and voice-over-IP has mandated an enhancement to

∗Corresponding author.E-mail addresses: [email protected] (E. Yaacoub),

[email protected] (Z. Dawy), [email protected] (A. El-Hajj),[email protected] (K.Y. Kabalan).

1434-8411/$ - see front matter � 2008 Elsevier GmbH. All rights reserved.doi:10.1016/j.aeue.2008.07.002

Release 0, the cdma2000 1xEV-DO Revision A, standard-ized in March 2004 by 3GPP2 and TIA [4]. The enhancedsystem enables these traffic types to achieve latency targetsby allowing them to benefit from high uplink spectral effi-ciency and advanced packet scheduling strategies. In fact,distributed scheduling of mobile users in CDMA networkshas lately gained more importance. The power and versa-tility of mobile devices have leveraged running more pow-erful applications on them [5,6]. Mobile devices are givenmore autonomy in making transmission decisions, and thusmore freedom of action (e.g. see [5–7]). This differs fromthe traditional aspects of wireless networks, where the ac-cess network maintains full and centralized control in thedistribution of the system resources.Examples of centralized scheduling schemes include max-

imum C/I and proportional fair (PF). The maximum C/Ischeme was shown in [8] to maximize total uplink through-put, by allowing the user with the best channel at a giventime to transmit over the whole bandwidth, while keepingthe other users silent. However, this scheme raises the issueof fairness between the different users, since a user closeto the base station will probably have a better channel for

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842 E. Yaacoub et al. / Int. J. Electron. Commun. (AEÜ) 63 (2009) 841–852

longer time periods than a user located close to the cellboundary. The PF algorithm has been derived (e.g. see [9]) toaddress the issues of fairness and delay, while still exploitingthe multiuser diversity gain inherent in a system with usershaving independent fluctuating channel conditions.Conversely to centralized schemes, mobile devices have

more autonomy in making transmission decisions in dis-tributed schemes. Several standards for state-of-the-art 3Gcellular networks, e.g. 1xEV-DO [10], have introducedmechanisms that give devices greater independence inmaking transmission decisions best matched to their appli-cations, e.g. deciding when to transmit and at what rate.The cost of this flexibility is potentially higher interference,and a corresponding degradation in performance [5,6].To maintain some control over the interference in 1xEV-

DO, base stations set a reverse-link activity bit (RAB) onwhen the load increases, and clear it in the opposite case[1]. The RAB is sometimes used in conjunction with a tokenbucket, where tokens are in units of transmission power, andthe base station controls the token generation rate and thetoken bucket depth [5]. The reverse traffic channel MACdesign of cdma2000 1xEV-DO Rev A system is discussedin [11], where an algorithm is presented to update the tokengeneration rate and the token bucket depth based on thecomputation of the RAB. The reverse traffic channel ratecontrol algorithm for cdma2000 is presented in [3], wheretransition from one rate to another is performed by mobiledevices in a probabilistic manner based on the value of theRAB. A rate control algorithm inspired from the cdma20001xEV-DO rate control algorithm is proposed for high-speeduplink packet access (HSUPA) in [12], where it is shownthat the proposed algorithm outperforms the conventionalscheduling algorithm used in UMTS Release 6. Althoughthe transmission rates are varied in a probabilistic manner,no study of the optimal transition probabilities is presented(optimal in the sense of maximizing the average throughput).This issue is tackled in [5] in a basic scenario where a simpleon–off scheduler is studied, i.e. users either transmit at afixed rate R with a probability p, or do not transmit with aprobability (1 − p).The independence given to mobile devices in distributed

uplink scheduling leads potentially to higher interference.This would lead to a decrease in the average achievedthroughput. On the other hand, in centralized schemes, thetight control exercised by base stations allows to enhancethe throughput, but the flexibility for the users in distributedscheduling will be lost. It would be interesting to jointhe benefits of some centralized control with distributedscheduling, in order to enhance the throughput while at thesame time giving mobile devices more freedom of action.To reach this objective, we propose the use of adaptive

antenna arrays at the base stations along with distributeduplink scheduling. Adaptive antenna arrays would lead tothroughput enhancement and interference mitigation (e.g.see [13–18]), while distributed scheduling will provide theusers with more independence. Therefore, in this work,

we investigate the gains achieved by user-specific coherentbeamforming in the uplink of the 1xEV-DO rev A system. Adistributed uplink rate control scheme similar to the one pre-sented in [3] is utilized. The long-term control is exercisedby the base stations through a token bucket scheme inspiredfrom the one described in [11]. Antenna arrays with closespacing between elements are considered. A comparisonbetween the results obtained by using linear antenna arrayswith different number of elements is presented. A beamis formed in the direction of every user in the cell. With-out loss of generality, we assume a single path from eachuser. This assumption is not expected to have an impact onthe paper conclusions and insights, since beamforming canbe performed for the different individual paths detectableby the RAKE receiver (e.g. see [19], where an overviewof different beamforming–RAKE receiver combinations ispresented, and a novel scheme for combining a RAKE re-ceiver with beamforming is proposed and shown to havebetter performance and less complexity than other schemes).Furthermore, it is normally argued that the performancegains of scheduling algorithms are higher with less diver-sity due to the higher channel variation among users (e.g.see [9]).The system model is described in Section 2. The uplink

rate control algorithm is described in Section 3, along withthe token allocation scheme. In Section 4, we introduce thevarious antenna arrays used in the simulations and discusstheir radiation characteristics. Monte Carlo simulation re-sults of the scenarios with and without adaptive antennas arecompared in Section 5 and the improvements obtained arediscussed. Finally, conclusions are drawn in Section 6.

2. System model

In this section, we generalize the uplink rate control andscheduling approach of the 1xEV-DO system to the caseof base stations equipped with adaptive antenna arrays, bymodifying the derivations and analysis to include the antennaarray gain as a function of the different users’ directions.This is a novelty over the existing literature (e.g. see [5]),where the antenna gain is omitted, since in the omnidirec-tional case it is the same in all directions and consequentlynormalized to one.The achievable data rate in the uplink of the 1xEV-DO

system is strongly influenced by the transmission powerused by all the mobile devices. Therefore, the uplink of the1xEV-DO system is interference limited. Hence, a device’stransmission decisions are governed by the trade-off betweenincreasing a device’s own signal strength and causing inter-ference among other devices. Consequently, a decision mustbe made by the mobile device about its transmission powerand data rate. The 1xEV-DO uplink incorporates several ad-vanced physical andMAC layer design principles to improvethe flexibility of transmission decisions, and to facilitate dis-tributed operation and give devices greater independence

E. Yaacoub et al. / Int. J. Electron. Commun. (AEÜ) 63 (2009) 841–852 843

[6]. In the Rev A specifications, the pilot-assisted transmis-sion guides the choice of the transmission power, and tokenbucket control influences the frequency (and scheduling) ofpacket transmissions.During uplink transmission in the 1xEV-DO system, each

device transmits a pilot signal whose power is controlled bythe access network using a fast closed power control loop,such that the pilot power received at the access networkfrom each device is approximately the same, even in caseof channel fluctuations. The power transmitted in a giventime slot in order to achieve a data rate R is then relatedto the pilot power through a proportionality factor that is afunction of the desired rate:

PiD[Ri (t), t] = TTP[Ri (t)]P

iS(t) (1)

where

• PiD[Ri (t), t] is the transmitted power of user i at a time

slot t when the transmission rate is Ri (t),• Pi

S(t) is the transmitted pilot power of user i, varied ac-cording to the fast inner-loop power control,

• TTP[Ri (t)] is the total-to-pilot (TTP) transmit power ratio.It is a proportionality factor function of the rate Ri (t). Itscales the transmission power in units of the transmittedpilot power.

In the above mechanism, the fast inner-loop power con-trol keeps the received pilot signal approximately constant,by allowing it to track variations of the wireless channel.Consequently, the choice of transmission power for the datais de-coupled from the problem of coping with fading andattenuation on the wireless channel. Hence, the data trans-mission power can be set relative to the pilot strength. Al-though mobile devices are allowed distributed usage of re-sources at short time scales, control is still exercised bythe base stations on the allocation of long-term resourcesper device. In this way, the access network prevents usersfrom becoming persistently greedy and thus generating toomuch interference, which in the long run can degrade systemthroughput.The 1xEV-DO Rev A system achieves this long-term con-

trol through a token bucket. Each device has a bucket ofmaximum depth L in which it stores its current credit oftokens. The bucket is filled at a rate of � tokens per trans-mission slot. The number of tokens present in the bucketdetermines the set of rates at which the device is entitled totransmit, through the TTP power ratio which represents therate to token mapping [11]. Naturally, a rate-to-token map-ping should entail larger amounts of tokens when the rateincreases, since this is translated into an increase of trans-mission power.The system is assumed to consist of a single cell with n+1

homogeneous and continuously backlogged users sharing atime-slotted uplink. The SINR of user i in slot t is then

given by

Si [Ri (t), t]=G[Ri (t)]Gi

loss(t)Ai [�i (t)]PiD[Ri (t), t]

�2+∑j � i G

jloss(t)Ai [� j (t)]P

jD[R j (t), t]

(2)

where

• Ri (t) is the transmission rate of user i at time slot t,• Gi

loss(t) represents the channel variation experienced byuser i in time slot t. It is a time-varying function of the userdistance as well as log-normal shadowing and fast-fading,

• G[Ri (t)]=W/Ri (t) is the processing gain associated withrate Ri where W is the spread-spectrum bandwidth. For1xEV-DO systems, W = 1.25MHz,

• �2 = N0W is the thermal noise power, with N0 being thenoise power spectral density,

• Ai [� j (t)] is the antenna gain due to the beam pointed inthe direction of user i, measured in the direction � j (t) ofuser j at time slot t.

When omnidirectional antennas are used, Ai (�) is the samefor all i and �. However, when adaptive antennas are de-ployed, Ai is maximum in the direction of �i (t) and de-creases in the other directions. Hence, Ai [�i (t)] correspondsto the direction of the main lobe, whereas Ai [� j (t)] corre-sponds to the direction of sidelobes and nulls (unless usersi and j are in the same direction). Thus, adaptive antennaswill increase the SINR since the desired signal is multipliedby Ai [�i (t)] (gain in the direction of the main beam) andthe interfering signals are reduced due to their multiplica-tion by Ai [� j (t)], contrarily to the omnidirectional antennacase where both the signal and the interference are weightedequally by the receive antenna.Since perfect power control is assumed, the received pilot

power at the base station is considered to be constant for allusers:

Giloss(t)Ai [�i (t)]P

iS(t) = � = �2

� − n(3)

where 1/� is a common target SINR that each pilot signalshould reach at the base station.

3. Rate control algorithm

The rate control algorithm used in this work follows theguidelines of the uplink channel MAC protocol describedin [2]. It defines the rules used by the mobile device todetermine its transmission data rate on the uplink channel.Two mechanisms allow the base station to control the trans-mission data rate of a given device. First, the device mayperiodically receive a message from the base station indi-cating the maximum data rate it may transmit on the uplink.In this work, the rate limit is assumed to be the maximumallowed rate. Secondly, the mobile device receives an RABfrom each base station in its active set, indicating whether


Table 1. Transmission probabilities and total-to-pilot (TTP) transmit power ratios [3]

Rate (kbps) 0 9.6 19.2 38.4 76.8 153.6

q 1 3/16 1/16 1/32 1/32 0p 0 0 1/16 1/16 1/8 1TTP 2 4.37 6.73 11.44 23.13 72.79

the total uplink traffic channel interference received at thesector is above a certain value. From this information, thedevice determines whether it should increase or decrease itsdata rate. This rate modification (increase or decrease) isperformed in a probabilistic manner. The probabilities gov-erning these transitions are specified by the base station foreach mobile device, allowing the network to differentiate thebehavior of the uplink traffic channel rate control algorithmamong different mobiles. The procedure used by a mobiledevice to determine its uplink data rate is summarized as fol-lows: Defining RateLimit as the maximum rate allowed bythe network, CurrentRate as the device’s current transmis-sion data rate on the uplink (it may be 0 if the mobile deviceis not transmitting data),NearestLowerRate as the maximumavailable rate lower than CurrentRate, NearestUpperRate asthe minimum available rate higher than CurrentRate, Low-estAllowedRate as the lowest allowed data rate, HighestAl-lowedRate as the maximum permissible data rate, and Com-binedRAB as the logical OR operation on the most recentRABs received from all base stations in the active set,

1. If CombinedRAB = 1 (i.e. the interference is high inat least one base station in the active set), then setMaxRate = max(LowestAllowedRate, NearestLowerRate) with probability p or MaxRate=CurrentRate withprobability (1 − p). The transition probability p is afunction of CurrentRate. The transition probabilities arespecified in Table 1.

2. If CombinedRAB = 0 (i.e. the interference is low at allthe base stations in the active set), then set MaxRate =min(HighestAllowedRate, NearestUpperRate) withprobability q or MaxRate = CurrentRate with probabil-ity (1 − q). The transition probability q is a function ofCurrentRate. The transition probabilities are specifiedin Table 1.

3. The new transmission data rate may not exceed thelimit given by the network, thus, set NewRate =min(MaxRate, RateLimit).

4. If the transmit power available at the mobile device isnot sufficient to support transmission at NewRate, thenthe mobile device decreases NewRate to the highest datarate that can be accommodated by the available transmitpower.

5. The mobile device transmits at NewRate.

The base station controls the actions of the mobile de-vices by the rate limit, the transition probabilities and the

RAB. The algorithm presented above sets the rate limit foreach mobile device to 153.6kbps, the highest rate allowed,as in [3], and sets the transition probabilities as specifiedin Table 1. In a single-cell scenario, the CombinedRAB isequivalent to the RAB set by the base station of the cell.To determine the value of the RAB, the rise of interferenceover the thermal noise (RoT) is computed. If it is above acertain threshold, the RAB is set to 1; otherwise, it is set to0. We consider the average interference obtained by averag-ing the second term in the denominator of (2) over all users.Denoting the result by I0 and the noise spectral density byN0, the value of the ratio I0/N0 is computed in order to set(or unset) the RAB:

I0N0

=1

n + 1

∑n+1i=1

∑j � i G

jloss(t)Ai [� j (t)]P

jD[R j (t), t]

N0(4)

The above discussion does not take into account the in-corporation of token bucket constraints. Token buckets allowbase stations to prevent users from becoming persistentlygreedy and thus generating too much interference. The pro-cedure used to add and/or remove tokens from the bucket ofeach user is described as follows:

1. At each time slot, � tokens are added to the bucket ofeach user, in condition that the total number of tokens inthe bucket does not exceed the depth L.

2. If the user transmits at a rate Ri (t) at a certain time slott, then TTP[Ri (t)] tokens are removed from the bucket.This way, users requesting high transmission rates arepenalized by losing more tokens.

The algorithm described above makes use of the proba-bilities of Table 1, which are not necessarily the best com-bination of transition probabilities. The problem of findingthe optimal transition probabilities is tackled in [6], wherea simple on–off scheduler is considered instead of allowingtransitions between all available rates as in [3]. With on–offscheduling, a user either transmits at a rate R with a proba-bility p or does not transmit with a probability (1− p). Thepurpose is to find the value of p that leads to a maximumthroughput. However, the average on–off throughput is com-puted in [6] by assuming it varies linearly with the SINR.In this work, we resort to a more accurate system model bytreating on–off scheduling as a special case of the uplinkrate control of the 1xEV-DO system with multiple rates, andthen we find the optimal probabilities via simulation. We


also show that the optimized on–off system outperforms theunoptimized system with multiple rates.

4. Antenna arrays

Single antenna elements have lower gains and higher sidelobe levels than antenna arrays constructed from the sameelements. In an antenna array, the number of elements, thespacing between them, their excitation coefficients, and theirrelative phases are parameters that can be adjusted not onlyto increase the antenna gain but also to narrow the beam(i.e. decrease the beamwidth), steer the beam in a givendirection, and/or control the side lobes level (by adjustingthe excitation coefficients of the antenna array, e.g. using theDolph–Chebyshev method [20]). These factors determinethe array factor, which is used in the calculation of the arraydirectivity and consequently the array gain. The total field ofan array can be calculated by multiplying the field of a singleelement at a selected reference point (usually the origin) andthe array factor. The array gain is equal to the directivitymultiplied by the loss coefficient, which in turn depends onthe antenna type. When the losses are negligible, the gainis approximately equal to the directivity [20]. Widely usedantenna arrays are the uniform linear arrays (ULAs) wherethe radiating elements are placed on a line with equal spacingand excitation.The normalized array factor of an N element ULA with

equal amplitude excitation and inter element spacing d isgiven by [20]

AFULA(�) = sin((N/2)�)

sin((1/2)�)(5)

where

� = kd cos(�) − kd cos(�0) (6)

�0 is the direction of maximum radiation and k is the wavenumber. To steer the beam in the direction �0, the progressivephase between the elements should be −kd cos(�0).Fig. 1 shows the normalized array factors of 2-element

and 4-element ULAs. We varied the inter-element spacingin order to obtain narrower main beams with higher direc-tivities while keeping the same maximal side lobe level, andwe used the spacing that yielded the best results. An exam-ple is shown in Fig. 1 for the 2-element array, whereas forthe 4-element array, only the best result is plotted. In thesimulations, we used the 2-element array with a spacing of0.532, and the 4-element array with a spacing of 0.8.As stated previously, the pattern of an antenna array is

the product of the element pattern and the array factor. Asa constituent element for the array factors shown in Fig. 1,we select a microstrip patch designed in [21]. The design ofthe patch was performed with the objective of meeting therequirements of base station antenna arrays in mobile com-munication systems. One of the contributions of this work

0 20 40 60 80 100 120 140 160 180−50

−45

−40

−35

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−25

−20

−15

−10

−5

0

θ

Nor

mal

ized

Arr

ay F

acto

r (dB

)

2−element, d = 0.5 λ2−element, d = 0.532 λ4−element, d = 0.8 λ

Fig. 1. Normalized array factors of the uniform linear arrays usedin the simulations.

2

4

6

8

30

210

60

240

90

270

120

300

150

330

180 0

Fig. 2. Pattern of the microstrip patch used as the constituentelement of the antenna arrays.

is using the patch of [21] in linear antenna arrays after op-timizing their inter-element spacing, and showing that evenwith simple antenna configurations, substantial throughputgains can be achieved in the context of distributed uplinkscheduling in cdma2000. The pattern of the microstrip patchis shown in Fig. 2. The array patterns obtained by the multi-plication of the element pattern of Fig. 2 by the array factorsof Fig. 1 are shown in Fig. 3.The characteristics of the linear arrays obtained by using

the patch of [21] are shown in Table 2 . In Table 2, the di-rectivities, half-power beam widths (HPBW), and the inter-element spacings d are shown.Eq. (5) is independent of � since it expresses the array

factor of a linear array in the vertical direction. It should be


−150 −100 −50 0 50 100 150−50

−45

−40

−35

−30

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−20

−15

−10

−5

0

φ

Nor

mal

ized

Arr

ay P

atte

rn (d

B)

2−element, d = 0.5 λ2−element, d = 0.532 λ4−element, d = 0.8 λ

Fig. 3. Normalized array patterns of the uniform linear arrays usedin the simulations.

Table 2. Properties of the different antenna arrays

Array Directivity (dB) HPBW (deg) d (in )

2-Element ULA 21.99 44.75 0.52-Element ULA 22.37 43.35 0.5324-Element ULA 29.21 16.31 0.8

noted that the array factors of Fig. 1 correspond to arraysplaced on the vertical direction (z-axis). This position wasonly used to simplify the forms of the equations since whenthese arrays are placed along other axes their properties willnaturally still be the same but their mathematical expressionswill be more complex. However, in this position, these ar-rays are broadside arrays having omnidirectional propertiesin the azimuth (x–y plane). In order to use them as adaptiveantennas, we must place them in the azimuth plane, perpen-dicularly to the vertical direction (z-axis). Still, even in thisposition, the array factors of linear arrays have major lobesin two opposite directions (e.g. � = 0◦ and � = 180◦ whenplaced on the y-axis). But Fig. 2 shows that the element usedhas very low back lobes. Hence, when the patch is used toform the arrays, its main lobe will enhance the main beamof the array factor (�=0), whereas its back lobe will reducesignificantly the undesired lobe at �=180◦. In addition, themultiplication property of the array pattern will lead to sidelobes of lower level than those in the array factor. Theseresults can be verified by inspecting Fig. 3.It should be noted that only a single antenna array is used

for all the users in a cell. The steering of the main beamis performed by multiplying the signals collected from eachantenna element of the antenna array by specific weightsdepending on the location of the user (e.g. see [22,23]).Hence, at every time slot, the base station will have a specificset of coefficients for each user, used to weigh the signalscollected from the elements of the single antenna array.

5. Simulation results and analysis

This section presents the simulation results obtained byapplying the distributed scheduling concept presented inSection 2 and the rate control algorithm of Section 3 to acell with a base station equipped with adaptive antenna ar-rays, and compares the results to the case of omnidirectionalantennas.

5.1. Simulation environment

The results are obtained using a simulation of the uplinkof the 1xEV-DO system. The simulation attempts to accu-rately emulate the impact of the channel on the transmis-sions from different users, and compares the performanceof omnidirectional and adaptive antennas within a singlecell. The carrier frequency of the CDMA system was set to1900MHz, its bandwidth to W = 1.25MHz, and the targetpilot SINR 1/� to −17dB. The duration of transmissionslots was taken to be 16.667ms, the frame length on the up-link of 1xEV-DO. Hence, each device is making schedulingdecisions at this time granularity. The thermal noise power,�2, was set as per the following equation:

�2 = N0W = kTWN F (7)

where k is Boltzman’s constant, T the temperature in Kelvin,and NF the receiver noise figure. The temperature was setto 300K and the receiver noise figure to 9dB. Users aregenerated randomly within a cell of 1km radius. Initial ratesfor each user were also selected arbitrarily. Each experimentwas repeated 100 times, and during each time it was runfor 11000 slots. The results of the first 1000 slots were notconsidered in the averaging in order to allow the system tostabilize. This step is necessary to overcome the effects ofthe random selection of the initial user rates.The path loss of user i is of the form

Giloss(t) =

d�iF(t) (8)

In (8), the first factor captures propagation loss, with aconstant chosen to be 100, di the distance from mobile i tothe base station, and � the path loss exponent, which wasset to a value of 4 [24]. The second factor, F(t), captureslog-normal shadowing (with an 8-dB standard deviation) inaddition to flat fading (assumed to be Rayleigh distributedwith a Rayleigh parameter a such that E[a2] = 1). An RoTthreshold of 5dB was used to set the RAB to 1. The maxi-mum transmit power for each mobile was set to 23dBm. Ateach time slot, (4) is computed. If the result is greater thanthe RoT threshold, the RAB is set to 1; otherwise, it is setto 0. Then, the transmission rate of each mobile device isdetermined according to the algorithm in Section 3. Whenthe power required by a mobile to transmit at a given rateexceeds the maximum power, the mobile attempts transmis-sion at the nearest lower rate, until it finds a suitable rate.


Otherwise, it refrains from transmission. The average userthroughput is obtained by averaging the transmission ratesover all users and all time slots.

5.2. Simulation with multiple transmission rates

Fig. 4 shows the average throughput results, obtainedby using the different antenna arrays, versus the numberof users. No token constraints are considered. The transi-tion probabilities between the rates are the ones shown inTable 1. Clearly, adaptive antenna arrays outperform omni-directional antennas, and the 4-element array is superior tothe 2-element array. It can be seen that for a fixed numberof users, the average throughput is considerably higher withadaptive antennas. In addition, for a fixed desired averagethroughput, a system with adaptive antennas can accom-modate much more users. For example, fixing the desiredthroughput at 153.6kbps (the maximum available rate), theproposed 4-element linear array can accommodate 18 users(all achieving the desired rate), whereas the 2-element arrayallows 8 users to achieve the desired rate, compared to only2 users when omnidirectional antennas are used. When thenumber of users increases, the user rates decrease due to theincrease in interference. After a certain limit, users are onlyable to achieve the lowest allowed rate. In Fig. 4, this limitis reached with 48 users when using the 4-element array, 42users when using the 2-element array, and 20 users whenomnidirectional antennas are used.Taking token bucket constraints into account, the results

of Fig. 5 are obtained with �=5 and L =150 tokens. Thoseof Fig. 6 are obtained with � = 50 and L = 150 tokens,whereas Fig. 7 shows the results obtained with � = 50 andL =1500 tokens. The superiority of adaptive antenna arraysis evident. However, the effect of adding token constraints isa limitation of the maximum achieved average throughput.The effect of increasing the token rate � for the same bucket

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Number of Users

Ave

rage

Thr

ough

put (

kbps

)

Omnidirectional2 elements4 elements

Fig. 4. Throughput comparison between different antennas whenthe number of users is varied and multiple rates are allowed.

0 10 20 30 40 509.5

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Fig. 5. Throughput comparison with token constraints: � = 5 andL = 150.

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)Omnidirectional2 elements4 elements

Fig. 6. Throughput comparison with token constraints: �=50 andL = 150.

depth L is an increase in the average throughput, as seen bycomparing Figs. 5 to 6. Increasing the bucket depth L whilekeeping the same filling rate � has a similar effect, as shownby comparing Figs. 6 to 7. In Fig. 5, the average throughputin the case of 18 users is around 12.2kbps, whereas it is9.6kbps for 20 users. This explains the sharp transition, sincethe range between the two rates is not high enough to allowa smooth transition as in Figs. 6 and 7.In Fig. 8, a comparison between the results obtained with

token constraints and those obtained without token con-straints is presented. The results of Fig. 4 are shown alongwith those of Fig. 7 (� = 50, L = 150). Interestingly, theplots representing the token constrained case coincide withthose representing the absence of token constraints, exceptfor the maximum value. The effect of adding token bucketconstraints is in the reduction of the maximum achievable


0 10 20 30 40 500

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Fig. 7. Throughput comparison with token constraints: �=50 andL = 1500.

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Omnidirectional − without Token Bucket2 elements − without Token Bucket4 elements − without Token BucketOmnidirectional − with Token Bucket2 elements − with Token Bucket4 elements − with Token Bucket

Fig. 8. Throughput comparison with and without token constraints(� = 50 and L = 1500).

average throughput. This result is not surprising, since hightransmission rates require high transmission power (relativeto the pilot power), and hence are penalized by a greateramount of tokens, thus draining the token bucket of thegreedy users, and consequently reducing the throughput.

5.3. On–off transmission

In Section 5.2, each user tries to transmit at the highestpossible rate, with the transition probabilities regulating theinterference level at the base station. The maximum through-put would be achieved when optimal transition probabilitiesare used. However, the transition probabilities of Table 1were used without any optimization, since the optimizationprocess would be of considerable complexity. Nevertheless,in order to show the importance of optimizing the probabil-

Table 3. Transition probabilities in the on–off transmission case

Rate (kbps) 0 R

q p 0p 0 1 − p

ities, we consider a simple on–off system where users eithertransmit at a rate R with probability p or do not transmitwith a probability (1 − p). We aim at finding the optimaltransition probabilities that maximize the average through-put in this scenario, and show that the average throughputwith optimization in the on–off scheduling scenario is higherthan the case of multiple transition rates without optimiza-tion. Table 3 shows the transition probabilities in the on–offtransmission case. No token constraints are assumed.Simulations performed in the case of 24 users and R =

76.8kbps are shown in Fig. 9, and those performed in thecase of 48 users with R = 153.6kbps are shown in Fig. 10.However, in the case of 48 users, letting TTP(0) = 2 as inTable 1 leads to enough interference to exceed the 5-dBthreshold and set RAB= 1. Consequently, no user is able totransmit in this case, except when the 4-element array is used(see Fig. 10). Therefore, we resort to the assumption made in[5,6], where TTP(0)=0 is used. We keep q(0)= p. However,since in [5] the RAB is not considered, we implement a thirdscenario: we let q(0)=1 and keep p(R)= (1− p). This way,when RAB = 0, all users either transmit with a probabilityp or do not transmit with a probability (1 − p). Similarscenarios were implemented in the case of 24 users andR=76.8kbps for comparison purposes. The three scenariosare summarized below:

1. p(R) = (1 − p), TTP(0) = 2 and q(0) = p,2. p(R) = (1 − p), TTP(0) = 0 and q(0) = p,3. p(R) = (1 − p), TTP(0) = 0 and q(0) = 1.

Fig. 9 shows the results obtained in the case of 24 usersand R = 76.8kbps. The average throughput at base stationsequipped with adaptive antennas is considerably higherthan in the omnidirectional case. The performance of adap-tive antenna arrays is very similar in all three scenarios. Inaddition, it can be noticed that with the 4-element array, allusers are able to achieve the desired rate R = 76.8kbps inthe three scenarios. With the 2-element array, the through-put approaches the desired rate as p increases. Hence,the optimal probability in this case is p∗ = 1. As ex-pected, the omnidirectional case is the most sensitive tointerference from other users, since the performance differssignificantly between the three scenarios. The throughputin scenario 2 is higher than in scenario 1, and the optimalprobability is p∗ = 1. However, for scenario 3, the optimalprobability is p∗ = 0.04 ≈ 1/24. In fact, when q(0)= 1, allusers attempt to transmit at rate R = 76.8kbps with proba-bility p. Since the omnidirectional case is the most sensitiveto interference, the maximum throughput is achieved when


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

Probability p

Ave

rage

Thr

ough

put (

kbps

)Omnidirectional with q(0) = p and TTP(0) = 22 element with q(0) = p and TTP(0) = 24 element with q(0) = p and TTP(0) = 2Omnidirectional with q(0) = p and TTP(0) = 02 element with q(0) = p and TTP(0) = 04 element with q(0) = p and TTP(0) = 0Omnidirectional with q(0) = 1 and TTP(0) = 02 element with q(0) = 1 and TTP(0) = 04 element with q(0) = 1 and TTP(0) = 0

Fig. 9. Throughput comparison in the case of on–off scheduling for different antennas used in the case of R = 76.8kbps, and 24 users.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

50

60

70

80

Probability p

Ave

rage

Thr

ough

put (

kbps

)

Omnidirectional with q(0) = p and TTP(0) = 22 element with q(0) = p and TTP(0) = 24 element with q(0) = p and TTP(0) = 2Omnidirectional with q(0) = p and TTP(0) = 02 element with q(0) = p and TTP(0) = 04 element with q(0) = p and TTP(0) = 0Omnidirectional with q(0) = 1 and TTP(0) = 02 element with q(0) = 1 and TTP(0) = 04 element with q(0) = 1 and TTP(0) = 0

Fig. 10. Throughput comparison in the case of on–off scheduling for different antennas used in the case of R = 153.6kbps, and 48 users.

only one user transmits at a given time slot, i.e. p∗ = 124 .

The system in this case would be a pure TDMA system. Atother probabilities, the system would be a hybrid between

CDMA and TDMA. However, with adaptive antennas, theoptimal probability was found to be p∗ = 1, i.e. a pureCDMA system.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

20

40

60

80

100

120

140

160

180

200

Probability p

Ave

rage

Thr

ough

put (

kbps

)

Omnidirectional with q(0) = p and TTP(0) = 22 element with q(0) = p and TTP(0) = 24 element with q(0) = p and TTP(0) = 2Omnidirectional with q(0) = p and TTP(0) = 02 element with q(0) = p and TTP(0) = 04 element with q(0) = p and TTP(0) = 0Omnidirectional with q(0) = 1 and TTP(0) = 02 element with q(0) = 1 and TTP(0) = 04 element with q(0) = 1 and TTP(0) = 0

Fig. 11. Throughput comparison in the case of on–off scheduling for different antennas used in the case of R = 153.6kbps and 24 users.

The results of a more loaded system (48 users and R =153.6kbps) are displayed in Fig. 10. The performance ofthe 2-element array is close to the omnidirectional case.This is due to its relatively wide main lobe. In fact, whenthe number of users increases, the probability that they fallwithin the beam dedicated to the user of interest increases,thus increasing interference. Nevertheless, the 4-element ar-ray leads to a major throughput increase, due to its muchnarrower beam and much higher directivity. As mentionedpreviously, when scenario 1 is applied, interference is highenough to prohibit transmission in the cases of the omnidi-rectional and 2-element antennas. In scenario 2, the optimalprobability is p∗ = 1 for the three array types. However, forscenario 3, the optimal probability is p∗ = 0.02 ≈ 1/48. Infact, when q(0) = 1, all users attempt to transmit at a rateR = 153.6kbps with probability p. Although throughput ishigher with adaptive antennas, all three array types are af-fected by interference in such a loaded system. Hence, themaximum throughput is achieved when only one user trans-mits at a given time slot, i.e. p∗ = 1

48 . The system in thiscase would be a pure TDMA system.Comparing the results of on–off transmission at the op-

timal probability to those of multiple rates transmission for24 users, i.e. comparing Fig. 9 at p = p∗ for each case toFig. 4 at 24 users, we can see that the omnidirectional caseand the 2-element case in the on–off scheme outperformtheir counterparts in the multiple transmission rates scheme,although the maximum allowed rate in the on–off scenariois 76.8kbps, half of the maximum rate in the multiple rates

scenario, which explains the fact that this superiority doesnot apply to the 4-element array case. However, Fig. 11shows that when the comparison is performed with the samemaximum rate, the on–off transmission scenario at optimalprobabilities clearly outperforms the multiple rates scenariowithout optimization. Considering 48 users, Fig. 10 showsthat, at the optimal transmission probability for each case ofscenarios 2 and 3, the superiority to the results of Fig. 4 at48 users is evident.

5.4. Extension to future research

Finally, we discuss some possible enhancements to thiswork, and present some suggestions for future extension.When steering the antenna beam towards a desired direc-tion, beam pointing errors were not taken into account. Inaddition, beam broadening due to steering was not investi-gated. However, this effect is usually represented by a beam-broadening factor when the main beam is steered not too farfrom its main pointing direction [20]. This effect is not ex-pected to be of major importance, since the 2-element arrayachieved good results with a beam relatively large comparedto the 4-element array, and the beam broadening factor willnever be large enough to make the beam of the 4-elementarray as large as that of the 2-element array.From a scheduling point of view, users with different

rates were considered. However, the investigation of opti-mal transmission probabilities was performed on the on–off


case. Varying transition probabilities for all possible ratessimultaneously to find an optimal combination is a topicfor future research. Heuristic optimization techniques likegenetic algorithms and the simulated annealing algorithmscould be used in this regard. Another natural extension to thiswork would be to investigate average throughput in the caseof on–off transmission with the presence of token bucketconstraints, since we only considered on–off transmissionwithout token constraints as a special case of probabilisticscheduling.

6. Conclusion

Distributed uplink scheduling in a probabilistic mannerwas studied in the presence of adaptive antennas at the basestation. Results were compared between different linear an-tenna arrays, and the omnidirectional case. Scenarios stud-ied included multiple transmission rates, average and highlyloaded systems, variations of the number of users, and differ-ent token bucket constraints. The directivity, narrow beams,and low side lobe levels of adaptive antenna arrays lead toa major decrease in interference and hence an increase inSINR, and consequently in the average achieved through-put. The optimal transition probabilities in a simple on–offtransmission case were also investigated. It was shown thatin moderately loaded systems, with adaptive antennas, theoptimal transmission case approaches that of a pure CDMAsystem, not a hybrid TDMA–CDMA system. In addition, inhighly loaded systems, the throughput was considerably en-hanced by the use of adaptive antenna arrays, although theoptimal transmission probability was less than one.

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Elias Yaacoub received the B.E. de-gree in Electrical Engineering from theLebanese University in 2002, and theM.E. degree in Computer and Commu-nications Engineering from the Amer-ican University of Beirut in 2005. Heworked as a Research Assistant in theAmerican University of Beirut from2004 to 2005, and in the Munich


University of Technology in Spring 2005. From 2005 to 2007,he was a Telecommunications Engineer with Dar Al-Handasah,Shair and Partners. He is currently a Ph.D. student at the Amer-ican University of Beirut. His research interests include wirelesscommunications and antenna theory.

Zaher Dawy received the B.E. degreein Computer and Communications En-gineering from the American Univer-sity of Beirut in 1998. He received hisM.Sc. and Dr.-Ing. degrees in Electri-cal Engineering from Munich Univer-sity of Technology (TUM) in 2000 and2004, respectively. Between 1999 and2000, he worked as a part-time Com-munications Engineer at Siemens AGresearch labs in Munich focusing on

the development of enhancement techniques for UMTS. At TUM,between 2000 and 2003 he managed and developed a researchproject with Siemens AG where he designed advanced multiuserreceiver structures for UMTS base stations. Since September 2004,he is an Assistant Professor at the Electrical and Computer En-gineering Department at the American University of Beirut. Hisresearch interests include Cooperative Communications, CellularTechnologies (WCDMA, HSPA, LTE), Radio Network Planningand Optimization, Multiuser Information Theory, Multimedia overIP Networks, and Computational Biology.

Ali El-Hajj received the License de-gree in Physics from the Lebanese Uni-versity, Lebanon in 1979, the degree of“Ingenieur” from L’Ecole Superieured’Electricite, France, in 1981, and the“Docteur Ingenieur” degree from theUniversity of Rennes I, France, in1983. From 1983 to 1987, he was withthe Electrical Engineering Departmentat the Lebanese University. In 1987,he joined the American University of

Beirut where he is currently Professor of Electrical and ComputerEngineering. His research interests are numerical solution of elec-tromagnetic field problems and engineering education.

Karim Y. Kabalan received the B.S.degree in Physics from the LebaneseUniversity in 1979, and the M.S.and Ph.D. degrees in Electrical andComputer Engineering from SyracuseUniversity, in 1983 and 1985, respec-tively. During the 1986 Fall semester,he was a visiting assistant professorof Electrical and Computer Engineer-ing at Syracuse University. Currently,

he is the Chairperson of the Electrical and Computer EngineeringDepartment, Faculty of Engineering and Architecture, AmericanUniversity of Beirut. His research interests are numerical solutionof electromagnetic field problems and software development.

distributed uplink scheduling and rate control in cdma2000 using adaptive antenna arrays

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