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An Admission Control Scheme for Opportunistic Scheduling Riku Jantti, Member IEEE, and Mohammed Al Rawi Department of Computer Science, Faculty of Technology, University of Vaasa FIN-65101 Vaasa, Finland Email: {rikujantti,mrawi}@uwasa.fi Abstract- In this paper we suggest a new Call Admission Control (CAC) algorithm for High Speed Downlink Packet Access UMTS systems. In this algorithm the user requesting admission is gradually admitted to the system. This is done by setting a back-off factor limiting the new user's throughput. This factor tends to protect the already existing links that their rates do not drop below a certain Quality of Service (QoS) level. I. INTRODUCTION Opportunistic, channel adaptive, scheduling have drawn a lot of attention since the introduction of Qualcomm's High Data Rate (HDR) system [1]. It is also an essential part of the upcoming high speed downlink packet access HSDPA for UMTS [2]. In opportunistic downlink scheduling, the mobiles estimate their channel conditions and report them back to the base station which then allocates all the radio resources to the user who would benefit the most from the opportunity to transmit. Adaptive coding and modulation is utilized to match the users data rate to the current channel. Such a scheduling benefits from the multiuser diversity gain discussed e.g. in [3]. Several different scheduling rules have been introduced in the literature. The max-CIR rule always selects the user having the highest carrier-to-interference+noise ratio (CIR). This rule maximizes the throughput, but leads to very unfair division of resources as only users close to the base station are allowed to transmit. A very good trade-off between fairness and throughput can be obtained by utilizing the proportional fair (PF) scheduler, which utilizes the instantaneously achievable data rate divided by its time average as a decision variable. Such a scheduling rule leads to resource fairness: all users as- ymptotically get equal access to the channel. Their throughput, however, depend on their positions. Many modifications of the original PS rule have been suggested to control the quality of service level perceived by the users. See e.g. [4], [5], and [6]. The performance of opportunistic schedulers depend on the number of users. Although it was shown in [3] that the gain of using channel adaptive scheduling compared to round robin scheduling increases as the number of users increases, the throughput per user decreases rapidly as the load increases. Under ideal conditions, the rate obtained using PF Scheduling is independent of the rates of the other users and only depend on the mean channel gain of the user and the total number of users. However, this functional relation can vary from user to another and depend on parameters such as quantization levels of the rates and measurement delays. See [3]. In addition, 0-7803-9206-X/05/$20.00 ©2005 IEEE impairments such as retransmissions can cause dependencies among the user rates if priority is given to retransmitted packets. This means that simple number based admission control which would make the admission decision directly based on number of users might not perform adequately. The importance of combining the opportunistic scheduling with admission control have been recognized in many papers. However, surprisingly little results have been published on the matter so far. In [7] a simple iterative admission control scheme was suggested in which some weight in the decision rule was gradually increased to limit the impact of new users on the active packet calls. In this paper, we will suggest new admission control scheme, which allows the operator to limit the maximum impact that the new user can cause to the already active ones in terms of throughput loss. Our scheme resembles the sliding window based call admission control scheme suggested in [8] and can be interpreted as a modification of the active link protection scheme [10] to the multiuser diversity channel. The paper is organized as follows. In Section II we will describe the system model considered in this paper, Section III describes the suggested admission control scheme. Sections IV and V discuss how to utilize time averages instead of expected values. Section VI contains the numerical results. Section VII compares the proposed scheme with another method for evaluation and finally Section VIII concludes the paper. II. SYSTEM MODEL Consider a downlink of a DS-CDMA system. Let (i(t) denote the carrier-to-interference ratio of a user i at time instant t and (i denote its mean value. The mobile is assumed to estimate the channel based on a pilot signal transmitted by the base station. Based on the channel measurement the mobile then determines the maximum data rate that it could achieve under the current channel condition pi (t) = f(i (t)) and reports that back to the base station which then utilizes this information for making the scheduling decision. We say that a user is active if it at time instant t contained data in its transmission buffer. That is, if bi(t) > 0; otherwise a user is said to be idle. Let A(t) denote the set of active users. In that case, the proportional fair scheduling rule would allocate the next time slot to the user i*(t) that fulfills i* (t)-argmax IPpi (t) I i E A(t)} (1) 298

[IEEE 2005 2nd International Symposium on Wireless Communication Systems - Siena, Italy (05-09 Sept. 2005)] 2005 2nd International Symposium on Wireless Communication Systems - An

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An Admission Control Scheme for OpportunisticScheduling

Riku Jantti, Member IEEE, and Mohammed Al RawiDepartment of Computer Science, Faculty of Technology, University of Vaasa

FIN-65101 Vaasa, FinlandEmail: {rikujantti,mrawi}@uwasa.fi

Abstract- In this paper we suggest a new Call AdmissionControl (CAC) algorithm for High Speed Downlink Packet AccessUMTS systems. In this algorithm the user requesting admissionis gradually admitted to the system. This is done by setting aback-off factor limiting the new user's throughput. This factortends to protect the already existing links that their rates do notdrop below a certain Quality of Service (QoS) level.

I. INTRODUCTIONOpportunistic, channel adaptive, scheduling have drawn a

lot of attention since the introduction of Qualcomm's HighData Rate (HDR) system [1]. It is also an essential part ofthe upcoming high speed downlink packet access HSDPA forUMTS [2]. In opportunistic downlink scheduling, the mobilesestimate their channel conditions and report them back to thebase station which then allocates all the radio resources tothe user who would benefit the most from the opportunity totransmit. Adaptive coding and modulation is utilized to matchthe users data rate to the current channel. Such a schedulingbenefits from the multiuser diversity gain discussed e.g. in [3].

Several different scheduling rules have been introduced inthe literature. The max-CIR rule always selects the user havingthe highest carrier-to-interference+noise ratio (CIR). This rulemaximizes the throughput, but leads to very unfair division ofresources as only users close to the base station are allowedto transmit. A very good trade-off between fairness andthroughput can be obtained by utilizing the proportional fair(PF) scheduler, which utilizes the instantaneously achievabledata rate divided by its time average as a decision variable.Such a scheduling rule leads to resource fairness: all users as-ymptotically get equal access to the channel. Their throughput,however, depend on their positions. Many modifications of theoriginal PS rule have been suggested to control the quality ofservice level perceived by the users. See e.g. [4], [5], and [6].The performance of opportunistic schedulers depend on the

number of users. Although it was shown in [3] that the gainof using channel adaptive scheduling compared to round robinscheduling increases as the number of users increases, thethroughput per user decreases rapidly as the load increases.Under ideal conditions, the rate obtained using PF Schedulingis independent of the rates of the other users and only dependon the mean channel gain of the user and the total number ofusers. However, this functional relation can vary from user toanother and depend on parameters such as quantization levelsof the rates and measurement delays. See [3]. In addition,

0-7803-9206-X/05/$20.00 ©2005 IEEE

impairments such as retransmissions can cause dependenciesamong the user rates if priority is given to retransmittedpackets. This means that simple number based admissioncontrol which would make the admission decision directlybased on number of users might not perform adequately.

The importance of combining the opportunistic schedulingwith admission control have been recognized in many papers.However, surprisingly little results have been published onthe matter so far. In [7] a simple iterative admission controlscheme was suggested in which some weight in the decisionrule was gradually increased to limit the impact of new userson the active packet calls. In this paper, we will suggestnew admission control scheme, which allows the operatorto limit the maximum impact that the new user can causeto the already active ones in terms of throughput loss. Ourscheme resembles the sliding window based call admissioncontrol scheme suggested in [8] and can be interpreted as amodification of the active link protection scheme [10] to themultiuser diversity channel.The paper is organized as follows. In Section II we will

describe the system model considered in this paper, Section IIIdescribes the suggested admission control scheme. Sections IVand V discuss how to utilize time averages instead of expectedvalues. Section VI contains the numerical results. SectionVII compares the proposed scheme with another method forevaluation and finally Section VIII concludes the paper.

II. SYSTEM MODEL

Consider a downlink of a DS-CDMA system. Let (i(t)denote the carrier-to-interference ratio of a user i at timeinstant t and (i denote its mean value. The mobile is assumedto estimate the channel based on a pilot signal transmittedby the base station. Based on the channel measurement themobile then determines the maximum data rate that it couldachieve under the current channel condition pi (t) = f(i (t))and reports that back to the base station which then utilizesthis information for making the scheduling decision.We say that a user is active if it at time instant t contained

data in its transmission buffer. That is, if bi(t) > 0; otherwisea user is said to be idle. Let A(t) denote the set of activeusers. In that case, the proportional fair scheduling rule wouldallocate the next time slot to the user i*(t) that fulfills

i* (t)-argmax IPpi (t) I i EA(t)} (1)

298

where pi denotes the mean value of pi (t) averaged over sometime window of length T.

Let ZN = (1i(2,.. ,(N) denote a vector of averagechannel conditions and let ri(ZN) denote the average rateachieved by user i in some time window of length T in casethe average channel conditions were defined by ZN.

ri(ZN) = E{X{i = i- (t)ri((i(t), i(t- ))} (2)where ri ((i (t), (i (t + r)) denotes the instantaneous data rateachieved when coding and modulation is chosen based on (i(t)and the actual channel condition is equal to (j (t + r). Thevariable r denotes measurement delay. In ideal case, we wouldhave ri ((i (t), ((t + r)) pPi (t). The operator X{E} is anindicator function of an event E: X{E} = 1 if the event Eoccurs and zero otherwise.

III. ADMISSION CONTROL SCHEME

Assume that we would restrict the amount of new usersseeking admission to the network to just a single user. Assumethat there were N users in the system before user N+1 arrived.Let us divide the time into frames of several slots and observethe mean rates of the users over the whole frame. Let F(n)denote the average rate of user i in the frame n. The lengthof the frame is assumed to be long compared to the numberof users such that the mean rate observed in the frame isapproximately the same as the expected rate of the user.

Consider the following iterative admission procedure. Whena new user first arrives to the network it will set a back-offprobability p, 0 < p < 1. A new user is excluded from theactive set A with this probability, even if it has data in itstransmission buffer. After a frame has passed, the rate of thesystem is observed.

..(1) ()ra p(1)ri(ZN)+(1d-P())ri(ZN+1) i = 1d2. N (3)

andr( = (1 -P('))¾N+1(ZN+l) (4)

Where p(l) denotes the back-off probability utilized after oneframe. The impact of adding the new user after one frame withthe back-off probability is thus at most (1 -p(l))ri (ZN) forthe active users. That is, the fraction of lost throughput is lessthan or equal to (1 - p(l)). In frame n we select the back-offprobability p(n) to be equal to pn. That is, we let p(n) decreaseexponentially fast.

n(n) = pnr-(ZN) + (1 _ p)n(ZN+1) i = 1 2,... N (5)

We can write the throughput obtained in frame n with the helpof the throughput obtained in frame n- 1 as follows

i(n) _(-(and pri + (l -p)ri(ZN+ ) i , 2, N (6)and

rn+ PrN+l-) + (l-P)rN+1(ZN+±)

which is smaller than or equal to (1 - p). That is,-in) > (n-1)ri > pri (8)

The rate of the new user is in turn monotonically increasing_(n) > _(n-1)N+1 N+> (9)

This behavior resembles the active link protection (ALP)scheme suggested by Bambos et. al. [10] for power controlledsystems.Assume now that quality of service requirement in the

systems is expressed in terms of minimum tolerable data ratermin. In that case, the admission decision depends on the worstuser's performance. We can apply the rate equations (6) and(7) for admission control as follows:

Iterative ALP CAC: Iteratively decrease the back-off prob-ability until some of the rates of the active users deterioratebelow some minimum tolerable value. That is, a new packetcall is rejected if F(n) < rmin for any i = 1,2,.... N at someiteration n. Otherwise pn -O 0 and the user is admitted tonetwork.

We can generalize the admission control scheme by allow-ing the decrease rate of the back-off probability to change fromiteration to another. Let the back-off probability at iteration nbe p(n) = P(nl)Pn. It thus follows that p(n) = _ Pk andthe rate equation for active users becomes

ri =pnri + (1-Pn) i(ZN+j) i = 1. 2 N (IO)

Hence, r-(n) > Pn -i For instance we could selectrmin

P = _(n)r1

(11)

If pn = 1, the new packet call is rejected; otherwise we keepiterating. As long as 0 < Pn < 1 for all n, p(n) - 0oc.

IV. IMPERFECT ESTIMATES

So far we have assumed that expected value r-n) is availablefor the admission control. In practice, we have to use timeaverage values rf(n) that in case of ergodic channel would

-(n)converge to ri when the frame length approaches infinity.In practice, we have to cope with finite frame sizes and thusnoisy estimates for the mean value.

Let us define two state variables x(n) = r(n) and x(n) =ri(ZN+l) and state vector Xi(n) = (x(nj)Q(n)' Assume thatthe state noise and measurement error are Gaupsian whitenoise processes described by Vi(n) - ((n )(n) ) and ei(n).The two processes are assumed to have zero mean and followlJvv = E{V( (Vif2))}, I,ee = E{e n)(e(7l))'}, and q!Ve =E{V (n) (e,n) )'}.Now the state equations can be written as follows

(7)

Hence, we can conclude that the rate at which the throughputof the old users is deteriorating is proportional to a factor

X4n+) = j(n)X (n) + V(n)

f (n) - CX(n) + e(n)

299

(12)(13)

TABLE ISYSTEM PARAMETERSwhere (D(n) PI -P Pn ],C =[1 0 ]

It is well-known that the optimal state estimator for theprocess is the Kalman filter which can be written as follows

fC(n+l) = >(n)f(n) + K(n) - CXI(n) (14)

K(n)- (db(n)p(n) C/ + XIVe)(C/P(n)C + ,ee)l (15)

p(n+l) - ¢(n)p(n) (¢(n) )/ + SIVV-K(n) (Cp(n) C/ + TIee)(K(n)y (16)

Unfortunately, it is difficult to determine the covariancematrices 'vv, ', and vI accurately. Instead they can beused as tuning parameters. The larger we set the parameters in4Tee the less, we trust in the measurements. Hence, the shorterthe averaging window the larger ,ee The covariance matrixIvv describes the rate at which the mean values change in

the channel and is thus related to the mobility of the users.Hence, the faster the mobiles move the larger ''vv and themore weight is given to the instantaneous channel estimate.The above state estimation approach can also be generalized

to the M user admission case.

V. SLIDING WINDOWS ESTIMATE

Assume that the mean rate is estimated using a slidingwindow estimator based on F most recent estimates. We letthe back-off factor vary from slot to slot. Let p(k) denote theback-off factor used in slot k. Let Xi(i = i*(Z, k)) denote theindicator function that user i was chosen at slot k when thefading state is determined by the vector Z. Let X(bN+l,k = 1)denote the indicator function that the new user backs off in slotk. The expected value of the indicator function is the back-offprobability used at slot k. That is, E{X(bN+l,k = 1)} = Pk-Let r -(Z, k) denote the rate that the user would get in slot k.Now the the estimator output can be written as

F

rj(n) = F (ri(ZN, k)X(i = i*(ZN))X(bN+l,k = 1)k=n-F+1

+ri(ZN+l ,k)X(i = i*(ZN+1))X(bN+l,k = 0)) (17)

Taking the expected value of the above yieldsn

ri = F E (Pkri(ZN) + (1-pk)ri(ZN+1)) (18)k=n-F+1

Let n+(p(n+l) k=n-F+2Pk (19)

Zk=n-F+l Pk

It follows that (18) becomes equal to (10).Consider the special case, in which Pk - Pk, k > F. In that

case, we have

n5 (1 F1(k=n-F+l p -(-p) (0

Parameter ValueCarrier frequency 2 GHzSpreading factor 16

Number of multicodes 10TII duration 2 msFading model One path Rayleigh (Jake's model)

Minimum throughput allowed 256 kbps384 kbps

Max. number of associated DPCH 15 for QoS 256 kbps10 for QoS 384 kbps

Radio propagation Site to site distance 500 mPath loss component 4

Std. of shadow fading 6 dBMin mobile speed 3 km/hMax mobile speed 10 km/h

BS Tx power 17 WEc/lor 0.7

Hybrid ARQ Combining method Chase methodSched. retran. Highest priority

Back-off probability 0.999Admission decision time Slot 2100 = 4.2s

Tee values 2 x 105,4 x 104, x 103Pve, vv 0, 1012X2 respectively

Hence, we have p(n) = p and (18) is reduced to (6).Thus, we can directly apply the Kalman filter described inthe previous section even if we change to using the slidingwindows estimator. The gain of using the sliding windows isin convergence speed. Now we are operating with slots whilepreviously we operated with frames of F slots.

VI. SIMULATIONSAll simulations were carried out using Matlab. A simulator

was constructed that creates an environment of users in amobile cell. The simulator would create N users havingdifferent packet sizes. In the beginning it was assumed thatall users have full buffers, so they all had data to transmit.The scheduling rule that was used in this simulator was theProportionally Fair (PF) scheduler where users are selected inevery Transmission Time Interval (TTI) based on how goodthe instantaneous channel condition was relative to the averagecondition, equations (1) and (2).

Table I shows the parameters that were used in the simu-lation program. The simulation was considered for WCDMAHigh Speed Download Packet Access HSDPA where AdaptiveModulation and Coding (AMC) is used to guarantee highthroughputs depending on the channel condition as shown inTable II [9].The admission stage was based on adding one user at a time

using the iterative CAC procedure described in Section III anddue to the fact we are dealing with noisy estimators, equations(14)-(16) were employed.The initial values for X (n)were the actual average rates of theexisting users before a new user enters the system. A Raleighfading vector was generated for each user. The generator isimplemented in accordance with Jake's fading simulator [11],

300

TABLE II

THRESHOLDS OF SINR

Index i 1 2 3 4 5 6 7

Threshold (dB) -1.9 1.25 4.5 6.5 10.2 14 16.2

Modulation QPSK QPSK QPSK 16QAM l6QAM 64QAM 64QAMand Code rate 1/4 1/2 3/4 1/2 3/4 5/8 3/4

Throughput (Mbps) 1.2 2.4 3.6 4.8 7.2 9.0 10.8

y r-'S0

e,

0 500 1000 1500 2000 2500 3000Time slot

Fig. 1. Throughput of worst user (Back-off factor=O.999)

[12]. The calculation of actual average rates was done inaccordance with table II since we have different users withdifferent channel conditions that vary depending on the user'sdistance from the base station and its velocity. The mobilespeed of each user was randomly selected from a normaldistribution ranging from 3 km/h up to 10 km/h.

In the simulation a new user was added every 6000 slots.The user's average rate in the beginning would experience a

transient state for a while and then gradually stabilizes, themore it remains in the system the more stable it becomes.The the last 3000 slots were considered as the time windowfor applying the admission scheme, since the admission controlscheme assumes that the system starts from steady-state.

Figure 1 shows the Kalman estimate along with the actualthroughput for the worst user when when a new user isadmitted.Time slot 2100 (t = 4.2s) was assumed as the time slot a

new user is accepted if none of the existing users experienceda fall in throughput below rmin before time slot 2100. Theperformance of the admission scheme is measured from theadmission errors. There are two types of CAC errors:

Type I error: Where a new user is erroneously acceptedresulting in outage.Type II error: Where a new user is erroneously rejectedresulting in blocking.

Due to fading, the mean rate of the users will keep suf-fering variance causing time outage which notably affects theadmission decision. For example an admission error may occur

because an active user was under a bad fading pattern causing

300

Packet inter-arrival tire=80 ms

0 -|i_~20 100 200 300 400 500 60m \ ~~~~Newuser:

-b-100.)

5o10 ____

50.

_~~~~~~~~~~~~~~~~~~~~~~~~~~~.... T___..._ _

CL 250 .... . . .

New,user Packettnter-arrival bme_3v0 E . j-~~~~ms ................ -_

1000 2000 3000 4000 5000 6000Time slot

Fig. 2. Dynamic traffic users with different packet inter-arrival times

a temporarily drop in its throughput below rmin which in tumcauses an admission error type II if it happened before timeslot 2100 and error type I if after.

Dynamic TrafficWe consider the case, in which the buffer occupancy of theusers is allowed to vary so that not all users have data totransmit at each time slot. This differs from the previous staticcase discussed earlier, in which all the users were assumed tohave full transmission buffers all the time. The mean inter-arrival time of the packets will play an important role as rateswill also be a function of packet arrival as well as channelconditions. With few packet arrivals the rates of users will bedivided into two groups as seen in part (a) of Fig. 2 whereit clearly shows that rates are mostly a function of packetarrival. Using a large mean inter-arrival time does not revealthe necessary information to make the admission decision.Therefore, the mean inter-arrival time was decreased to createmore packets and consequently making the rates be more ofa function of channel conditions than packet arrivals. Thedifference between dynamic users with two different mean

inter-arrival times is illustrated in Fig. 2. In our simulation,the inter-arrival times follow the log-normal distribution withstandard deviation of 4.24 ms.

Table III illustrates the possibilities of a user being erro-

neously accepted (Type I CAC error) or erroneously rejected(Type II CAC error). Static traffic is the case where all users

have data in their buffers ready to be transmitted at each timeslot while in dynamic traffic the occupancy of the buffers

301

405.- - Kalman estimate

400 - lA Actual rate

395

390

r_ in

380 ~~~~~~~~~~~~~.380

375

370

365 -.

360

3550

TABLE IIITYPE I AND II CAC ERRORS

TABLE IVIMPACT OF I,ee ON STATIC TRAFFIC USERS

Tee 2 x 105 4 x 104 1 x 103256 kbps QoS type I error 6% 4% 4%

384 kbps QoS type I error 12% 8% 4%

varies. Tuning x!ee in some cases can affect the admissiondecision as it determines how fast the Kalman filter estimateconverges to the actual value leading to an increase or decreasein CAC errors as shown in table IV.

VII. COMPARISONIn this section we will perform the comparison against a

Recursive Least Square (RLS) scheme which is a simple one-

shot admission control scheme that estimates the impact ofadding a new user to the data rates of active users. This kindof admission control scheme has been suggested in [13].RLS Estimate

The basic RLS scheme was used where a filter of weight wis used to predict future values of the rates depending on pastobserved data.The filter weight is updated using the RLS equations

k(n) A -P(n - 1)u(n) (21)1fj I+ A-10H(n)P(n 1)u(n)

e(n) = ri(n)-w(n-1)u(n) (22)w(n) = w(n - 1) + k(n)E((n) (23)P(n) A-1P(n - 1)--lk(n)uH (n)P(n - 1)(24)

where ri here denotes the average of the mean rate values foruser i at admission n. The inputs to update the filter weightwere the actual values of ri when up to 3 users were added thatis u(n) = [ ri(n-4) ri(n-3) ri(n-2) ri(n-1)].A one-tap filter w was considered due to the limited number

of users, so

r^i (n) = w r-i (n-1) (25)

The RLS admission control scheme can be summarized as

follows

RLS CAC: Record the throughput losses caused by previousadmissions. Utilize RLS to estimate the impact of adding a

new user. If the predicted rate of the worst active user is abovermin, admit the new user; otherwise reject it.

TABLE V

COMPARISON OF ALP AND RLS SCHEMES

Table V shows the comparison between the RLS and ALPschemes in terms of admission error. The results indicate thatthe ALP scheme is superior in all cases.

VIII. CONCLUDING REMARKS

The suggested iterative CAC method proves to be very

promising and satisfies minimum QoS throughput level forall users in an ongoing system as it tends to protect theexisting users in a system and guarantee that the new user

being admitted will not deprive the existing users the QoS levelprovided to them. The main issue remaining is to distinguishif the error happened due to time outage or was it a genuineadmission error.

REFERENCES[1] P. Bender, P. Black, M. Grob, R. Padovani, N. Sindhushayana, and A.

Viterbi, "CDMA/HDR: A bandwidth-efficient high-speed wireless dataservice for nomadic users," IEEE Communications Magazine, Vol. 38,No. 7, pp. 70-77, 2000.

[2] S. Parkvall, E. Dahlman, P. Frenger, P. Beming, and M. Persson "Thehigh speed packet data evolution of WCDMA," in Proc. IEEE VTCSpring, Vol. 3, pp. 2287-2291, 2001.

[3] F. Berggren and R. Jantti "Asymptotically fair transmission schedulingover fading channels," IEEE Transactions on Wireless Communications,Vol. 3, No. 1, pp. 326-336, 2004.

[4] S. Shakkottai and A. L. Stolyar "Scheduling for Multiple Flows Sharinga Time Varying Channel: the Exponential Rule", Bell Labaratories, Tech.Rep., 2000.

[5] S. Shakkottai and A. Stolyar, "Scheduling Algorithms for a Mixture ofReal-Time and Non-Real-Time Data in HDR", in Proc. Int. TeletraficCongress, pp. 793-804, 2001.

[6] Kapseok Chang and Youngnam Han, "QoS-based Adaptive Schedulingfor a Mixed Service in HDR System", in Proc. IEEE PIMRC 2002,Vol. 4, pp. 1914-1918, 2002.

[7] X. Liu, E. K. P. Chong, N. B. Shroff, "Transmission schedulingfor efficient wireless resource utilization with minimum-performanceguarantees," in Proc. IEEE VTC2001 Fall Vol. 2, pp. 824 838.2001.

[8] P. Zhao, and H. M. Zhang "Sliding window based CAC for adaptiveservice in mobile network," in Proc IEEE PIMRC 2002 Vol. 5, pp.

2165 2169, 2002.[9] J. Horng, Jinyun Zhang and Debang Lao. "Throughput analysis for

W-CDMA system with MIMO and AMC," TR-2003-48, May 2003.[10] B. Bambos, S.C. Chen, and G. J. Pottie, "Channel access algorithms

with active link protection for wireless communication networks withpower control," IEEE/ACM Transactions on Networking Vol. 8, No. 5,pp. 583 597, 2000.

[11] W.C. Jakes, Microwave Mobile Communications. Wiley, NY, 1974.Section 1.7.2.

[12] Pop and Beaulieu,"Limitations of sum of sinsoids fading simulatorsimulators, " IEEE Trans.Commun.,vol. 49, pp.669-708, 2001 for thecase where random phases have been introduced to the low-frequencyoscillators.

[13] K. Gribanova, Packet Scheduling for Video Streaming Data in the HDRsystem", Master's thesis, Telecommunication software and multimedialaboratory, Helsinki University of Technology, 2004.

302

Traffic type QoS level Error type I Error type II

Static 256 kbps 4% 6%

384 kbps 8% 4%

Dynamic 256 kbps 9.09% 3.03%

384 kbps 6.25% 3.12%

Traffic type Scheme Error type I Error type II

Static ALP 4% 6%RLS 13.7% 18.5%

Dynamic ALP 9.09% 3.03%RLS 16% 22%