THRESHOLD-BASED PARALLEL MULTIUSER SCHEDULING

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1 The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC 7 THRESHOLD-BASED PARALLEL MULTIUSER SCHEDULING Sung Sik Nam Dept of ECE College Station, Texas ssnam11@tamuedu Mohamed-Slim Alouini Dept of EE at Qatar, Doha, Qatar alouini@tamuedu Khalid A Qaraqe Dept of EE at Qatar, Doha, Qatar kqaraqe@tamuedu Hong-Chuan Yang Dept of ECE University of Victoria Victoria, BC hyang@eceuvicca ABSTRACT In this paper, we propose two new threshold based parallel multiuser scheduling schemes, namely i an on-off based scheduling OOBS scheme and ii a switched based scheduling scheme The objective is to reduce the complexity of implementation without a considerable performance loss in comparison with selection based scheduling While the OOBS scheme schedules all the users with an SNR above a fixed preselected signal to noise ratio SNR threshold, the scheme schedules only the K s users with an acceptable SNR if there are enough acceptable users Otherwise, the scheduler selects the best K s users We analyze statistical characteristics and performances of these proposed schemes Numerical results show that the proposed schemes can offer some decrease in the average number of feedback load without an important degradation in average bit error rate and average spectral efficiency I INTRODUCTION Traditional multiuser scheduling schemes 1] rely on time division multiple access TDMA type of systems to schedule the user with the best channel quality to either upload or download data With this type of system, the average spectral efficiency ASE can be maximized because the selected channel supports the highest possible rate However, this high spectral efficiency comes at the ense of a high feedback load since the scheduler needs to probe all active users before it can identify the most qualified one To simplify the selection process and reduce the feedback load, a multiuser switched diversity scheme based on the switched diversity scheme was proposed in 2] By using a signal to noise ratio SNR threshold a multiuser switched diversity was shown to reduce significantly the feedback load 2,3] With this scheme, the BS probes the users in a sequential manner, not looking for the best one but just for an acceptable user In addition, to the reduction in feedback load, this scheme was shown to erience minimal ASE loss and increase in fairness by randomizing the probing sequence from one scheduling round to the next The TDMA-based scheduling schemes mentioned above schedule only one user at a given time In order to improve the frequency of access of such kinds of systems, a multiuser simultaneous scheduling scheme based on generalized selection combining GSC was proposed in 4] In this scheme, the scheduler selects in each time-slot the K s users with the largest This work was supported in part by the Qatar Foundation for Education, Sciences, and Community Development, Doha, Qatar and in part by Qatar Telecom Qtel, Qatar SNRs among the K active users K s K Similar to the selection based TDMA scheme described above, the scheme in 4] needs to probe then rank all the active K users In this paper, we propose two new parallel multiuser scheduling schemes that rely on a SNR threshold to reduce the complexity of implementation and increase the user frequency of access withouteriencing aconsiderable ASE loss in comparison with the GSC based scheduling scheme presented in 4] The first scheme termed on-off based scheduling OOBS scheme is based on the absolute threshold generalized selection combining AT-GSC scheme 5] and the on-off type of schemes introduced in 3,6] With this scheme, the scheduler selects in each time-slot all the users with a SNR above a preselected threshold SNR The second scheme termed switched based scheduling scheme is based on the switched diversity concept 2, 7] Along the spirit of multiuser switched diversity transmission described in 2], the scheduler selects K s users with acceptable SNRs instead of the ones with the best K s SNRs If the acceptable K a users are less than K s,the scheduler selects the best unacceptable K s K a users II MODELS AND MODE OF OPERATION A System Model In our system model, we consider a code division multiple access CDMA system instead of a TDMA system because the BS needs to simultaneously schedule K s K s =, 1, 2,,K users among K users per time-slot We assume that multiuser signals are orthogonal and there are no inter-cell interference and no co-interference among the users We also assume that the proposed OOBS and schemes have a reliable feedback path between the receiver and transmitter and that they are implemented in a discretetime fashion More specifically, a single time-slot is composed of a guard time period and a data transmitting time period During the guard time period, the BS makes the necessary actions to schedule the K s users that will be granted channel access in the following transmission time Finally, it is assumed that the channel estimation is perfect at the receiver and that the feedback to the transmitter is performed without error upon request For scheduled users, a rate-adaptive N multidimensional trellis coded M-quadrature amplitude modulation M-QAM for additive white Gaussian noise AWGN channels is employed to ensure a high system ASE 8] In 8], rate adaptation is performed by dividing the SNR range into N +1fading regions which are defined by the SNR thresholds <γ T1 < < γ TN <γ TN+1 = When the estimated SNR of scheduled user is in the nth region, the constellation size M n with spectral /7/$25 c 27 IEEE

2 The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC 7 efficiency bits/s/hz] is transmitted The lower boundary of each fading region is set to the lowest SNR required to achieve the predefined target BER B Channel Model We denote by γ i i =1, 2,,K, the received SNR of the ith user and we adopt a block flat fading channel model More specifically, assuming slowly-varying fading conditions, the different paths from users erience roughly the same fading conditions during the data burst and its preceding guard time period In addition, the fading conditions are assumed to be independent across the paths from users and between guard time period and data burst pairs C Mode of Operation 1 OOBS Scheme The OOBS scheme is inspired from the AT-GSC scheme 5] and the on-off type of schemes discussed in 3, 6] The difference between the OOBS scheme and the AT-GSC scheme is that there is no combining process in the OOBS scheme With the OOBS scheme, at the beginning of the guard time period, the BS sends a pilot signal to all K users at a time Once the pilot signal is received by all users, during the guard time period, these users estimate the SNR γ i and compare it to a preselected threshold SNR, denoted by γ T which is known ahead of time by all users The users feed back their channel state information to the BS only if their SNRs are above the preselected threshold SNR γ T Only these acceptable users are then scheduled by the BS for the subsequent transmission time If all users do not have an acceptable SNR, the BS simply waits a period of the order of a channel coherence time before starting a new round of scheduling Note that with the GSC based scheduling scheme, the BS needs always full K feedbacks from all K users for SNRs comparison before ranking and determination of the K s scheduled users From the mode of operation of the OOBS scheme, the number of feedbacks from users is random and this scheme needs to perform at most K feedbacks during the guard time period Therefore, the OOBS scheme requires, on average, fewer feedbacks than the GSC based scheduling scheme 2 Scheme The scheme is inspired from the switched diversity based schemes 2, 7] With the scheme, the BS schedules a predetermined total number, denoted by K s, of acceptable users and if necessary, the best unacceptable users in a GSC fashion More specifically, in each guard time period, the BS sends a pilot signal sequentially to each user in order to request a channel state information from each user in a sequential manner After receiving the pilot signal from the BS, each user estimates its SNR γ i and compares it to the preselected SNR threshold After that, each user sends back its channel state information to the BS If the SNR γ i is acceptable, this user is considered for scheduling by the BS This process repeats until either the BS finds all K s acceptable users or fails to find all K s users ie finds only K a < K s acceptable users after estimating and comparing all K users In the former case, the BS does not need to probe all K users and just stops the process after finding the K s acceptable users In the latter case, the BS ranks the K K a unacceptable users and schedules the best K s K a unacceptable users along the already acceptable K a users Compared to the GSC based scheduling scheme, the user with the best SNR can be excluded with this scheme Therefore, for low γ T in comparison with average SNR, the outage performance of the GSC based scheduling scheme is ected to be better than that of the scheme because the probability that the best user can not be selected increases as γ T decreases On the other hand, the scheme approaches the outage performance of the GSC based scheduling scheme as γ T increases However, the scheme needs less than K feedbacks whereas the GSC based scheduling scheme needs always full K feedbacks during the guard time period III PERFORMANCE ANALYSIS In this section, we analyze the performance of the OOBS and schemes in terms of average bit error rate BER, ASE, and average number of feedback load AFL ie, average number of users transmitting feedback information to the BS over iid Rayleigh fading conditions Based on the iid Rayleigh fading assumption, the received SNR γ i will share a common probability density function PDF and the corresponding cumulative distribution function CDF given by p γ γ = 1 γ and P γ γ =1 γ, respectively where is the common average SNR for all users A OOBS Scheme 1 Statistics of the Output SNR of a Scheduled User with the OOBS Scheme Based on the mode of operation of OOBS, the scheduled user has a conditional PDF of a truncated above γ T random variable RV γ i With the help of 9, Eq 5], it can be shown that the PDF of the output SNR of a scheduled user is given by p γoobs γ = p γ γ 1 P γ γ T U γ γ T 1 For the iid Rayleigh fading condition, 1 can be re-written p γoobs γ = 1 γt γ U γ γ T 2 2 AFL In this section, we calculate the AFL required by OOBS during the guard period Based on the mode of operation of OOBS, the number of feedback is the same as the number of acceptable users and number of scheduled users The number of acceptable users K a being above the threshold value is random and takes values from to K and each user among the total K users can be either scheduled or not Therefore, the number of acceptable users follows a binomial distribution Since the diversity paths are assumed to be iid faded, we can write the AFL of OOBS during the guard period as

3 The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC 7 AFL= k= K k 1 P γ γ T ] k P γ γ T ] K k =K 1 P γ γ T ] 3 k For the iid Rayleigh fading condition, the AFL reduces to K γ T 3 ASE The ASE of a scheduled user is obtained as the sum of the all spectral efficiencies { } N of the individual codes, weighted by the probability P n that the SNR of a scheduled user is assigned to the nth region: where BE denotes the average BER when code n is used BE = = BE p γoobs γ dγ a n bnγ p γoobs γ dγ, 11 M n where a n and b n are code-dependent constants which were found by least square fitting to simulated data on AWGN channels 8, Table I] For the iid Rayleigh fading assumption, we can write the 11 in the closed form as ASE = P n = p γoobs γ dγ 1 ] = P γ +1 P γ 4 1 P γ γ T In this case, to obtain the ASE of scheduled users for each time-slot, we need to multiply the average number of scheduled users by 4 Since the number of scheduled users is the same as the number of feedbacks, the average number of scheduled users of OOBS is also K 1 P γ γ T ] Finally the ASE of the scheduled users for each time-slot becomes ASE time slot =K 1 P γ γ T ] = K p γoobs γ dγ, 5 p γ γ U γ γ T dγ 6 For the iid Rayleigh fading assumption, we can write where ASE time slot = K P γn, 7 BE anmn γt Mn+b n max γ M n+b n M n T, ] = Mn+b n γ M n Tn+1 if +1 γ T, 12 if +1 <γ T and the P n can be re-written as ] γt maxγ T, if γ P n= Tn+1 γ T if +1 <γ T 13 Substituting 12 and 13 in 1 gives a closed form ression for the average BER of a scheduled user with OOBS When the SNR threshold γ T = γ Tq,wehave and anm n γtq BE= M n + b n { } Mn + b n Mn + b n +1 M n M n an M N γtq MN + b N + R N γ TN, 14 M N + b N M N maxγ T, if γ P γn = Tn+1 γ T 8 if +1 <γ T If the SNR threshold γ T = γ Tq where q {1, 2, 3,,N}, then { } q 1 =and 7 simplifies to ASE time slot,γtq = K γtn { } +R N γ T N 9 4 BER The average BER for over all codes and SNRs of the scheduled users is given as the average number of bits in error divided by the average number of bits transmitted 8] / N BER = BE P n, 1 P n = γtq γtq γ TN + R N { γ T n γ } T n+1 15 Substituting 14 and 15 in 1 yields the average BER ression for the scheduled users for γ T = γ Tq B Scheme 1 Statistics of the Output SNR of a Scheduled User with the Scheme Based on the mode of operation of, we need to condition on the number of acceptable users K a being greater or equal to K s and K a being smaller than K s From these conditions, we can write the PDF of the output SNR of a scheduled user as p γ γ=pr K a <K s] p γs1 γ+prk a K s] p γs2 γ, 16 where p γs1 γ and p γs2 γ is the PDF of a scheduled user

4 The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC 7 Ks 1 ] K! Ka ] γt γt K Ka1 Ks 1 { 1 K p γ γ = s 1! K K Ka= a!k a! K s K i=1 s i 1! i 1! ] γ i ] ] minγt,γ γ Ks i 1 K Ks+1 minγ T,γ 2F 1 1+i K s,k K s+1; K K s +2; γ ] γt K Ks+1 γt 2F 1 1 K s,k K s +1; K K s+2; + 1 U γ γtk Ks +1 K! + K K Ka=Ks a!k a! γt γt ] Ka ] γ Ks ] γ K Ks ] K Ks+1 2F 1 γt 1 K s,k K s +1; K K s+2; γt ] K Ka 1 γt γ U γ γ T, 18 in case of K a K s and K a <K s, respectively Note that K a K s holds if and only if the K s th selected user is above threshold Also K a <K s holds if and only if the K s best users is below threshold Finally, we can write the PDF 1 of the output SNR of a scheduled user for the iid fading case as 3 ASE p γ γ In this case, the ASE of a scheduled user is the same as 4 1 s 1 = PrK a <K s] p K s γi γ Ks γ+ pγ γ Based on the scheme, the number of scheduled users for Ks P i=1 γks γ T 1 U γ γ T each time-slot has the same value K s Therefore, we can get the ASE of the scheduled users for each time-slot in the same p γ γ + PrK a K s] 1 P γ γ T U γ γ T 17 manner as that of OOBS For the iid Rayleigh fading conditions, after some manipulations and with the help of 1, Eq 31941], we can re-write 17 in the closed form ression given at the top of this page and where 2 F 1 α, β; γ; z is the Hypergeometric function defined in 1, Eq 91] and 1, Eq 9111] In Fig 1, we present the PDF of the analytical result and the simulation result Note that our simulation results match perfectly our analytical results 2 AFL In case of K a <K s, the BS needs to ask and check feedbacks of the all K users As a result, the number of feedback becomes K and the number of unacceptable users is random and takes values from K K s +1to K and follows a binomial distribution In case of K a K s, the BS will terminate the process of asking and checking the feedback of the user In this case, the number of feedback takes values from K s to K and the probability of the number of required feedbacks follows a Pascal distribution Since we assumed that the diversity paths from all K users have the iid Rayleigh fading distribution, we obtain the following closed form of the AFL 1 : 1 Because of space limitations, we only present the final results in this paper The specific details behind the derivation can be found in the journal version 11] AFL = k=k s k k 1 k K s γt ] Ks ] k Ks γt K ] l ] K l γt γt + K 19 l l=k K s+1 N ASE time slot = K s p γ γ dγ { } = K s P γ +1 P γ + R N { 1 Pγ γtn }], 2 where P γ γ is the CDF of 18 and which unfortunately cannot be found in a simple closed form 4 BER In this case, the average BER for over all codes and SNRs of scheduled users is the same as 1 and using the summation part of 2, it can be re-written as BER +1 a n bnγ p M γ γdγ n = ] P γ +1 P γ ]+R 21 N 1 Pγ γtn IV NUMERICAL EXAMPLES Fig 2, Fig 3, and Fig 4 show the AFL, the ASE, and the average BER of adaptive coded M-QAM modulation with the OOBS scheme, the scheme, and the GSC based scheduling scheme, respectively, as a function of the average SNR

5 The 18th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications PIMRC 7 over iid Rayleigh fading conditions with K =5, K s =3, and using the equivalent threshold γt = ln K s 1 K Considering Fig 2 together with Fig 3 and Fig 4, the numerical results show that the OOBS scheme provides a slightly higher ASE without eriencing considerable BER loss in comparison with the in the low to medium average SNR range In the high average SNR range, the OOBS scheme provides a better error performance than the for a similar AFL and ASE Note that for fair comparison purposes, we choose an equivalent threshold of the OOBS scheme in a way that the average number of scheduled users equal to K s Comparing the scheme with the, we observed that when the threshold γ T is slightly higher than then the scheme has nearly the same average BER performance as the but when γ T is slightly lower than, the scheme suffers a minimal BER and ASE performance loss but offers a certain reduction in the AFL Although the average BER performance degrades, this average BER performance still meets the average BER requirement Note that from Fig 4 the average BER of the OOBS scheme fluctuates around that of the because the combined effect of the adaptive modulation and scheduling threshold γt Similar to the OOBS scheme, the average BER of the scheme also fluctuates due to the adaptive modulation However, we can not recognize it because the fluctuation is very small in comparison with the OOBS scheme REFERENCES 1] R Knopp and P A Humblet, Information capacity and power control in single cell multiuser communications, in IEEE Int Confs on Commun ICC 95, Seattle, WA, June 1995, pp ] G B Holter, M-S Alouini, G E Øien and H-C Yang, Multiuser switched diversity transmission, in Proc IEEE Vehicular Technology Conf VTC 4-Fall, Los Angeles, CA, 24, pp ] D Gesbert and M-S Alouini, How much feedback is multi-user diversity really worth? in Proc of IEEE Int Conf on Commun ICC 4, Paris, France, June 24, pp ] Y Ma and D Zhang, Performance of generalized selection multiuser scheduling over generalized fading channels, in Proc IEEE Int Wireless Commun and Mobile Comput Conf IWCMC 6, Vancouver, Canada, July 26 5] M K Simon and M-S Alouini, Performance analysis of generalized selection combiningwith threshold test per branch T-GSC, IEEE Trans Veh Technol, vol 51, no 5, pp , 22 6] J Hömäläinen and R Wichman, Capacities of physicallayer scheduling strategies on a shared link, Wireless Personal Communications, vol 39, no 1, pp , Oct 26 7] L Yang and H-C Yang, GSECps: A diversity technique with improved performance-complexity tradeoff, in Proc of IEEE Global Telecomm Conf GLOBECOM 5, St Louis, Mo, Nov 25 8] K J Hole, H Holm, and G E Øien, Adaptive multidimensional coded modulation on flat fading channels, IEEE J Select Areas Commun, vol 18, no 7, pp , July 2 9] H-C Yang and M-S Alouini, Generalized switch-and-examine combining GSEC: A low-complexity combining scheme for diversity-rich environments, IEEE Trans Commun, vol COM-52, no 1, pp , Oct 24 1] I S Gradshteyn and I M Ryzhik, Table of Integrals, Series, and Products, 5th ed San Diego, CA: Academic Press, ] S S Nam, M-S Alouini, K A Qaraqe and H-C Yang, Threshold based parallel multiuser scheduling, IEEE Trans Wireless Com, submitted PDF of a Scheduled User Simulation result Analytical result SNR γ Figure 1: PDF comparison between the analytical and the simulation results of the scheme for K =5, K s =3, γ T =1dB, = 1 db, and iid Rayleigh fading condition Average Feedback Loads of scheduled users OOBS OOBS scheme with equivalent γ T Average SNR db] Figure 2: Average feedback loads for the i OOBS scheme, ii scheme, and iii GSC based scheduling scheme K =5and K s = 3 Average Spectral Efficiencies of scheduled users OOBS scheme with equivalent γ T scheme with γ T OOBS Average SNR db] Figure 3: Average spectral efficiencies of adaptive coded M-QAM modulation for the i OOBS scheme, ii scheme, and iii GSC based scheduling scheme over iid Rayleigh fading conditions with K =5and K s =3 Average BER of a scheduled user Average SNR db] GSC based scheduleing scheme OOS scheme with equivalent γ T Figure 4: Average BER of adaptive coded M-QAM modulation with the i OOBS scheme, ii scheme, and iii GSC based scheduling scheme for K =5, K s =3, and iid Rayleigh fading conditions

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