weighted cdf-based scheduling for an ofdma relay...

IntroductionSystem model and performance

Extension - with RelaysConclusions

Weighted CDF-based Scheduling for anOFDMA Relay Downlink with Partial Feedback

Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao.University of California, San Diego

November 14, 2012

Anh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego



Outline

1 Introduction

2 System model and performanceSystem modelAnalysisWeights settingExperimental results

3 Extension - with RelaysFast fadingSlow fading

4 Conclusions




OFDMA system - Multiuser diversity

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

10−4

10−3

10−2

10−1

100

101

102

Frequency (MHz)

|h|2

Frequency selective fading

Best of 30 usersUser 1User 2

Effects of fading on channels of usersMultiuser diversity and frequency selectivity

Multiuser diversity: channels to different users are differentFrequency selectivity: channels on different frequency are different

Goal: Exploit the diversity to improve system’s performance




Performance measures vs. Challenges

Measures of System’s PerformanceThroughputFairness: meet users’ requirementsFeedback constraint

ChallengesA large number of usersA large number of resource blocksDiversity in users’ characteristics

Users’ location: different channel gainand channel statistic...Users’ requirements: types of service,power, data rate, delay tolerance,...

At first, we introduce the system model

Multimedia

News

Pictures

…..

OFDM: NRB resource blocks

Web surfing

Email

Download

Youtube …..

Voice

SMS …..

resource

block 4

resource

block 2,3,5

resource

block 1,6

Relay node

Figure: A multiuser system




System modelAnalysisWeights settingExperimental results

Outline

1 Introduction



4 Conclusions





System, Feedback and Scheduling

System: Groups of users with differentpriority

Groups of macro usersGroups of cell edge users, each group isserved by a relay

OFDM with Partial feedbackUsers feed back the best M amongchannels on N resource blocksOn resource block r , there are subset ofusers to feed back

SchedulingUsers are selected based on weightedcdf of the SNR.

Base Station

Selected user on resource bock r

Group 1

Group i

Users provide feedback

weighted w1

weighted wi

W

f1 f2 f3 f4 f5

best M=2

N=5 resource blocks

Figure: partial feedback in anOFDMA signal





Weighted CDF scheduling

How weighted CDF work [5]From SNR Yki of user ki

Obtain uki = FYki(x),

Uniformly distributed in [0, 1]Identical for all users

Compare and prioritize usersSelect the user with the largest weighted CDFk∗ = arg maxk{FYki

(x)}1

wi

Advantage: can control precisely selection probability of all the users

[5] D. Park, H. Seo, H. Kwon, and B. Lee, “Wireless packet scheduling based on the cumulativedistribution function of user transmission rates", IEEE Trans on Communications, Nov. 2005.





System’s performance - average sum rate

The average system sum rate is

R =1N

N∑r=1

E log(1 + Xr ) = E log(1 + Xr ) (1)

where Xr is SNR to the selected user on resource block r





Performance analysis

Steps in analyzing system performance [4]Framework CQI feedback

Random variable OutputStep 1 Zk ,r : CQI at a receiver FZk

Step 2 Yk ,r : SNR seen at a transmitter FYk

Step 3 Xr : SNR of a selected user FX |cond

Step 4a FX = EcondFX |cond

Step 4b EcondEXr [log(1 + Xr )|cond ]k: user index, r: block index

[4] Seong-Ho Hur, and Bhaskar Rao, “Sum rate analysis of a reduced feedback

OFDMA system employing joint scheduling and diversity", IEEE Transactions on Signal

Processing, 2011.






TheoremIn an OFDMA system where all equipments have a single antenna, with Lgroups of users, each group i has Ki users, if only CQI on M best among Nresource blocks is fed back, the CDF of system’s throughput is

FR(ζ(x)) =L∑

l=1

Kj∑nj =0

j=1,...,L;n̄ 6=0

L∏j=1

Pr{|Sr ,j | = nj}

×

nl wl∑Lj=1 nj wj

∑∞t=1 e3(αl , t)

∑t(M−1)m=0 e2(m)FZk

(xρ

)Nt−mαl 6= 1∑M−1

m=0 e1(m)∑N−m

k=0 FZk

(xρ

)N−mαl = 1

,

(2)






where

ζ(x) = log(1 + x)

FZk

(xρ

)is CDF of SNR from the BS to user k

Pr{|Sr ,l | = nl} =( Kl

nl

) (MN

)nl (1− MN

)Kl−nl

αl =∑L

j=1 wj nj

nl wl;

e1(m) =∑M−1

i=mM−i

M ( Ni )(

im )(−1)i−m

e2(0) = e1(0)t ; e2(m) = 1me1(0)

∑min(M−1,m)k=1 (kt −m + k)e1(k)e2(m − k);

e3(αl , t) =∑∞

i=t (αli )(

it

)(−1)i−t .





Weights for groups of users

The probability of selection of user kl is

Pr{k∗r = kl} =

∑π(n̄)

wl∑Lj=1 njwj

nl

Kl

( K1n1

)( KL

nL

)(MN

)∑Lj=1 nj

(1− M

N

)∑Lj=1(Kj−nj )

. (3)

Initialize w(0) = [Palloc,1

Kl, . . . ,

Palloc,LKL

] which isthe weights for the full feedback case.

Solving δw(t)φ(w(t)) = −∇φ(w(t)).

Update w(t + 1) = w(t) + δw(t). Normalizew so that ‖w‖2 = 1 which does not changeφ(w).

End ‖φ(w)‖2 < ε.

Set ε = 10−10

Target Palloc = [0.2, 0.8]

Found weightw = [0.318, 0.682] after 4iterations

Iteration Norm ‖φ(w)‖2

0 2.4691512e-0011 6.2304622e-0022 3.0325582e-0033 7.4881615e-0064 4.5758897e-011

Table: Convergence behaviorAnh H. Nguyen, Yichao Huang, and Bhaskar D. Rao. University of California, San Diego




Experimental results

We consider an OFDMA system withN = 10 resource blocks and groups ofusers with different priority

Group 1K1 = 10 users, weight w1 = 0.4,located at d1 = 414m

Group 2 - cell edgeK2 = 5 users, weight w2 = 0.6,located at d2 = 834m

Base Station


Group 1

Group 2

weighted w1

weighted w2

Figure: A partial feedback OFDMAsystem





System’s performance with partial feedback

27 28 29 30 31 32 33 34 35 36 37 383

3.5

4

4.5

5

5.5

6

6.5

7

Power (dBm)

Thr

ough

put b

ps/H

z

Achievable throughput with weighted priotization with K=[10,5], N=10, w=[0.4,0.6]

M=1 simulatedM=2 simulatedM=3 simulatedM=4 simulatedM=5 simulatedM=1 analyzedM=2 analyzedM=3 analyzedM=4 analyzedM=5 analyzed

Figure: Analyzed and simulated performance of a partial feedback OFDMAsystem with N = 10, K = [10,5], w = [0.4,0.6]





System’s performance with different number of users

5 10 15 20 25 303

4

5

6

7

8

9

10

11

Number of users K (K=K1+K2; K1=2K2)

Thr

ough

put b

ps/H

z

Achievable throughput with weighted priotization with N=10, M=5 w=[0.4,0.6]

P=32 dBm simulatedP=37 dBm simulatedP=42 dBm simulatedP=47 dBm simulatedP=32 dBm analyzedP=37 dBm analyzedP=42 dBm analyzedP=47 dBm analyzed

Figure: Analyzed system throughput of a partial feedback OFDMA systemwith N = 10, M = 5, w = [0.4,0.6], K1 = 2K2




Fast fadingSlow fading

Outline

1 Introduction



4 Conclusions





Fast fading BS-RS links

We consider an OFDMA system withN = 10 resource blocks and groups ofusers with different priority

Group 1K1 = 10 users, weight w1 = 0.4,located at d1 = 414m

Group 2 - cell edgeK2 = 5 users, weight w2 = 0.6,located at d2 = 834m

A relay located at dr = 815m

Base Station


Group 1

Group 2

weighted w1

weighted w2

relay






System’s performance with relays

2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Achievable throughput with weighted priotization

Throughput bps/Hz

cdf

w=[0.5 0.5]T

w=[0.4 0.6]T

w=[0.2 0.8]T

without relaywith relay

Figure: Performance tradeoff due to the biased treatment with users; OFDMA systemwith N = 10, K = [10, 5], P = 37dBm, the distance BS-macro MS is d1 = 414m andthe distance BS-MS group 2 is d2 = 834m which are aided by a relay with power30dBm located 815m from the BS, full feedback is provided





Slow fading BS-RS links

Group 1Macro users, located at d1 = 414m

5 groups (2,...,6) - at the cell edgeUsers, each group served by arelaysLocated at d2 = 834m

A relay located at dr = 815mParameters

Number of users K = [2 2 2 3 3 3]Weightsw = [0.05 0.1 0.15 0.2 0.2 0.3]Log-normal shadowing fading 8dB...

Base Station


Group 1

Group 2

weighted w1

weighted w2

relay

Group Ng

weighted wNg







Allocation of users does not meetrequirementsGroups in resource starvation

Out of service if the coherencetime is large

Short term adjustment can notmaintain fairness among users

2 4 5 6 3 10

0.1

0.2

0.3

0.4

User groups

Sel

ectio

n P

roba

bilit

y

Long Term Fairness

Conditional CDF − simulatedConditional CDF − analyzedCDF of whole link BS−RS−MS

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

User groups

Sel

ectio

n P

roba

bilit

y

Short Term Fairness


Figure: Selection probability of usersin an OFDMA system






The proposed solutions

Interpolate CDF to create anartificial CDF

ContinuousUniformly distributed [0,1]

Can, again precisely controlallocation probability for users

2 4 5 6 3 10

0.1

0.2

0.3

0.4

User groups

Sel

ectio

n P

roba

bilit

y

Long Term Fairness


1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

User groups

Sel

ectio

n P

roba

bilit

y

Short Term Fairness


Figure: Selection probability of usersin an OFDMA system






Tradeoff in system’s performanceGoal: propose a modified technique

Similar allocation managementBetter tradeoff in performance

27 28 29 30 31 32 33 34 35 36 37 383

3.5

4

4.5

5

5.5

6

6.5

7

Power (dBm)

Sys

tem

thro

ughp

ut

Performance tradeoff − CDF based scheduling in Relay OFDMA networks

long term fairnessshort term fairness

Figure: Tradeoff in system’sthroughput




Outline

1 Introduction



4 Conclusions




Conclusion

Consider a Weighted CDF-based scheduling OFDMA system withpartial feedback

Ensures fairnessSupports user priorityExploits multiuser diversity users

Developed an analytical expression for system throughputThe simulations verify the performance of the scheduling methodon OFDMA systems




ReferencesAnh H. Nguyen, and Bhaskar D. Rao, “User selection schemes for maximizingthroughput of multiuser MIMO systems using Zeroforcing Beamforming",ICASSP, 2011.

Anh Nguyen, Yichao Huang, and Bhaskar Rao, “Weighted CDF-basedScheduling for an OFDMA Relay Downlink with Partial Feedback", AsilomarConference on Signals, Systems, and Computers, Nov. 2012.

T. Yoo, A. Goldsmith, "On the optimality of multiantenna broadcast schedulingusing zero-forcing beamforming", IEEE Journal on Selected Areas in Comms,Mar. 2006.

Seong-Ho Hur, and Bhaskar Rao, “Sum rate analysis of a reduced feedbackOFDMA system employing joint scheduling and diversity", IEEE Transactions onSignal Processing, 2011.

D. Park, H. Seo, H. Kwon, and B. Lee, “Wireless Packet Scheduling Based on theCumulative Distribution Function of User Transmission Rates", IEEE Trans onCommunications, Nov. 2005.

I. Gradshteyn, and I. Ryzhik, “Table of Integrals Series and Product", AcademicPress 2007.

G. Senarath et al. “Multi-hop relay system evaluation methodology (channelmodel and performance metric)",http://ieee802.org/16/relay/docs/80216j-06_013r3.pdf, Feb.2007.

Thank you!


http://ieee802.org/16/relay/docs/80216j-06_013r3.pdf

weighted cdf-based scheduling for an ofdma relay...

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