1. Proportional Fair Frequency-Domain Packet Scheduling for 3GPP LTE Uplink
Suk-Bok Lee, Ioannis Pefkianakis, Adam Meyerson, Shugong Xu, Songwu Lu
IEEE INFOCOM 2009 proceedings.
Speaker：Tsung-Yin Lee

2. Outline Introduction Heuristic Algorithm Simulation Conclusion
The Model
Problem Formulation
Heuristic Algorithm
Simulation
Conclusion

3. OFDMA for LTE
Orthogonal Frequency Division Multiple Access (OFDMA) has been considered as a strong candidate for the broadband air interface
robustness to multipath fading
higher spectral efficiency
bandwidth scalability

4. Disadvantage of OFDMA
one major disadvantage of OFDMA is that the instantaneous transmitted RF power can vary dramatically within a single OFDM symbol
high peak-to-average power ratio (PAPR) (decrease battery life)

5. Single-Carrier FDMA selected for LTE uplink multiple access scheme
keeping most of the advantages of OFDMA
SC-FDMA has significantly lower PAPR
benefits the mobile terminal in terms of transmit power efficiency

6. LTE Uplink Scheduler
a scheduler needs to know the instantaneous radio channel conditions across all users and all resource blocks (RBs)
LTE UL each user transmits a Sounding Reference Signal (SRS) to the BS
channel quality indicator (CQI)

7. Proportional Fair (PF) algorithm
PF algorithm as a basic scheduling principle and apply the PF algorithm directly over each RB one-by-one independently
SC-FDMA requires that all the RBs allocated to a single user must be contiguous in frequency within each time slot [5][6]
[5] Moray Rumney. 3GPP LTE: Introducing SIngle-Carrier FDMA Agilent MeasurementJournal, 2008.
[6] 3GPP TSG-RAN WG2 Meeting #57, R , “Resource fragmentation in LTEuplink”, St. Louis, USA, Feb, 2007.

8. The Model The base station can allocate m RBs to a set of n users
At each time slot multiple RBs (with the contiguity constraint) can be assigned to a single user
indicate whether or not RB c is assigned to user i at time slot t
denote the instantaneous channel rate for user i on RB c at time t

9. Problem Formulation (1/3)
the well known PF algorithm aims to maximize the logarithmic utility function
In order to maximize , one should maximize where di(t) is total data transmitted to user i at time t ( this paper change di(t) to ) [7][10][14]
[7] M. Andrews. A survey of scheduling theory in wireless data networks. IMA, 2005.
[10] H. Kushner and P. Whiting. Asymptotic properties of proportional-fair sharing
algorithms. Allerton, 2002.
[14] D. Tse. Multiuser diversity in wireless networks.
dtse/stanford416.ps , 2002.

10. Problem Formulation (2/3)
Let be the PF metric value that user i has on RB c at time slot t
We can establish PF objective function when scheduling time slot t as follows:
(1)

11. Problem Formulation (3/3)
for LTE UL we need to incorporate the contiguous RB constraint into this objective (1) due to the physical layer requirement of SC-FDMA
serve users with suboptimal PF metric value for some RBs so as to optimize the PF objective (1)

12. Hardness Result Theorem 1
LTE UL PF-FDPS problem (i.e. maximizing objective (1) with the contiguous RB constraint) is NP-hard [11]
[11] S.-B. Lee, I. Pefkianakis, A. Meyerson, S. Xu, and S. Lu. Proportional Fair
Frequency-Domain Packet Scheduling for 3GPP LTE Uplink. UCLA TR , 2009.

13. Heuristic Algorithm
Paper’s heuristics do not give guaranteed error bound, and moreover we believe that no practical greedy algorithms can give an approximation to this particular problem [11]
[11] S.-B. Lee, I. Pefkianakis, A. Meyerson, S. Xu, and S. Lu. Proportional Fair
Frequency-Domain Packet Scheduling for 3GPP LTE Uplink. UCLA TR , 2009.

14. carrier-by-carrier in turn (1/2)
As a starter, our first greedy heuristic Alg1 schedules data from RB1 to RBm in sequence, and for each RB c it assigns the best user i who
1) has the maximum PF metric value on c
2) satisfies the contiguity constraint.

15. carrier-by-carrier in turn (2/2)

16. largest-metric-value-RB-first (1/2)
Assign all the “in-between” RBs to a candidate user
it assigns RB5 to i, which as a result comes with assignment of RB4 to i, since i is already assigned RB3
Assigned RB
Between RB3 and RB5
RB5 Assigned Now
RB3 Already Assigned
RB3
RB4
RB5

17. largest-metric-value-RB-first (2/2)

18. riding peaks (1/3)
Seeing the drawback of Alg2, we would like to utilize each user’s high valued RBs as much as possible
Fundamental physical layer characteristic is that in multi-carrier systems the channel SNR values (i.e. CQI) are correlated in both time and frequency

19. riding peaks (2/3)
if for each user i RB c has good channel rate, then the neighboring RBs (c−1, c+1) have high channel rate as well with high probability

20. riding peaks (3/3)

21. RB grouping (1/2)
Alg3 relies on the strong frequency-domain correlation, it is easily cheated by the small-scale variation

22. RB grouping (2/2)
This RB grouping might be helpful to catch a bit large-scale fluctuation
divide m RBs into n groups
apply the “peak riding” over those RB groups

23. Simulation Parameter (1/2)
use traces generated as specified in 3GPP deployment evaluation [2]
[2] Technical specification group radio access networks - Deployment aspects. 3GPP TR

24. Simulation Parameter (2/2)
paper use an algorithm that optimizes objective (1) without the constraint as our reference, and we refer to this algorithm as OPT∗ (upper bound of the optimum)
Jain’s fairness index [9], measured by the data-rate fairness criterion
[9] R. Jain, D. M. Chiu, and W. Hawe. A Quantitative Measure of Fairness and Discrimination for Resource Allocation in Shared Systems. DEC Research Report TR-301.

25. System throughput and fairness with varying number of users

26. Average number of users scheduled per 1 TTI

27. Conclusion
Due to its single carrier property of SC-FDMA, LTE UL requires the RBs allocated to a single user to be contiguous in frequency
NP-hard nature of this problem
Four Heuristic Algorithm to solve this problem

28. Comment
In LTE scheduling problem, we will handle uplink and downlink from different scheme
We should combine uplink and downlink to increase network performance