1. Scheduling in Wireless Communication Systems
ECE559VV Presentation
Loc Xuan Bui

2. ECE559VV Presentation - Loc Bui
Outline
Introduction
Sum-rate Maximization Scheduling
Proportional Fair Scheduling (PFS)
Opportunistic Beamforming
Conclusions
11/9/2018
ECE559VV Presentation - Loc Bui

3. ECE559VV Presentation - Loc Bui
Introduction
Single-cell, downlink channels: A base station communicates with K users.
Base-band time-slotted block-fading channel model:
Power constraint:
Full channel state information at both transmitter and receivers.
11/9/2018
ECE559VV Presentation - Loc Bui

4. Information Theoretic Capacity
For AWGN, two-user case [Cover & Thomas ‘06]:
If , with each possible power split:
The optimal scheme is superposition coding.
Orthogonal scheme is sub-optimal.
If , then orthogonal scheme is also optimal.
11/9/2018
ECE559VV Presentation - Loc Bui

5. ECE559VV Presentation - Loc Bui
Illustration
11/9/2018
ECE559VV Presentation - Loc Bui

6. Sum-rate maximization
Goal: maximizing the sum-rate subject to the power constraint.
Solution: (P2 = P, P1 = 0), i.e., allocating all power to user 2 which has better channel.
11/9/2018
ECE559VV Presentation - Loc Bui

7. ECE559VV Presentation - Loc Bui
Illustration
11/9/2018
ECE559VV Presentation - Loc Bui

8. “Max Sum-rate” scheduling
Generalize to fading channels, K users [Tse ‘97]:
In each time slot, observe the channels of all users.
Only transmit to the user i* which has the best channel:
The optimal power allocation is the water-filling solution:
where  is chosen such that
11/9/2018
ECE559VV Presentation - Loc Bui

9. “Max Sum-rate” scheduling
Intuition:
In order to maximize the total rate, we should give all resources to the user who can best use them.
Problem: highly unfair!!!
If users are not symmetric, the users with better channels will get higher rates.
11/9/2018
ECE559VV Presentation - Loc Bui

10. A “fairer” solution: PFS
Fixed transmit power P(t)  P.
Let Ri(t) be the instantaneous rate that user i can receive at time t, e.g.,
BS keeps track of the average throughput over a past window of length W for each user:
11/9/2018
ECE559VV Presentation - Loc Bui

11. Proportional Fair Scheduling
At each time slot, transmit to user i* where
Comparing to “Max Sum-rate” scheduling:
PFS gives priority to users with high instantaneous rate and low current average throughput -> fairer to users with bad channels than “Max Sum-rate” scheduling.
11/9/2018
ECE559VV Presentation - Loc Bui

12. Why is it called “proportional fair”?
Main result:
Let Ti be the long-term average throughput of user i as the window length W goes to infinity.
Then, PFS maximizes
almost surely among all feasible scheduling policies.
Note:
The objective is known as the proportional fair metric.
11/9/2018
ECE559VV Presentation - Loc Bui

13. Proportional fair metric
In other words, if we move from Ti* to Ti , and scale the improvement in proportion to the current allocation, then the aggregate improvement is negative.
11/9/2018
ECE559VV Presentation - Loc Bui

14. ECE559VV Presentation - Loc Bui
Optimality of PFS
Given {Ri(t)} and {Ti(t)}, in order to maximize U(t+1),
11/9/2018
ECE559VV Presentation - Loc Bui

15. ECE559VV Presentation - Loc Bui
More about PFS
Formal proofs of asymptotic optimality of PFS regarding to proportional fair metric: Agrawal & Subramanian ‘02, Kushner & Whiting ‘04, Stolyar ‘05.
PFS is implemented in the downlink of CDMA2000 EV-DO (IS-856) system.
One can also compute the sum-rate achieved by PFS (Caire et al. ‘06).
11/9/2018
ECE559VV Presentation - Loc Bui

16. ECE559VV Presentation - Loc Bui
More about PFS
Questions:
In PFS, we assume that power is fixed at every time slot. If we relax that condition, then what is the optimal power allocation?
In other words, can we obtain a similar “water-filling” solution as in the case of “Max Sum-rate” scheduling?
What if the traffic is real-time with delay requirements?
11/9/2018
ECE559VV Presentation - Loc Bui

17. ECE559VV Presentation - Loc Bui
Multiuser diversity
So far, we have seen the benefit of multiuser diversity:
“Riding on the peaks”: scheduling users when their channels are good.
Multiuser diversity: there is a high chance that a user’s channel is near its peak.
Fading is actually useful!
The larger the dynamic range of channel fluctuations, the higher the peaks.
But what if that not the case?
Little scattering in environment / LOS path
Really slow fading
11/9/2018
ECE559VV Presentation - Loc Bui

18. Opportunistic Beamforming
Induce faster and larger fluctuations when the environment has little scattering and/or the fading is slow.
11/9/2018
ECE559VV Presentation - Loc Bui

19. ECE559VV Presentation - Loc Bui
Conclusions
Scheduling is to determine what users to serve and how they are served.
Depending on what our goal is, we’ll have different scheduling policy:
“Max Sum-rate” scheduling
Proportional Fair Scheduling
Fading sometimes can be exploited
11/9/2018
ECE559VV Presentation - Loc Bui

20. ECE559VV Presentation - Loc Bui
Thank you!
Questions?
11/9/2018
ECE559VV Presentation - Loc Bui