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Scheduling in Wireless Communication Systems

Scheduling in Wireless Communication Systems. ECE559VV Presentation Loc Xuan Bui. Outline. Introduction Sum-rate Maximization Scheduling Proportional Fair Scheduling (PFS) Opportunistic Beamforming Conclusions. Introduction.

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Scheduling in Wireless Communication Systems

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

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

  3. 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. 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. ECE559VV Presentation - Loc Bui

  5. Illustration 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. ECE559VV Presentation - Loc Bui

  7. Illustration 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 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. 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: ECE559VV Presentation - Loc Bui

  11. Proportional Fair Scheduling • 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. 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. 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. ECE559VV Presentation - Loc Bui

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

  15. 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). ECE559VV Presentation - Loc Bui

  16. 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? ECE559VV Presentation - Loc Bui

  17. 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 ECE559VV Presentation - Loc Bui

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

  19. 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 ECE559VV Presentation - Loc Bui

  20. Thank you! • Questions? ECE559VV Presentation - Loc Bui

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