Scheduling in Wireless Communication Systems ECE559VV Presentation Loc Xuan Bui

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

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

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

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

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

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

“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

“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

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

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

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

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

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

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

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

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

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

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

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