October 28, 2005 Single User Wireless Scheduling Policies: Opportunism and Optimality Brian Smith and Sriram Vishwanath University of Texas at Austin October 28 th, 2005 The 2005 Texas Wireless Symposium
October 28, 2005 Overview Introduction Wireless Downlink Model Multi-User Diversity Single User Scheduling Gaussian Broadcast Channel Capacity Ergodic Capacity Achieving Boundary Points Summary
October 28, 2005 Introduction Discuss Rate Capacity for Wireless Downlink Information theoretic viewpoint Packet scheduling Max-Rate Max-Quantile Simultaneous scheduling in Broadcast Channel Capacity Region Achieving maximum rates Inspired by MIMO systems
October 28, 2005 Wireless Base Station with Two Users Channel gains drawn independently from random distribution Constant over time-slots, independent between time-slots Both distribution and realization known to Base Station Independent Gaussian noise Transmit power budget P Single User Rate Capacity: R 1 ≤ lg (1+ 1 P/N) Wireless Downlink Model Base Station P Receiver #1 Receiver #2 22 11
October 28, 2005 Channel Randomness Helps Schedule Better User in each time Slot Two State Example Each State occurs with 50% probability Multi-User Diversity Example R1R1 R1R1 R2R2 R2R2 5 5 R1R1 R2R2 State #1 State #2 Ergodic Capacity (4,3)
October 28, 2005 Opportunism Apply Multi-user diversity to Downlink Problem Fairness can become an issue with max-sum rate Max Quantile Schedule user who has best channel, with respect to his own channel distribution Each user is served equal amount of the time Many practical strategies to exploit diversity Base Station P Receiver #1 Receiver #2 22 11
October 28, 2005 Information Theoretic Broadcast Channel Transmit messages at reduced rate to both receivers simultaneously Message intended for other user treated as noise Better user decodes both messages, discards unintended message Interesting Feature of this Capacity Region Max sum-rate always at endpoint Send message exclusively to better user Base Station P Receiver #1 Receiver #2 22 11 CAPACITY REGION PLOT HERE
October 28, 2005 Ergodic Capacity of Fading Broadcast Channel Assumptions: Exponential distribution of received powers In example plot, average powers received are 1 and 3 No power control Max sum-rate point no longer at endpoint Consequence of the fact that sometimes, Channel #1 is better than Channel #2 Max Sum- Rate Point
October 28, 2005 Optimality: Achieving Boundary Points Observation: Already shown how to achieve three boundary points with single-user scheduling Always User #1, Always User #2, Always best User Assertion: No other boundary point can be achieved with a single-user strategy Simultaneous scheduling on Broadcast channel required
October 28, 2005 Convex Region: Boundary Points and Maximization Problem The boundary points of a convex region can be described by a maximization problem: argmax{R 1 + R 2 : (R 1,R 2 ) in S} is a boundary point of S Tangent line with a given slope To achieve this boundary point in the ergodic capacity region, then we must operate at this maximum in every realization (timeslot)
October 28, 2005 Ergodic Capacity: Maximizing at Each Time-Slot Achieving the corresponding ergodic capacity boundary point requires solving the maximization problem for every realization argmax{R 1 + R 2 : (R 1,R 2 ) in S} is a boundary point of S For any parameter other than 0, 1, infinity (slope of 0º, 45º, 90º) some set of realizations will require simultaneous (multi-user) scheduling No single-user scheduling can be optimal
October 28, 2005 Simulation: Max-Quantile Max Quantile Rate Point What is the capacity region for single-user scheduling policies?
October 28, 2005 Summary Wireless downlink with two or more users Information theoretic Gaussian broadcast channel Multi-user diversity valuable There exist easily implementable single-user scheduling policies Sometimes very close to optimal Optimal scheduling requires simultaneous broadcast channel policy unless the goal is one of three specific rate points Required for MIMO to achieve capacity