October 28, 2005

Single User Wireless Scheduling Policies:

Opportunism and Optimality

Brian Smith and Sriram VishwanathUniversity of Texas at AustinOctober 28th, 2005The 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:

R1≤ lg(1+ 1P/N)

Wireless Downlink Model

BaseStation

P Receiver #1

Receiver #22

1

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

6

2

4

8 R1R1

R2 R2

5

5 R1

R2

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

BaseStation

P Receiver #1

Receiver #22

1

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

BaseStation

P Receiver #1

Receiver #22

1 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{R1 + R2 : (R1,R2) 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{R1 + R2 : (R1,R2) 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