05/19/2005 Wireless Communications Lab, KAIST 1

Scheduling Considerations for Multi-User MIMO

Sae-Young ChungWireless Communications Lab

KAIST05/19/2005

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Overview Introduction Multi-user MIMO Dirty paper coding Optimal schedulers Summary

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Small-Scale Fading

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Channel Knowledge Assume perfect CSI at Tx and at Rx

Requires CSI feedback from Rx to Tx Is it a realistic assumption?

If packet duration << coherence time E.g., 3km/h, 2GHz: ~ 30 msec Packet duration: ~> 1 msec in 3G

If packet duration >> coherence time Channel coding provides time diversity

CSI feedback consumes resource Worse for MIMO

Penalty due to time delay Estimation errors

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Single-User MIMO

Capacity increases as at high SNR Dimension-limited regime # of spatial dimensions = w.p. 1

Capacity increases as at low SNR Uses only one spatial dimension, i.e., beamforming Only the quality of the best spatial channel matters

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Multi-User MIMOBroadcast

Multiple access

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키스의 고유 조건은 입술끼리

만나야 되고 특별한 요령은 필요치 않다

Thequick

brownjumpsover

lazythe

dog

fox

Dirty Paper Coding

The quick brown fox

jumps over the lazy dog

The quick brown fox

jumps over the lazy dog

키스의 고유 조건은 입술끼리

만나야 되고 특별한 요령은 필요치 않다

The quick brown fox

jumps over the lazy dog

키스의 고유 조건은 입술끼리

만나야 되고 특별한 요령은 필요치 않다

Thequick

brownjumpsover

lazythe

dog

fox

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Dirty Paper Coding DPC: M. Costa ’83 DPC achieves capacity of Gaussian MIMO broadcast ch

annel H. Weingarten, Y. Steinberg, S. Shamai ’04

Practical schemes Interference cancelling at the transmitter

Erez, Shamai, Zamir ’00

But, complicated to implement More practical schemes are yet to be discovered

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Single Tx Antenna Channels become degraded

BC

DPC is equivalent to SIC Sum capacity is achievable

with TDM Other boundary points are not

achievable by TDM in general E.g., rates achieved by PF

scheduler

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

3.5

R1 [b/s/Hz]

R2 [

b/s

/Hz]

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Scheduling Gain Three sources of scheduling gain in wireless

Channel variation over time Channel variation over frequency Channel variation over space

Optimal scheduling Allocates dimensions and power optimally across time, frequency and

space Peak or average power constraints

Constant power allocation or optimal power allocation

over Time, frequency, and space

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Opportunistic Scheduling

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Optimal Scheduler Scheduler maximizes the following for each channel

state

It maximizes Therefore the following is on the boundary of the capacity region

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PF Scheduler achieves PF since for all T

implies for all T Therefore, PF scheduler should maximize

for each channel state, where is the measured throughput of user k

This generalizes Qualcomm’s PF scheduler H. Viswanathan, S. Venkatesan, H. Huang ’03

Equivalent to max sum-rate scheduler if channel statistics are the same for all users

DPC and PF scheduling can be combined

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Other Schedulers Maximize sum-rate: Fair (equal throughput):

Same as max min Max harmonic mean throughput

Circuit capacity

PF scheduler Sum-rate Fair scheduler

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Calculation of DPC Capacity Convert to a convex optimization by using dualit

y between BC and MAC S. Viswanath, N. Jindal, A. Goldsmith ’02

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DPC Capacity Example 4x1 (solid) or 4x2 (dashed)

MIMO 10 users Simultaneously scheduled

users: 1, 2, 3, or 4 (from bottom to up)

Plots sum capacity, i.e., scheduler maximizes sum throughput

-20 -10 0 10 20 300

5

10

15

20

25

30

35

40

SNR [dB]

R [

b/s

/Hz]

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Asymptotic Behavior Low SNR

Power limited, dimension irrelevant Picking one user is enough (i.e., TDM) Pick the best eigen mode for the chosen user

High SNR Dimension limited, power irrelevant Number of dimensions:

Number of users: Maximum number of users scheduled simultaneously:

Picking users is enough High # of users

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Current Research Areas at WCL Practical multi-user MIMO schemes

Beamforming Combined with LDPC codes Iterative decoding techniques Limited CSI feedback

Cross layer optimization Scheduler design OFDM Network information theory

Relay channels Interference channels Ad-hoc networks

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Summary MIMO can increase capacity Multi-user MIMO can increase capacity further Good practical schemes are desirable Optimal scheduling for multi-user MIMO Many research problems

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Thank You