Multiuser Resource Allocation in Multichannel Wireless Communication Systems

Zukang ShenPh.D. Defense

Committee Members:Prof. Jeffrey G. Andrews (co-advisor)

Prof. Melba M. CrawfordProf. Gustavo de Veciana

Prof. Brian L. Evans (co-advisor)Prof. Robert W. Heath, Jr.Prof. Edward J. Powers

Communications, Networks, and Systems AreaDept. of Electrical and Computer Engineering

The University of Texas at AustinJan. 19, 2006

(updated slides)

2

Outline

Contribution Multichannel Objective New Constraints

Low Complexity Algorithm

#1: Multiuser orthogonal

frequency division multiplexing

Frequency domain

Sum capacity

Proportional user data

rates

Decouple subchannel and power allocation

#2: Multiuser multi-antenna systems

with block diagonalization

Spatial domain

Sum capacity

Joint precoding and post-

processing

Receive antenna selection

#3: User selection in multi-antenna

systems with block diagonalization

Spatial domain

Sum capacity

Systems with a large number of

users

Greedy capacity and channel norm based algorithms

3

Resource Allocation in Wireless Systems High data rate transmission

Wireless local area networks (WLAN) 54 -- 108 Mbps Metropolitan area networks (WiMAX) ~10 -- 100 Mbps Cellular systems (3GPP) ~1 -- 4 Mbps

Limited resources shared by multiple users Transmit power Frequency bandwidth Transmission time Code resource Spatial antennas

Resource allocation impacts Power consumption User throughput System latency

user 4 user 5 user 6

user 1 user 2 user 3

time

frequency

code/spatial

4

Multiuser Diversity Multiuser wireless communication systems

Independent fading channels Multiuser diversity

0 0.1 0.2 0.3 0.4 0.5-40

-30

-20

-10

0

10

Time (sec)

Cha

nnel

gai

n (d

B)

Rayleigh Fading Channel in a 10-user System

single user gainmax user gain

Resource Allocation

Static Adaptive

Users transmission

order

Pre-determined

Smartly scheduled

Channel state

information

Not exploited

Wellexploited

SystemPerformance Poor Good

time/frequencytim

e/frequency

user 1 user 2 user 3 user K

5

Downlink Multiuser Multichannel Systems Downlink systems

Centralized basestation transmits to multiple users simultaneously

Limited resources at basestation Multiple channels created in

Frequency: orthogonal frequency division multiplexing (OFDM) Space: multiple transmit and receive antennas

Adaptive resource allocation Goal: Optimize system throughput subject to constraints Method: Formulate resource allocation as optimization problem

Optimal solution typically computationally prohibitive to findLow complexity resource scheduling algorithms desired

Assumption: Perfect channel state information of all users known at basestation

6

Outline Introduction Contribution #1: Adaptive resource allocation in multiuser

OFDM systems with proportional rate constraints Optimization framework balancing throughput and fairness Decoupling subchannel and power allocation Allocating power optimally for a given subchannel allocation

Contribution #2: Sum capacity of downlink multiuser MIMO systems with block diagonalization

Contribution #3: Low complexity user selection algorithms in multiuser MIMO systems with block diagonalization

Conclusion

7

Multiuser OFDM (MU-OFDM) Orthogonal frequency division multiplexing

Zero inter-symbol interference Parallel frequency subchannels Multiple access technology

Downlink multiuser OFDM Users share subchannels and basestation transmit power Users only decode their own data

Resource allocation methods Static: TDMA, FDMA Dynamic: multiuser diversity

Users feedback channelinformation to basestation

Basestation determinesresource allocation

frequency

gain

8

MU-OFDM Adaptive Resource Allocation

Objective Advantage Disadvantage

Max sum capacity

[Jang et al., 2003]

Best sum capacity

No data rate fairness among users

Max minimum user’s capacity [Rhee et al., 2000]

Equal user data rates

Inflexible user datarates distribution

Max weightedsum capacity

[Cendrillon et al., 2004]

Data rate fairness

adjustable by varying

weights

No guarantee for required proportional

user data rates

: user k’s capacity (bits/s/Hz) as continuous function for single cell

9

MU-OFDM with Proportional Rates Objective: Sum capacity

Constraints Total transmit power No subchannel shared by multiple users Proportional rate constraints

Advantages In theory, fill gap of max sum capacity & max-min capacity In practice, allow different service privileges and different pricing

B Transmission bandwidth

K # of users

N # of subchannels

pk,npower in user k’s

subchannel n

hk,nchannel gain of user k’s

subchannel n

N0 AWGN power density

Rk User k’s capacity

System parameter for proportional rates

Contribution #1

10

Subchannel Allocation Modified method of [Rhee et al., 2000], but we keep the

assumption of equal power distribution on subchannels1. Initialization (Enforce zero initial conditions)

Set , for . Let

2. For to (Allocate best subchannel for each user)a) Find satisfying for allb) Let , and update

3. While (Then iteratively give lowest rate user first choice) a) Find satisfying for allb) For the found , find satisfying for allc) For the found and , Let , and

update

Contribution #1

11

Power Allocation for a Single User Optimal power distribution for user

Order Water-filling algorithm

How to find for

Contribution #1

K # of users

N # of subchannels

pk,npower in user k’s nth assigned subchannel

Hk,nChannel-to-noise ratio in

user k’s nth assigned subchannel

Nk# of subchannels

allocated to user k

Pk,totTotal power allocated to

user k

subchannels

Water-level

12

Power Allocation among Many Users Use proportional rate and total power constraints

Solve nonlinear system of K equations: /iteration Two special cases

Linear case: , closed-form solution High channel-to-noise ratio: and

Contribution #1

where

13

Comparison with Optimal SolutionContribution #1

-10 -5 0 5 100

0.5

1

1.5

2

2.5

3

3.5

10*log10(1/2)

Ove

rall

capa

city

(bits

/s/H

z)

optimal, E(ch1)/E(ch2)=1decoupled, E(ch1)/E(ch2)=1optimal, E(ch1)/E(ch2)=0.1decoupled, E(ch1)/E(ch2)=0.1optimal, E(ch1)/E(ch2)=10decoupled, E(ch1)/E(ch2)=10

14

Comparison with Max-Min Capacity Contribution #1

8 10 12 14 160.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Number of users K

Min

imum

Use

r's C

apac

ity (b

it/s/

Hz) proposed

max-min:equal powerTDMA

15

Comparison with Max Sum CapacityContribution #1

0 1 2 3 4 5 6 76

7

8

9

10

Fairness Index m

Erg

odic

Sum

Cap

acity

(bits

/s/H

z)

max sum capacitysingle user (higher SNR)proposedstatic TDMAsingle user (lower SNR)

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

Nor

mal

ized

Erg

odic

Cap

acity

Per

Use

r

User Index k

ideal, m=3proposed m=3max sum capacitystatic TDMA

16

Summary of Contribution #1 Adaptive resource allocation in multiuser OFDM systems

Maximize sum capacity Enforce proportional user data rates

Low complexity near-optimal resource allocation algorithm Subchannel allocation assuming equal power on all subchannels Optimal power distribution for a single user Optimal power distribution among many users with proportionality

Advantages Evaluate tradeoff between sum capacity and user data rate

fairness Fill the gap of max sum capacity and max-min capacity Achieve flexible data rate distribution among users Allow different service privileges and pricing

17

Outline Introduction Contribution #1: Adaptive resource allocation in multiuser

OFDM systems with proportional rate constraints Contribution #2: Sum capacity of downlink multiuser MIMO

systems with block diagonalization Block diagonalization with receive antenna selection Sum capacity of BD vs. DPC for given channels Upper bound on the ratio of DPC and BD sum capacity in Rayleigh

fading channels Contribution #3: Low complexity user selection algorithms

in multiuser MIMO systems with block diagonalization Conclusion

18

Multi-Antenna Systems Exploit spatial dimension with multiple antennas Improve transmission reliability – diversity

Combat channel fading [Jakes, 1974] Combat co-channel interference [Winters, 1984]

Increase spectral efficiency – multiplexing Multiple parallel spatial channels created with multiple antennas at

transmitter and receiver [Winters, 1987] [Foschini et al., 1998] Theoretical results on point-to-point multi-input multi-output (MIMO)

channel capacity [Telatar, 1999]

Tradeoff between diversity and multiplexing Theoretical treatment [Zheng et al., 2003] Switching between diversity and multiplexing [Heath et al., 2005]

19

MIMO Gaussian Broadcast Channels Duality with multiple access channels [Vishwanath et al., 2003]

Dirty paper coding (DPC) [Costa, 1983] Sum capacity achieved with DPC [Vishwanath et al., 2003] Iterative water-filling algorithm [Yu et al., 2004] [Jindal et al., 2005]

Capacity region [Weingarten et al., 2004]

Coding schemes approaching DPC sum capacity[Zamir et al., 2002] [Airy et al., 2004] [Stojnic et al., 2004] Too complicated for cost-effective implementations

+

+

+

+

BroadcastChannel

MultipleAccessChannel

20

Block Diagonalization (BD) Linear precoding technique

Zero inter-user interference [Spencer et al., 2004]

in the null space of Advantages: Simple transceiver design

Effective point-to-point MIMO channel Disadvantages: Suboptimal for sum capacity

Channel energy wasted for orthogonalizing user channels Transmit signal covariance matrices not optimal

21

BD with Receive Antenna Selection Why joint processing?

Confine to be selection matrix, e.g. Lower system overhead for conveying BD with receive antenna selection Exhaustive search for optimal selection matrices

Contribution #2

22

BD vs. DPC: Given Channels

Theorem: The ratio of DPC sum capacity over BD is bounded by Ratio of DPC sum capacity over TDMA bounded by

[Jindal et al., 2005] TDMA only serves one user at a time BD supports multiple users: Valid for any SNR, , , and

Lemma: If user channels are orthogonal, then

Lemma: If and user channelsare in same vector space

Contribution #2

23

BD vs. DPC: Rayleigh Fading Channels Lower bound on BD ergodic sum capacity

Fix a subset of users to serve Each user’s effective channel still Rayleigh Equal power allocated for every MIMO eigenmode

Upper bound on DPC ergodic sum capacity Allow user cooperation (effectively point-to-point channel) Cooperative channel Space-time water-filling for effective cooperative MIMO channel

Upper bound on ratio of DPC and BD ergodic sum capacity Easy evaluation with numerical integrations Bound is tight for

Medium to high SNR, or

Contribution #2

24

Simulation ResultsContribution #2

-20 0 20 40 601

1.5

2

2.5

3

SNR (dB)Erg

odic

Sum

Cap

acity

Gai

n: D

PC

vs.

BD

Proposed boundMonte Carlo, DPC/BD w RxASMonte Carlo, DPC/BD w/o RxAS

-20 0 20 40 600

50

100

150

200

SNR (dB)

Erg

odic

Sum

Cap

acity

(bits

/s/H

z) DPCBD w RxASBD w/o RxAS

25

Simulation ResultsContribution #2

6 8 10 12 14 16 18 200

10

20

30

40

50

# of Transmit Antennas Nt

Erg

odic

Sum

Cap

acity

(bit/

s/H

z) DPCBD w RxASBD w/o RxAS

SNR 20 dB

SNR 10 dB

SNR 0 dB

6 8 10 12 14 16 18 201

1.1

1.2

1.3

1.4

# of Transmit Antennas NtE

rgod

ic S

um C

apac

ity G

ain:

DP

C v

s. B

D

Proposed boundMonte Carlo, DPC/BD w RxASMonte Carlo, DPC/BD w/o RxAS

SNR=20 dB

26

Summary of Contribution #2 Sum capacity in downlink multiuser MIMO systems with

block diagonalization Formulated joint transmitter precoding and receiver post-processing

(shown in dissertation) Combined block diagonalization with receive antenna selection

Block diagonalization vs. dirty paper coding Sum capacity for given channels Ergodic sum capacity in Rayleigh fading channel

Block diagonalization achieves a significant part of the optimal sum capacity

27

Outline Introduction Contribution #1: Adaptive resource allocation in multiuser

OFDM systems with proportional rate constraints Contribution #2: Sum capacity of downlink multiuser MIMO

systems with block diagonalization Contribution #3: Low complexity user selection algorithms

in multiuser MIMO systems with block diagonalization Capacity based user selection Channel Frobenius norm based user selection

Conclusion

28

Need of User Selection for BD Zero inter-user interference requires in null space of

Dimension of : Maximum number of simultaneous users:

Assuming active users utilize all receive antennas Select subset of users to maximize total throughput Exhaustive search

Optimal for total throughput Computationally prohibitive

Related work Semi-orthogonal user set construction [Yoo et al., 2005] Antenna selection [Gharavi-Alkhansari et al., 2004]

29

Greedy User Selection AlgorithmsContribution #3

Capacity based algorithm(c-algorithm)

Channel norm algorithm(n-algorithm)

, apply BD to

users selected

Yes

No users selected or sum capacity decreases

apply c-algorithmto select subset

No

Yes

30

Computational Complexity

Proposed algorithms have complexity Average CPU run time

(Pentium M 1.6G Hz PC)

(m x n) complex matrix operation Flop counts

Frobenius norm

Gram-Schmidt orthogonalization

Water-filling algorithm

Singular value decomposition

Contribution #3

3 10 20 30 40 500

20

40

60

80

100

120

140

# of Total Users K

Tim

e (m

illis

econ

ds)

BD capacity algorithmBD channel norm algorithm

31

Monte Carlo ResultsContribution #3

2 10 20 30 40 500

5

10

15

20

25

30

35

# of Total Users K

Erg

odic

Sum

Cap

acity

(bits

/s/H

z) DPCBD OptimalBD c-algorithmBD n-algorithmBD no selection

SNR 20 dB

SNR 10 dB

SNR 0 dB

32

Summary of Contributions

Adaptive resource allocation in multiuser OFDM Balanced throughput and proportional user data rates Derived optimal power allocation given subchannel allocation

Sum capacity of downlink multiuser MIMO systems Combined block diagonalization with receive antenna selection Analyzed sum capacity of BD vs. DPC for given channels Derived upper bound on ratio of DPC and BD sum capacity in

Rayleigh fading channels

Low complexity user selection algorithms in multiuser MIMO systems with block diagonalization Proposed two algorithms with linear complexity in no. of total users Achieved near-optimal sum capacity