Resource Allocation for Mobile Multiuser OFDM Systems Prof. Brian L. Evans Embedded Signal...

Resource Allocation forMobile Multiuser OFDM Systems

Prof. Brian L. EvansEmbedded Signal Processing Laboratory

Dept. of Electrical and Computer Engineering

The University of Texas at Austin

February 17, 2006

[email protected]

Featuring work by ESPL students Zukang Shen and Ian WongCollaboration with Prof. Jeffrey G. Andrews and Prof. Robert W. Heath

2

Outline

Introduction Resource allocation in wireless systems Multiuser OFDM (MU-OFDM) Resource allocation in MU-OFDM

MU-OFDM resource allocation with proportional rates Near-optimal solution Low-complexity solution Real-time implementation

OFDM channel state information (CSI) prediction Comparison of algorithms High-resolution joint estimation and prediction

MU-OFDM resource allocation using predicted CSI

3

Resource Allocation in Wireless Systems

Wireless local area networks (WLAN) 54--108 Mbps Metropolitan area networks (WiMAX) ~10--100 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

Orthogonal Frequency Division Multiplexing

Adopted by many wireless communication standards IEEE 802.11a/g WLAN Digital Video Broadcasting – Terrestrial and Handheld

Broadband channel divided into narrowband subchannels Multipath resistant Receiver equalization simpler than single-carrier systems

Uses static time or frequency division multiple access

subcarrier

frequency

mag

nitu

de

channel

Bandwidth

OFDM Baseband Spectrum

5

Multiuser OFDM

Orthogonal frequency division multiple access (OFDMA) Adopted by IEEE 802.16a/d/e standards

802.16e: 1536 data subchannels with up to 40 users / sector

Users may transmit on different subcarriers at same time Inherits advantages of OFDM Exploits diversity among users

. . .User 1

User 2

frequencyBase Station(Subcarrier and power allocation)

User K

6

Exploiting Multiuser Diversity

Downlink multiuser OFDM Users share subchannels and

basestation transmit power Users only decode their own data

0 0.1 0.2 0.3 0.4 0.5-40

-30

-20

-10

0

10

Time (sec)

Channel g

ain

(dB

)

Rayleigh Fading Channel in a 10-user System

single user gainmax user gain

Resource Allocation

Static Adaptive

Users transmission

order

Pre-determined

Dynamically scheduled

Channel state

information

Not exploited

Wellexploited

SystemPerformance

Poor Good

7

MU-OFDM Resource Allocation

Objective Advantage Disadvantage

Max sum capacity

[Jang et al., 2003]

Best sum capacity

No data rate proportionality among users

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

Equal user data rates

Inflexible user data

rates distribution

Max weightedsum capacity

[Cendrillon et al., 2004]

Data rate fairness

adjustable by varying

weights

No guarantee for meeting

proportional user data rates

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

8

Outline

Introduction Resource allocation in wireless systems Multiuser-OFDM (MU-OFDM) Resource allocation in MU-OFDM




9

MU-OFDM with Proportional Rates Objective: Sum capacity

Constraints Total transmit power

No subchannel shared by multiple users

Proportional rate constraints

Advantages Allows different service privileges and different pricing

BTransmission

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

10

Two-Step Near-Optimal Solution

Subchannel allocation step Greedy algorithm – allow user with least

allocated capacity/proportionality to choosebest subcarrier [Rhee & Cioffi, 2000]

Modified to incorporate proportional rates Computational complexity O(K N log N)

Power allocation step [Shen, Andrews & Evans, 2005]

Exact solution given a subcarrier allocation General case

Solution to set of K non-linear equations in K unknowns Newton-Raphson methods are O(n K) where n is no. of iterations

Special case: High channel-to-noise ratio Solution finds a root of a polynomial with O(n K) complexity Typically 10 iterations in simulation

K - # usersN - # subchannelsn - # iterations

11

Lower Complexity Solution

In practical scenarios, rough proportionality is acceptable Key ideas to simplify Shen’s approach

[Wong, Shen, Andrews & Evans, 2004]

Relax strict proportionality constraint Require predetermined number of subchannels

to be assigned to simplify power allocation

Power allocation Solution to sparse set of linear equations Computational complexity O(K)

Advantages [Wong, Shen, Andrews & Evans, 2004]

Waives high channel-to-noise ratio assumption of Shen’s method Achieves higher capacity with lower complexity vs. Shen’s

method Maintains acceptable proportionality of user data rates

Example

108 7

4

12

Simulation Parameters

Parameter Value Parameter Value

Number of Subcarriers (N)

64 Channel Model

6-tap exponentially decaying power profile with Rayleigh fading

Number of Users (K)

4-16 Maximum Delay Spread

5 s

Bit Error Rate Constraint

10-3 Doppler Frequency

30 Hz

13

Total Capacity Comparison

4 6 8 10 12 14 164.45

4.5

4.55

4.6

4.65

4.7

4.75

number of users

cap

acity

(bit/

s/H

z)

Proposed Method

Shen's Method

N = 64 subchannelsSNR = 38 dBSNR Gap = 3.3 dB

Based on 10000 channel realizations

Proportions assigned randomly from {4,2,1} with probabilities[0.2, 0.3, 0.5]Wong’s Method

Shen’s Method

14

Proportionality Comparison

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

User Number (k)

No

rmal

ized

Ra

te P

rop

ort

ion

s

Proportions

Proposed Method

Shen's Method

Based on the 16-user case,10000 channelrealizations per user

Normalized rate proportions for three classes of users using proportions {4, 2, 1}

ProportionsWong’s MethodShen’s Method

15

Real-time Software Prototype

Matlab generates a frequency-selective Rayleigh channel for each user.

Matlab 6.5

LabVIEW 7.0

TMS320C6701 Digital Signal

Processor (DSP)

The DSP receives Channel State Information and performs

resource allocation algorithm.

LabVIEW handles the interface between Matlab and the DSP and automates allocation tests.

16

Computational Complexity

2 4 6 8 10 12 14 160

1

2

3

4

5

6

7

8

9

10x 10

5 DSP Imlementation Clock cycle count

Number of users

Clo

ck c

ycle

s

Channel Allocation-shenPower Allocation-shen

Channel Allocation-wong

Power Allocation-wong

Total-shenTotal-wong Code developed

in floating point C

Run on 133 MHzTI TMS320C6701 DSP EVM board

22% average improvement

17

Memory Usage

Memory Type *Shen’s Method *Wong’s Method

Program

Memory

Subcarrier Allocation

1660 2024

Power Allocation

2480 1976

Total 4140 4000Data Memory

System Variables

8KN+4K

O(KN)

8KN+4K

O(KN)Subcarrier Allocation

4N+8K

O(N+K)

4N+12K

O(N+K)Power Allocation

4N+24K

O(N+K)

4N+28K

O(N+K)

* All values are in bytes

18

Performance Comparison Summary

Performance Criterion Shen’s Method Wong’s Method

Subcarrier Allocation Computational Complexity

O(KNlogN) O(KNlogN)

Power Allocation Computational Complexity

O(N+nK), n~9 O(N+K)

Memory Complexity O(NK) O(NK)Achieved Capacity High Higher

Adherence to Proportionality

Tight Loose

Assumptions on Subchannel SNR

High None

19

Outline

Introduction Resource allocation in wireless systems Multiuser-OFDM (MU-OFDM) Resource Allocation in MU-OFDM




20

Delayed CSI

InternetBack haul

t=0: Mobile estimates channel and feeds this back to base stationt=ase station receives estimates, adapts transmission based on these t=0t=

Channel Mismatch Higher BERLower bps/Hz

mobile

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Prediction of Wireless Channels

Use current and previous channel estimates to predict future channel response

Overcome feedback delay Adaptation based on predicted channel response

Lessen amount of feedback Predicted channel response

may reduce how often directchannel feedback is provided

h(n-p)h(n-)

h(n)h(n+) ?

…

22

Related Work Prediction on each subcarrier [Forenza & Heath, 2002]

Each subcarrier treated as a narrowband autoregressive process [Duel-Hallen et al., 2000]

Prediction using pilot subcarriers [Sternad & Aronsson, 2003]

Used unbiased power prediction [Ekman, 2002]

Prediction on time-domain channel taps[Schafhuber & Matz, 2005]

Used adaptive prediction filters

… …

Pilot Subcarriers

Data Subcarriers

IFFT

Time-domain channel taps

23

Compared three approaches in unified framework[Wong, Forenza, Heath & Evans, 2004]

Analytical and numerical MSE comparison All-subcarrier and pilot-subcarrier methods have similar MSE

performance Time-domain prediction performs much better than the two other

frequency domain prediction methods

Complexity comparison All-subcarrier > Pilot-subcarrier ¸ Time-domain

OFDM Channel Prediction Comparison

24

High-resolution OFDM Channel Prediction

Combined channel estimation and prediction[Wong & Evans, 2005]

Outperforms previous methods with similar order of computational complexity

Allows decoupling of computations between receiver and transmitter

High-resolution channel estimates available as aby-product of prediction algorithm

25

Deterministic Channel Model

Outdoor mobile macrocell scenario Far-field scatterer (plane wave assumption) Linear motion with constant velocity Small time window (a few wavelengths)

Channel model

Used in modeling and simulation ofwireless channels [Jakes 1974]

Used in ray-tracing channelcharacterization [Rappaport 2002]

n OFDM symbol indexk subchannel index

26

Prediction via 2-D Frequency Estimation

If we accurately estimate parameters in channel model, we could effectively extrapolate the fading process

Estimation and extrapolation period should be within time window where model parameters are stationary

Estimation of two-dimensional complex sinusoids in noise Well studied in radar, sonar, and other array signal processing

applications [Kay, 1988]

Many algorithms available, but are computationally intensive

27

Two-step 1-D Frequency Estimation

Typically, many propagation paths share the same resolvable time delay

We can thus break down the problem into two steps1. Time-delay estimation

2. Doppler-frequency estimation

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IEEE 802.16e Simulation

0 0.5 1 1.5 2 2.5 3

x 10-6

0

0.1

0.2

0.3

0.4

0.5

Time delay

Pa

th p

ow

er

29

Mean-square Error vs. SNR

10 15 20 25 30 35-50

-45

-40

-35

-30

-25

-20

-15

-10

SNR in dB

MS

E in

dB

ACRLB

CRLB

2-Step 1-Dimensional

Burg

Prediction 2 ahead

ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound

30

Mean-square Error vs. Prediction Length

SNR = 7.5 dB

ACRLB – Asymptotic Cramer-Rao Lower Bound CRLB – Cramer-Rao Lower Bound

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

-9

Prediction length ()

MS

E in

dB

ACRLB

CRLB2-Step 1-Dimensional

Burg

31

Performance Comparison Summary

L - No. of paths M - No. of rays per path

32

MU-OFDM Resource Allocation with Predicted CSI (Future Work)

Combine MU-OFDM resource allocation with long-range channel prediction

Using the statistics of the channel prediction error, we can stochastically adapt to the channel Requires less channel feedback More resilient to channel feedback delay Improved overall throughput

33

Conclusion

Resource allocation for MU-OFDM with proportional rates Allows tradeoff between sum capacity and user rate “fairness”

Enables different service privileges and pricing

Derived efficient algorithms to achieve similar performance with lower complexity

Prototyped system in a DSP, showing its promise for real-time implementation

Channel prediction for OFDM systems Overcomes the detrimental effect of feedback delay Proposed high-performance OFDM channel prediction algorithms

with similar complexity Resource allocation using predicted channels is important for

practical realization of resource allocation in MU-OFDM

34

Director: Prof. Brian L. Evans http://www.ece.utexas.edu/~bevans/

WiMAX (OFDM) related research Algorithms for resource allocation in MU-OFDM Algorithms for OFDM channel estimation and prediction Key collaborators: Prof. Jeff Andrews and Prof. Robert Heath Key graduate students:

1. Zukang Shen, PhD2. Ian C. Wong, PhD Candidate3. Kyungtae Han, PhD Candidate4. Daifeng Wang, MS Student5. Hamood Rehman, MS Student

Embedded Signal Processing Laboratory

35

Backup

36

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

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

Set , for . Let

For to (Allocate best subchannel for each user) Find satisfying for all Let , and update

While (Iteratively give lowest rate user first choice) Find satisfying for all For the found , find satisfying for all For the found and , Let , and

update Back

37

Power Allocation for a Single User Optimal power distribution for user

Order Water-filling algorithm

How to find for

K # of users

N # of subchannels

pk,npower in user k’s nth assigned subchannel

Hk,n

Channel-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

38

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

where

Back

39

Comparison with Optimal Solution

-10 -5 0 5 100

0.5

1

1.5

2

2.5

3

3.5

10*log10(1/

2)

Ove

rall

capa

city

(bi

ts/s

/Hz)

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

Back

40

Comparison with Max-Min Capacity

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 (

bit/s

/Hz)

proposedmax-min:equal powerTDMA

41

Comparison with Max Sum Capacity

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

rUser Index k

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

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Summary of Shen’s Contribution

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

43

Wong’s 4-Step Approach

1. Determine number of subcarriers Nk for each user

2. Assign subcarriers to each user to give rough proportionality

3. Assign total power Pk for each user to maximize capacity

4. Assign the powers pk,n for each user’s subcarriers (waterfilling)

O(K)

O(N)

O(KNlogN)

O(K)

44

Simple Example

2 = 1/4

1 = 3/4

3

6 5

9

N = 4 subchannelsK = 2 usersPtotal = 10

108 7

4

Desired proportionality

among data rates

45

Step 1: # of Subcarriers/User

108 7

4

3

6 5

9

Nk

3

1

1 2 3 4

2 = 1/4

1 = 3/4

N = 4 subchannelsK = 2 usersPtotal = 10

46

Step 2: Subcarrier Assignment

Nk

3/4 3

1/4 11 2 3 4

3

6 5

9

1 2 3 4

Rk

log2(1+2.5*10)=4.70

log2(1+2.5*7)=4.21

108

478

47

47

1010log2(1+2.5*8)=4.39

Rtot

13.3

9log2(1+2.5*9)=4.55 4.55

4

108

10108 7

3

6 5

47

Step 3: Power per user

1 2 3 4

10108 7

9

P1 = 7.66 P2 = 2.34

N = 4 subchannels; K = 2 users; Ptotal = 10 Back

48

Step 4: Power per subcarrier

Nk

3/4 3

1/4 1

p1,1= 2.58 p1,2= 2.55p1,3= 2.53 p2,1= 2.34 Data Rates:R1 = log2(1 + 2.58*10) + log2(1 + 2.55*8)

+ log2(1 + 2.53*7) = 13.39008R2 = log2(1+ 2.34*9) = 4.46336

P1 = 7.66 P2 = 2.34

1 2 3 4

10108 7

9

• Waterfilling across subcarriers for each user

Back

49

Comb pilot pattern

Least-squares channel estimates

Pilot-based Transmission

t

f …

Dt

Df

50

Design prediction filter for each of the Nd data subcarriers

Mean-square error

Prediction over all the subcarriers

51

Design filter on the Npilot pilot subcarriers only Less computation and storage needed

Npilot << Nd (e.g. Npilot = 8; Nd = 192 for 802.16e OFDM)

Use the same prediction filter for the data subcarriers nearest to the pilot carrier

Prediction over the pilot subcarriers

… …

Pilot Subcarriers

Data Subcarriers

52

Design filter on Nt · Npilot time-domain channel taps Channel estimates typically available only in freq. domain IFFT required to compute time-domain channel taps

MSE:

Prediction on time-domain channel taps

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Parameter Value Parameter Value

N 256 Bandwidth 5 MHz

Guard Carriers (7)

[0-27] &

[201:256]

Fcarrier 2600 MHz

Channel Model ETSI Vehicular A Mobile Velocity 75 kmph

Prediction Order

75 Downsampling rate 25

(4*fd)

Simulation Parameters (IEEE 802.16e)

54

Prediction Snapshot

55

NMSE vs. Channel Estimation Error

56

NMSE vs. Prediction Horizon

57

Step 1 – Time-delay estimation

Estimate autocorrelation function using the modified covariance averaging method [Stoica & Moses, 1997]

Estimate the number of paths L using minimum description length rule [Xu, Roy, & Kailath, 1994]

Estimate the time delays using Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [Roy & Kailath, 1989]

Estimate the amplitudes cp(l) using least-squares Discrete Fourier Transform of these amplitudes could be used to

estimate channel More accurate than conventional approaches, and similar to parametric

channel estimation method in [Yang, et al., 2001]

58

Step 2 – Doppler Frequency Estimation

Using complex amplitudes cp(l) estimated from Step 1 as the left hand side for (2), we determine the rest of the parameters

Similar steps as Step 1 can be applied for the parameter estimation for each path p

Using the estimated parameters, predict channel as

59

Prediction as parameter estimation

Channel is a continuous non-linear function of the 4M-length channel parameter vector

60

Cramer-Rao Lower Bound (CRLB)

61

Closed-form expression for asymptotic CRLB

Using large-sample limit of CRLB matrix for general 2-D complex sinusoidal parameter estimation [Mitra & Stoica, 2002]

Much simpler expression Achievable by maximum-likelihood and nonlinear least-squares

methods Monte-Carlo numerical evaluations not necessary

62

Insights from the MSE expression

Linear increase with 2 and M Dense multipath channel environments are the hardest to predict [Teal, 2002]

Quadratic increase in n and |k| with f and estimation error variances Emphasizes the importance of estimating these accurately

Nt, Nf, Dt and Df should be chosen as large as possible to decrease the MSE bound

Amplitude & phase error variance

Doppler frequency & phase cross covariance

Doppler frequency error variance

Time-delay & phase cross covariance

Time-delay error variance

Resource Allocation for Mobile Multiuser OFDM Systems Prof. Brian L. Evans Embedded Signal...

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