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Resource Allocation for Mobile Multiuser OFDM Systems. Prof. Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University of Texas at Austin February 17, 2006. bevans@ece.utexas.edu.

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resource allocation for mobile multiuser ofdm systems

Resource Allocation forMobile Multiuser OFDM Systems

Prof. Brian L. Evans

Embedded Signal Processing Laboratory

Dept. of Electrical and Computer Engineering

The University of Texas at Austin

February 17, 2006

bevans@ece.utexas.edu

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

outline
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

2

resource allocation in wireless systems

frequency

code/spatial

user 4

user 5

user 6

user 1

user 2

user 3

time

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

3

orthogonal frequency division multiplexing

channel

magnitude

subcarrier

frequency

Bandwidth

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

OFDM Baseband Spectrum

4

multiuser ofdm

User 1

User 2

frequency

Base Station

User K

(Subcarrier and power allocation)

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

. . .

5

exploiting multiuser diversity
Exploiting Multiuser Diversity
  • Downlink multiuser OFDM
    • Users share subchannels and basestation transmit power
    • Users only decode their own data

6

outline8
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

8

mu ofdm with proportional rates
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

9

two step near optimal solution
Two-Step Near-Optimal Solution
  • Subchannel allocation step
    • Greedy algorithm – allow user with leastallocated 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 - # users

N - # subchannels

n - # iterations

10

lower complexity solution

10

8

7

4

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 subchannelsto 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

11

total capacity comparison
Total Capacity Comparison

N = 64 subchannels

SNR = 38 dB

SNR 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

13

proportionality comparison
Proportionality Comparison

Based on the

16-user case,

10000 channel

realizations per

user

Normalized rate proportions for three classes of users using proportions

{4, 2, 1}

Proportions

Wong’s Method

Shen’s Method

14

real time software prototype
Real-time Software Prototype

LabVIEW 7.0

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

TMS320C6701 Digital Signal Processor (DSP)

Matlab 6.5

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

The DSP receives Channel State Information and performs resource allocation algorithm.

15

computational complexity
Computational Complexity

22% average improvement

Code developed in floating point C

Run on 133 MHzTI TMS320C6701 DSP EVM board

16

memory usage
Memory Usage

* All values are in bytes

17

outline19
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

19

delayed csi

Back haul

t=

Internet

t=0

Delayed CSI

mobile

t=0: Mobile estimates channel and

feeds this back to base station

t=: Base station receives estimates,

adapts transmission based on these

Higher BER

Lower bps/Hz

Channel Mismatch

20

prediction of wireless channels

h(n-p)

h(n-)

h(n+) ?

h(n)

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 responsemay reduce how often directchannel feedback is provided

21

related work

Pilot Subcarriers

IFFT

Data Subcarriers

Time-domain channel taps

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

22

ofdm channel prediction comparison
OFDM Channel Prediction Comparison
  • 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

23

high resolution ofdm channel prediction
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

24

deterministic channel model
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

25

prediction via 2 d frequency estimation
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

26

two step 1 d frequency estimation
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 steps
    • Time-delay estimation
    • Doppler-frequency estimation

27

mean square error vs snr
Mean-square Error vs. SNR

Prediction 2  ahead

ACRLB – Asymptotic Cramer-Rao Lower Bound

CRLB – Cramer-Rao Lower Bound

29

mean square error vs prediction length
Mean-square Error vs. Prediction Length

SNR = 7.5 dB

ACRLB – Asymptotic Cramer-Rao Lower Bound

CRLB – Cramer-Rao Lower Bound

30

performance comparison summary31
Performance Comparison Summary

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

31

mu ofdm resource allocation with predicted csi future work
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

32

conclusion
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

33

embedded signal processing laboratory
Embedded Signal Processing Laboratory
  • 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:
      • Zukang Shen, PhD
      • Ian C. Wong, PhD Candidate
      • Kyungtae Han, PhD Candidate
      • Daifeng Wang, MS Student
      • Hamood Rehman, MS Student

34

subchannel allocation
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

36

power allocation for a single user

Water-level

subchannels

Power Allocation for a Single User
  • Optimal power distribution for user
    • Order
    • Water-filling algorithm
  • How to find for

37

power allocation among many users
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

38

summary of shen s contribution
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

42

wong s 4 step approach
Wong’s 4-Step Approach
  • Determine number of subcarriers Nkfor each user
  • Assign subcarriers to each user to give rough proportionality
  • Assign total power Pk for each user to maximize capacity
  • Assign the powers pk,n for each user’s subcarriers (waterfilling)

O(K)

O(KNlogN)

O(K)

O(N)

43

simple example

10

8

7

4

Simple Example

N = 4 subchannels

K = 2 users

Ptotal = 10

Desired proportionality among data rates

1 = 3/4

9

2 = 1/4

6

5

3

44

step 1 of subcarriers user

10

8

7

4

1

2

3

4

Step 1: # of Subcarriers/User

1 = 3/4

9

2 = 1/4

6

5

3

N = 4 subchannels

K = 2 users

Ptotal = 10

45

step 2 subcarrier assignment

9

10

8

7

10

10

10

4

8

7

10

8

4

7

9

4

6

10

4

5

6

8

7

5

3

3

1

1

2

2

3

3

4

4

Step 2: Subcarrier Assignment

Rk

Rtot

log2(1+2.5*10)=4.70

log2(1+2.5*8)=4.39

13.3

log2(1+2.5*7)=4.21

log2(1+2.5*9)=4.55

4.55

46

step 3 power per user

10

10

8

9

7

1

2

3

4

Step 3: Power per user

P1 = 7.66

P2 = 2.34

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

Back

47

step 4 power per subcarrier

10

10

8

9

7

1

2

3

4

Step 4: Power per subcarrier
  • Waterfilling across subcarriers for each user

P1 = 7.66

P2 = 2.34

p1,1= 2.58

p1,2= 2.55

p1,3= 2.53

p2,1= 2.34

Data Rates:

R1 = log2(1 + 2.58*10) + log2(1 + 2.55*8)

+ log2(1 + 2.53*7)

= 13.39008

R2 = log2(1+ 2.34*9)

= 4.46336

Back

48

pilot based transmission

f

Df

t

Dt

Pilot-based Transmission
  • Comb pilot pattern
  • Least-squares channel estimates

49

prediction over all the subcarriers
Prediction over all the subcarriers
  • Design prediction filter for each of the Nd data subcarriers
  • Mean-square error

50

prediction over the pilot subcarriers

Pilot Subcarriers

Data Subcarriers

Prediction over the pilot subcarriers
  • 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

51

prediction on time domain channel taps
Prediction on time-domain channel taps
  • 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:

52

step 1 time delay estimation
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]

57

step 2 doppler frequency estimation
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

58

prediction as parameter estimation
Prediction as parameter estimation
  • Channel is a continuous non-linear function of the 4M-length channel parameter vector

59

closed form expression for asymptotic crlb
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

61

insights from the mse expression
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, Dtand Df should be chosen as large as possible to decrease the MSE bound

Doppler frequency & phase cross covariance

Amplitude & phase error variance

Doppler frequency error variance

Time-delay & phase cross covariance

Time-delay error variance

62