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### 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

- 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

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

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

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

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

6

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

- 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

- 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

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

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

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

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

22% average improvement

Code developed in floating point C

Run on 133 MHzTI TMS320C6701 DSP EVM board

16

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

Back haul

t=

Internet

t=0

Delayed CSImobile

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

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

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

- 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

- 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

- 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

- 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

- 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

Prediction 2 ahead

ACRLB – Asymptotic Cramer-Rao Lower Bound

CRLB – Cramer-Rao Lower Bound

29

Mean-square Error vs. Prediction Length

SNR = 7.5 dB

ACRLB – Asymptotic Cramer-Rao Lower Bound

CRLB – Cramer-Rao Lower Bound

30

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

- 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

- 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

Backup

35

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

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

- 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

- 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

- 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

8

7

4

Simple ExampleN = 4 subchannels

K = 2 users

Ptotal = 10

Desired proportionality among data rates

1 = 3/4

9

2 = 1/4

6

5

3

44

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 AssignmentRk

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

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

Prediction over all the subcarriers

- Design prediction filter for each of the Nd data subcarriers
- Mean-square error

50

…

…

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

- 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

- 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

- 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

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

59

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

- 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

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