Resource Allocation for Mobile Multiuser OFDM Systems

1
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_at_ece.utexas.edu
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

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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
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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

. . .
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Exploiting Multiuser Diversity

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

Resource Allocation Resource Allocation
Static Adaptive
Users transmission order Pre-determined Dynamically scheduled
Channel state information Not exploited Wellexploited
SystemPerformance Poor Good
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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 users 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
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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

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MU-OFDM with Proportional Rates
B Transmission bandwidth
K of users
N of subchannels
pk,n power in user ks subchannel n
hk,n channel gain of user ks subchannel n
N0 AWGN power density
Rk User ks capacity
System parameter for 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

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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
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Lower Complexity Solution

• In practical scenarios, rough proportionality is
  acceptable
• Key ideas to simplify Shens approachWong,
  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
  Shens method
• Achieves higher capacity with lower complexity
  vs. Shens method
• Maintains acceptable proportionality of user data
  rates

Example
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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 ms
Bit Error Rate Constraint 10-3 Doppler Frequency 30 Hz
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Total Capacity Comparison
N 64 subchannels SNR 38 dB SNR Gap 3.3
dB Based on 10000 channel realizations Proportio
ns assigned randomly from 4,2,1 with
probabilities0.2, 0.3, 0.5
Wongs Method Shens Method
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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 Wongs Method Shens Method
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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.
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Computational Complexity
22 average improvement
Code developed in floating point C Run on 133
MHzTI TMS320C6701 DSP EVM board
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Memory Usage
Memory Type Memory Type Shens Method Wongs Method
Program Memory Subcarrier Allocation 1660 2024
Program Memory Power Allocation 2480 1976
Program Memory Total 4140 4000
Data Memory System Variables 8KN4K O(KN) 8KN4K O(KN)
Data Memory Subcarrier Allocation 4N8K O(NK) 4N12K O(NK)
Data Memory Power Allocation 4N24K O(NK) 4N28K O(NK)
All values are in bytes
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Performance Comparison Summary
Performance Criterion Shens Method Wongs Method
Subcarrier Allocation Computational Complexity O(KNlogN) O(KNlogN)
Power Allocation Computational Complexity O(NnK), n9 O(NK)
Memory Complexity O(NK) O(NK)
Achieved Capacity High Higher
Adherence to Proportionality Tight Loose
Assumptions on Subchannel SNR High None
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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

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Delayed CSI
mobile
t0 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
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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 responsemay reduce how often
  directchannel feedback is provided

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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
  tapsSchafhuber Matz, 2005
• Used adaptive prediction filters

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OFDM Channel Prediction Comparison

• Compared three approaches in unified
  frameworkWong, 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 gt Pilot-subcarrier Time-domain

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High-resolution OFDM Channel Prediction

• Combined channel estimation and predictionWong
  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

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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
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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

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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

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IEEE 802.16e Simulation
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Mean-square Error vs. SNR
Prediction 2 ? ahead
ACRLB Asymptotic Cramer-Rao Lower Bound CRLB
Cramer-Rao Lower Bound
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Mean-square Error vs. Prediction Length
SNR 7.5 dB
ACRLB Asymptotic Cramer-Rao Lower Bound CRLB
Cramer-Rao Lower Bound
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Performance Comparison Summary
L - No. of paths M - No. of rays per path
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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

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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

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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

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Backup
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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,n power in user ks nth assigned subchannel
Hk,n Channel-to-noise ratio in user ks nth assigned subchannel
Nk of subchannels allocated to user k
Pk,tot Total power allocated to user k
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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
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Comparison with Optimal Solution
Back
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Comparison with Max-Min Capacity
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Comparison with Max Sum Capacity
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Summary of Shens 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

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Wongs 4-Step Approach

• Determine number of subcarriers Nk for 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 users
  subcarriers (waterfilling)

O(K)
O(KNlogN)
O(K)
O(N)
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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
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Step 1 of Subcarriers/User
Nk
3
1
?1 3/4
9
?2 1/4
6
5
3
N 4 subchannels K 2 users Ptotal 10
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Step 2 Subcarrier Assignment
Rk
Rtot
log2(12.510)4.70
log2(12.58)4.39
13.3
log2(12.57)4.21
log2(12.59)4.55
4.55
? Nk
3/4 3
1/4 1
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Step 3 Power per user
P1 7.66 P2 2.34
N 4 subchannels K 2 users Ptotal 10
Back
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Step 4 Power per subcarrier

• Waterfilling across subcarriers for each user

P1 7.66 P2 2.34
? Nk
3/4 3
1/4 1
p1,1 2.58 p1,2 2.55 p1,3 2.53 p2,1 2.34

Data Rates R1 log2(1 2.5810) log2(1
2.558) log2(1 2.537)
13.39008 R2 log2(1 2.349) 4.46336
Back
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Pilot-based Transmission

• Comb pilot pattern
• Least-squares channel estimates

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Prediction over all the subcarriers

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

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Prediction over the pilot subcarriers

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

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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

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Simulation Parameters (IEEE 802.16e)
Parameter Value Parameter Value
N 256 Bandwidth 5 MHz
Guard Carriers (7) 0-27 201256 Fcarrier 2600 MHz
Channel Model ETSI Vehicular A Mobile Velocity 75 kmph
Prediction Order 75 Downsampling rate 25 (4fd)
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Prediction Snapshot
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NMSE vs. Channel Estimation Error
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NMSE vs. Prediction Horizon
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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

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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

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Prediction as parameter estimation

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

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Cramer-Rao Lower Bound (CRLB)
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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
Doppler frequency phase cross covariance
Amplitude phase error variance
Doppler frequency error variance
Time-delay phase cross covariance
Time-delay error variance

• 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