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Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems

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Title: Resource Allocation for Mobile Multiuser Orthogonal Frequency Division Multiplexing Systems


1
Resource Allocation for Mobile Multiuser
Orthogonal Frequency Division Multiplexing Systems
  • Prof. Brian L. Evans
  • Embedded Signal Processing Laboratory
  • Dept. of Electrical and Computer Engineering
  • The University of Texas at Austin
  • July 5, 2006

bevans_at_ece.utexas.edu
Featuring work by PhD students Zukang Shen (now
at TI) and Ian Wong Collaboration 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 prediction
  • Comparison of algorithms
  • High-resolution joint estimation and prediction
  • Multiuser OFDM resource allocation using
    predicted channel state information

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

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

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

. . .
6
Exploiting Multiuser Diversity
  • Downlink multiuser OFDM
  • Users share subchannels and basestation transmit
    power
  • Users only decode their own data

7
Multiuser OFDM Resource Allocation
8
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 prediction
  • Comparison of algorithms
  • High-resolution joint estimation and prediction
  • Multiuser OFDM resource allocation using
    predicted channel state information

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

10
Two-Step Near-Optimal Solution
  • Subchannel allocation step
  • Greedy algorithm allow user with
    least allocated capacity/proportionality to
    choose best 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
11
Lower Complexity Solution
  • In practical scenarios, rough proportionality is
    acceptable
  • Key ideas to simplify Shens 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
    Shens method
  • Achieves higher capacity with lower complexity
    vs. Shens method
  • Maintains acceptable proportionality of user data
    rates

Example
12
Simulation Parameters
13
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
probabilities 0.2, 0.3, 0.5
Wongs Method Shens Method
14
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
15
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.
16
Computational Complexity
22 average improvement
Code developed in floating point C Run on 133
MHz TI TMS320C6701 DSP EVM board
17
Memory Usage
All values are in bytes
18
Performance Comparison Summary
19
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 prediction
  • Comparison of algorithms
  • High-resolution joint estimation and prediction
  • Multiuser OFDM resource allocation using
    predicted channel state information

20
Delayed Channel State Information
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 bits/s/Hz
Channel mismatch Souryal Pickholtz, 2001
21
Prediction of Wireless Channels
  • Use current and previous channel estimates to
    predict future channel response
  • Overcome feedback delay
  • Adaptation based on predicted channel response
  • Reduce amount of feedback
  • Predicted channel response may reduce how often
    direct channel feedback is provided

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

23
OFDM Channel Prediction Comparison
  • Compared three approaches in unified
    framework Wong, Forenza, Heath Evans, 2004
  • Analytical and numerical mean squared error
    comparison
  • All-subcarrier and pilot-subcarrier methods have
    similar mean squared error performance
  • Time-domain prediction performs much better than
    the two other frequency domain prediction methods
  • Complexity comparison
  • All-subcarrier gt Pilot-subcarrier Time-domain

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
    a by-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 of wireless
    channels Jakes 1974
  • Used in ray-tracing channel characterization
    Rappaport 2002

n OFDM symbol index k 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 steps
  • Time-delay estimation
  • Doppler-frequency estimation

28
IEEE 802.16e Simulation
29
Mean-square Error vs. SNR
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
31
Performance Comparison Summary
L - No. of paths M - No. of rays per path
32
MU-OFDM Resource Allocation with Predicted
Channel State Infomation (Future)
  • 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 to enable 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
Embedded Signal Processing Laboratory
  • Director Prof. Brian L. Evans
  • http//www.ece.utexas.edu/bevans/
  • WiMAX (OFDM) related research
  • Algorithms for resource allocation in Multiuser
    OFDM
  • Algorithms for OFDM channel estimation and
    prediction
  • Key collaborators Prof. Jeffrey Andrews and
    Prof. Robert Heath
  • Key graduate students

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

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
Back
40
Comparison with Max-Min Capacity
41
Comparison with Max Sum Capacity
42
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

43
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)
44
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
45
Step 1 of Subcarriers/User
?1 3/4
9
?2 1/4
6
5
3
N 4 subchannels K 2 users Ptotal 10
46
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
47
Step 3 Power per user
P1 7.66 P2 2.34
N 4 subchannels K 2 users Ptotal 10
Back
48
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 2.5810) log2(1
2.558) log2(1 2.537)
13.39008 R2 log2(1 2.349) 4.46336
Back
49
Pilot-based Transmission
  • Comb pilot pattern
  • Least-squares channel estimates

50
Prediction over all the subcarriers
  • Design prediction filter for each of the Nd data
    subcarriers
  • Mean-square error

51
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

52
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

53

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
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

63
Selected Wireless Standards
  • Selected wireless data communication standards.
  • On June 8, 2006, IEEE suspended its 802.20 Mobile
    Broadband Wireless Access standard activities.
  • IEEE 802.20 is intended to operate at carrier
    frequencies below 3.5 GHz
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