Adaptive Resource Allocation in Multiuser OFDM Systems

1
Adaptive Resource Allocationin Multiuser OFDM
Systems

• Liang Chen, Brian Krongold and Jamie Evans

2
Outline

• Introduction to OFDM
• Resource Allocation in OFDM
• System Model Problem Formulation
• Convex Approach
• Combinatorial Approach
• Simulation Results
• Conclusions

3
Orthogonal Frequency Division Multiplexing (OFDM)

• Multicarrier transmission
• Bandwidth divided into a number of subchannels
• From frequency-selective fading in channel level
  to flat fading in subchannel level
• Special case of FDM

4
Orthogonal Frequency Division Multiplexing (OFDM)

• Overlapped subchannel spectrum
• FDM
• OFDM

5
Orthogonal Frequency Division Multiplexing (OFDM)

• Orthogonal tones
• Orthogonal sine waves
• for
  over

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OFDM Spectrum

• Subchannel orthogonality
• Rectangular impulse sinc function

NO ICI
1
2
3
4
5
7
Multicarrier Transmitter

• Data rate reduced by the factor of N
• Symbol period increased by the factor of N
• Symbol period gt Expected delay spread

S / P
Reduce ISI
8
Advantages of OFDM

• Superior in spectral efficiency
• Overlapped subchannel spectrum
• Superior in mitigation of Inter-Symbol
  Interference (ISI)
• Longer symbol period
• Superior in mitigation of Inter-Channel
  Interference (ICI)
• Orthogonal tones

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Outline

• Introduction to OFDM
• Resource Allocation in OFDM
• System Model Problem Formulation
• Convex Approach
• Combinatorial Approach
• Simulation Results
• Conclusions

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Resource Allocation

• Single user
• Multiuser

• Predetermined Bandwidth/Timeslot allocation
• Optimal bit loading

• Predetermined Bandwidth/Timeslot allocation
• Optimal bit loading

FDMA
TDMA
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Adaptive Resource Allocation

• Independent fading
• Orthogonal Frequency-Division Multiple-Access
  (OFDMA), dynamically allocates
• Bandwidth
• Power
• Bits

Multiuser diversity gain
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System Model

• Our OFDMA system is defined as
• Available band is divided into N independent AWGN
  subchannels, which are smaller than Channel
  Coherence Bandwidth (flat fading)
• Each user is assigned a set of the subchannels by
  adaptive allocation
• Each subchannel is assigned exclusively to one
  user
• Transmitter has full knowledge of instantaneous
  channel characteristics.

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Mathematical Model
Total Transmit Power

• Power minimization
• Capacity maximization (dual)

Total Rate Requirement
Subject to 1.
2. for all
, if , then
Exclusive Assignment
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Multiuser Water-filling

• Giving subchannel to its best user
• Limitations of Multiuser water-filling
• Does not ensure faireness among users
• Does not support different QoS requirements

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Mathematical Model

• We formulate the problem as

Total Transmit Power
Individual Rate Requirement
Exclusive Assignment
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Convex Approach

• Original problem is non-convex, NP-complete
• Objective function is convex
• Exclusive subchannel assignment
• Combinatorial Solution Space with size
• Sharing subchannel

Convex
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Convex Approach

• Cost Function
• Iterative Search to find the right set Wong
  et al
• Large , converge fast, limited
  performance
• Small , close-to-optimal solution, very
  slow

Which user gets it
Whats the rate on it
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Limitations of Convex Approach
not practical

• Computationally intensive
• Unsmooth convergence

no partial result
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Combinatorial Approach - Heuristic Decomposition

• Bandwidth allocation
• Number of subchannels each user is allocated
• Subchannel assignment
• Which subchannel goes to which user
• Optimal bit loading

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Bandwidth Allocation

• Instantaneous capacity based
• Maximize capacity when traffic load is very low /
  small
• High outage probability, otherwise
• Instantaneous rate based

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Bandwidth Allocation

• Bandwidth Assignment Based on SNR (BABS) Kivanc
  et al

• User experiences flat fading

• Start with min. No. of subchannel that could meet
  rate requirement, Sk ceil(Rk / Rmax)

• Assign one subchannel a time, giving it to user
  with most potential power reduction

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Subchannel Assignment

• Non-convex, Combinatorial problem
• Cost-scaling bipartition matching
• Hungarian Method for standard assignment
• Assume Flat Transmit Power
• Extend each user into Sk identical users
• N subchannels, N users

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Subchannel Assignment

• Amplitude Craving Greedy (ACG)
• when user k had Sk subchannels, bound the user
• Sub-optimal solution is unstable

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Subchannel Assignment
1
1
2
1
2
1
2
2

• Greedy search
• Start with best overall subchannel
• When user k had Sk subchannels, bound that user
• Performance loss 10

Sub.
User
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Subchannel Oriented Search

• Find Best User on each subchannel
• Allocate one each time, start from overall best
  subchannel
• Once user k has Sk Subchannels, Update the
  remaining best user list

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Subchannel Oriented Search
1
1
2
1
2
1
2
2
User
Sub.
5
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Complexity Analysis of SOS

• Find the best user
• Sorting the best user list
• Update the best user list
• At most K times
• Total complexity

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Add/Drop Subchannel

• Branch and Bound

Global Optimal
Local Optimal
Local Optimal
Local Optimal
Local Optimal
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Add/Drop Subchannel

• Giving extra subchannel to user with highest
  power per bit helps to reduce the total power
• Update the average user gain to
• Update the approximate power accordingly
• Adding/Dropping subchannel
• adjust to further reduce the power

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Simulation Result for AverSNR
PO w/o I
Total Transmit Power
BABSACG
BABSSOS

• AverSNR
• BABS
• SOS
• Add/Drop Sub.

AverSNR
Number of Users
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Limitations of AverSNR

• Adjust on a individual subchannel-to-subcha
  nnel basis
• Add/Drop subchannels is time consuming
• For each adding / dropping operation
• evaluations of
• evaluations of
• comparisons of
• Average user gain is calculated over all
  frequency band / subchannels

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Iterative AverSNR method (IterSNR)

• Average user gain calculation
• Over smaller but well-selected set
• Adjust on a user-to-user basis
• Update average user gain,
• Feed back to Bandwidth Allocation
• Use as the input of Subchannel Assignment
• Each iteration

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IterSNR Algorithm Flowchart
Average User SNR
Initial Setting
Bandwidth Allocation
Calculate User Gain
No. of Subchannels Required for Each User
Feedback Subchannel Allocation Information
Subchannel Allocation
Subchannel Allocation Information
Yes
Power Consumption
No
Optimal Bit Loading
Less Power?
Done
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Simulation Result for IterSNR
PO w/o I
Total Transmit Power
BABSACG
BABSSOS
IterSNR
Number of Users
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Contributions

• Liang Chen, Brian Krongold and Jamie Evans, An
  Adaptive Resource Allocation Algorithm for
  Multiuser OFDM, in Proc. AusCTW06, Perth, pp.
  141-145.
• --(Best Student Paper Award)
• Liang Chen, Brian Krongold and Jamie Evans, A
  Computational-Efficient Adaptive Resource
  Allocation Algorithm for Multiuser OFDM, to
  appear in Proc. of European Wireless 2006, April
  2006, Athens, Greece.

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Conclusions

• Resource Allocation Problem
• SOS, AverSNR, IterSNR
• Minimize total transmit power usage
• Fast sub-optimal solution
• Ensure fairness among user
• Guarantee improvement through iteration
• Complexity SOS lt IterSNR lt AverSNR
• Performance SOS lt IterSNR lt AverSNR

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Cyclic Prefix

• Maintain Orthogonality
• Eliminate ISI

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OFDMA System Configuration
Subchannel conditions
Combined Subchannel, bit power allocation
algorithm
User 1, R1
Adaptive modulator 1
Allocation scheme
User 2, R2
Add cyclic prefix
Adaptive modulator 2
IFFT
User k, RK
Adaptive modulator N
fading channel
Adaptive demodulator N
User k, RK
Extract bits
Remove cyclic prefix
FFT
Adaptive demodulator 2
User 2, R2
User 1, R1
Adaptive demodulator 1
Bit, power and subchannel allocation information
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Separated Allocation
Equal Power Spectrum Density

• Subchannel Allocation

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Typical OFDM System Parameters