Information Theory for Mobile Ad-Hoc Networks
(ITMANET): The FLoWS Project
Resource Allocation in Non-fading and Fading
Multiple Access Channel
Ali ParandehGheibi
Joint work with
Atilla Eryilmaz, Asu Ozdaglar, Muriel Medard
Resource Allocation in non-fading and fading multiple access channel
Achievement:
• Fair resource allocation with
arbitrary interference among
transmitters
Resource allocation policies in multiple- access channel for
concave utility function with unknown channel statistics
How it works:
• Existing work on optimal resource
• Gradient projection method with Approximate Projection
allocation policies for wireless
networks are mostly restricted to
specific physical layer models
(CDMA, OFDM, etc) and non-fading
channels.
FDMA
TDMA
• Resource allocation policies for
a multiple access channel
provides insights for efficient
utility maximization for each
group of relays
IMPACT
STATUS QUO
MAC RAC ACHIEVEMENT
• Insight in faster queue-length
based scheduling algorithms
• Greedy Policy vs. Queue-length-based policy
• Information theoretic capacity region vs. Stability region
• Efficient Approximate policies track greedy policy closely
…
s
t1
NEW INSIGHTS
CDMA
• Information theoretic approach to
resource allocation
• Consider capacity region of
multiple-access channel to address
interference among transmitters in
general SNR and INR regimes
• Utility maximization framework to
address fairness and QoS issues in
resource allocation
Assumptions and limitations:.
• Perfect channel state information available at the
transmitters as well as the receiver
NEXT-PHASE GOALS
by taking a single gradient projection iteration per time slot
t2
• Characterize the capacity
region or a large achievable
region for one layer of
transmitters and receivers
• Solve the resource allocation
problem in a distributed manner
by solving the sub-problems
• Optimal scheduling between
layers
• Asynchronous implementation
layer-by-layer transmission: Simpler capacity region characterization and distributed optimization
Resource Allocation in Multiple Access Channel
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•
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Multiple Access Channel: different users share the communication media
MAC challenges
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•
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Limited resources (battery life, Bandwidth/time slots)
Time varying channel
Interference
Fairness:
•
•
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3
•
•
•
FDMA
Utility maximization framework by assigning
values to different allocations
Concave utility function essential to capture
different fairness metrics [Sh’95]
TDMA
CDMA
Main approaches to resource allocation
Communications theory approach
-
No interference cancellation: CDMA [ODW’03], [KH’00]
TDMA [WG’05]
Queuing theory approach
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Queue-length based scheduling and congestion control [ES’05]
Information theoretic approach
-
Weighted sum rate maximization [TH’98]
Contributions
•
•
4
Information theoretic approach to resource allocation to obtain the
fundamental limits of the system
Rate and power allocation policies in two scenarios
1.
Channel statistics are known and users have power control capabilities
–
2.
Channel statistics are unknown and transmission powers are fixed
–
–
–
•
Explicit characterization of optimal rate and power allocation policies
A Greedy rate allocation policy performs closely to the optimal policy
Efficient computation of the greedy policy using the notion of approximate
projection and polymatroid structure of the capacity region of the multiple
access channel
Efficient approximate rate allocation policy to track the greedy policy
Information theory vs. Queuing theory
–
–
Equivalence relation between the information theoretic capacity region and the
stability region
Long-term optimality vs. short term performance
System Model
•
5
Gaussian Multiple Access Channel
where
•
Capacity region of Gaussian multiple access channel
Fixed power
Power control available
Resource Allocation with Known Channel Statistics
•
•
•
Assumption: Channel statistics are known and power control is possible
at the transmitters
Goal: Find feasible rate and power allocation policies such that the
average rate vector maximizes the utility function, and average power
transmission power constraint is satisfied
Assumptions on the utility function (
•
•
•
•
6
Concave
Monotonically increasing
Continuously differentiable
Example: Weighted sum
-fair function
)
Optimal Resource Allocation Policies
•
Linear utility function:
•
The greedy polices by Tse and Hanly [TH’98] are optimal
where
•
•
•
7
is a multiplier which depends on channel state distribution
Uniqueness of the optimal solution,
Closed-form solution for
Nonlinear utility function
•
Given , replace the nonlinear utility
with a linear utility with the same
optimal solution
, for
Optimal Resource Allocation Policies
•
How does the genie work?
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•
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The optimal solution lies on the boundary
Explicit characterization of a one-to-one correspondence between the
points on the boundary and positive unit norm vectors,
Conditional Gradient (Frank-Wolfe) method [B’99]
•
Reduce the nonlinear program to a sequence
of problems with linear objectives
where
8
Queuing Theory vs. Information Theory (Unknown Statistics)
(capacity region) C ≡ Λ (stability region)
•
•
Any achievable rate allocation policy can stabilize the queues
Two rate allocation policies:
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Greedy channel-state-based policy
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Maximize the instantaneous utility
Queue-length-based policy [ES’05]
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Performs arbitrarily closely to the optimal policy
Requires global queue-length information
Low convergence rate when increasing the accuracy
9
Simulation Results
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Limited-time communication session
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Low convergence rate for queue-length based policy
Improvement in performance of the greedy policy for
smaller channel variations
10
Simulation Results cont.
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11
File upload scenario (small traffic bursts)
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Limited file size leads to unfair allocation of the rates by queue-based
policy while emptying the queues
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Improvement in the performance of the queue-based policy by
increasing the file size
Average achieved rate for greedy and
queue-based policies as a function of
completion time
( Rg ) i 
fi
Ti
( Rq )i 
fi
Tˆi
Future Work
12
•
Improve upon the greedy policy by using the queue-length information in a
more efficient manner
•
Resource allocation for Gaussian broadcast channel using duality between
multiple access and broadcast channels
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Resource allocation for a multi-hop wireless network
– Layer-by-layer transmission to limit interference effects
s
…
t1
t2
– Distributed algorithm by reducing the main resource allocation problem to
sub-problems in each layer
– Model each layer as MAC, broadcast and interference channels to
characterize the largest tractable achievable region
– Optimal scheduling between layers