Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project

Resource Allocation in Non-fading and Fading Multiple Access Channel

Ali ParandehGheibiJoint work with

Atilla Eryilmaz, Asu Ozdaglar, Muriel Medard

•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

• Fair resource allocation with arbitrary interference among transmitters

• Resource allocation policies for a multiple access channel provides insights for efficient utility maximization for each group of relays

• Insight in faster queue-length based scheduling algorithms

Resource Allocation in non-fading and fading multiple access channel

layer-by-layer transmission: Simpler capacity region characterization and distributed optimization

Achievement:Resource allocation policies in multiple- access channel for

concave utility function with unknown channel statistics

How it works: •Gradient projection method with Approximate Projection

•Greedy Policy vs. Queue-length-based policy

•Information theoretic capacity region vs. Stability region

•Efficient Approximate policies track greedy policy closely by taking a single gradient projection iteration per time slot

Assumptions and limitations:.

•Perfect channel state information available at the transmitters as well as the receiver

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• Existing work on optimal resource allocation policies for wireless networks are mostly restricted to specific physical layer models (CDMA, OFDM, etc) and non-fading channels.

• 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

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CDMA

TDMA

FDMA

• Fairness:

• Utility maximization framework by assigning values to different allocations

• Concave utility function essential to capture different fairness metrics [Sh’95]

Resource Allocation in Multiple Access Channel

• Main approaches to resource allocation• Communications theory approach

- No interference cancellation: CDMA [ODW’03], [KH’00]

- TDMA [WG’05]

• Queuing theory approach- Queue-length based scheduling and congestion control [ES’05]

• Information theoretic approach- Weighted sum rate maximization [TH’98]

TDMA

FDMA

CDMA

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• Multiple Access Channel: different users share the communication media

• MAC challenges• Limited resources (battery life, Bandwidth/time slots)

• Time varying channel

• Interference

Contributions

• 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

– Explicit characterization of optimal rate and power allocation policies

2. Channel statistics are unknown and transmission powers are fixed

– 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

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System Model

• Gaussian Multiple Access Channel

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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 ( )

• Concave

• Monotonically increasing

• Continuously differentiable

• Example: Weighted sum -fair function

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Optimal Resource Allocation Policies

• Linear utility function:

• The greedy polices by Tse and Hanly [TH’98] are optimal

where is a multiplier which depends on channel state distribution

• Uniqueness of the optimal solution, , for

• Closed-form solution for

• Nonlinear utility function

• Given , replace the nonlinear utilitywith a linear utility with the same optimal solution

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Optimal Resource Allocation Policies

• How does the genie work?

• 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

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Queuing Theory vs. Information Theory (Unknown Statistics) 9

(capacity region) C ≡ Λ (stability region)

• Any achievable rate allocation policy can stabilize the queues

• Two rate allocation policies:

• Greedy channel-state-based policy

- Maximize the instantaneous utility

• Queue-length-based policy [ES’05]

- Performs arbitrarily closely to the optimal policy

- Requires global queue-length information

- Low convergence rate when increasing the accuracy

Simulation Results10

• Limited-time communication session

- Low convergence rate for queue-length based policy

- Improvement in performance of the greedy policy for smaller channel variations

Simulation Results cont.11

• File upload scenario (small traffic bursts)

- Limited file size leads to unfair allocation of the rates by queue-based policy while emptying the queues

- Improvement in the performance of the queue-based policy by increasing the file size

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Average achieved rate for greedy and queue-based policies as a function of completion time

Future Work

• 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

• Resource allocation for a multi-hop wireless network– Layer-by-layer transmission to limit interference effects

– 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

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