1. 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

2. Resource Allocation in non-fading and fading multiple access channel
IMPACT
NEXT-PHASE GOALS
MAC RAC ACHIEVEMENT
STATUS QUO
NEW INSIGHTS
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.
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
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 … s t1 t2
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
FDMA
TDMA
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
CDMA
layer-by-layer transmission: Simpler capacity region characterization and distributed optimization

3. Resource Allocation in Multiple Access Channel3
Multiple Access Channel: different users share the communication media
MAC challenges
Limited resources (battery life, Bandwidth/time slots)
Time varying channel
Interference
TDMA
FDMA
CDMA
Fairness:
Utility maximization framework by assigning values to different allocations
Concave utility function essential to capture different fairness metrics [Sh’95]
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]

4. Rate and power allocation policies in two scenarios
Contributions 4
Information theoretic approach to resource allocation to obtain the fundamental limits of the system
Rate and power allocation policies in two scenarios
Channel statistics are known and users have power control capabilities
Explicit characterization of optimal rate and power allocation policies
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

5. Gaussian Multiple Access Channel
System Model 5
Gaussian Multiple Access Channel
where
Capacity region of Gaussian multiple access channel
Fixed power Power control available

6. Resource Allocation with Known Channel Statistics6
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

7. Optimal Resource Allocation Policies7
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 utility
with a linear utility with the same
optimal solution

8. Optimal Resource Allocation Policies8
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

9. 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

10. Limited-time communication session
Simulation Results 10
Limited-time communication session
Low convergence rate for queue-length based policy
Improvement in performance of the greedy policy for smaller channel variations

11. 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
Average achieved rate for greedy and queue-based policies as a function of completion time

12. Resource allocation for a multi-hop wireless network
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
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 … s t1 t2