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

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

3. FDMA TDMA CDMA Resource Allocation in Multiple Access Channel 3 • Multiple Access Channel: different users share the communication media • MAC challenges • Limited resources (battery life, Bandwidth/time slots) • Time varying channel • Interference • 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. 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. 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 Statistics 6 • 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 Policies 7 • 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 Policies 8 • 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. 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. t1 … s t2 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