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 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

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 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]

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

Gaussian Multiple Access Channel 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 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

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

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

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

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

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

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