Distributed Learning Policies for Power Allocation in Multiple Access Channels

We analyze the problem of distributed power allocation for orthogonal multiple access channels by considering a continuous non-cooperative game whose strategy space represents the users' distribution of transmission power over the network's channels. When the channels are static, we find that this game admits an exact potential function and this allows us to show that it has a unique equilibrium almost surely. Furthermore, using the game's potential property, we derive a modified version of the replicator dynamics of evolutionary game theory which applies to this continuous game, and we show that if the network's users employ a distributed learning scheme based on these dynamics, then they converge to equilibrium exponentially quickly. On the other hand, a major challenge occurs if the channels do not remain static but fluctuate stochastically over time, following a stationary ergodic process. In that case, the associated ergodic game still admits a unique equilibrium, but the learning analysis becomes much more complicated because the replicator dynamics are no longer deterministic. Nonetheless, by employing results from the theory of stochastic approximation, we show that users still converge to the game's unique equilibrium. Our analysis hinges on a game-theoretical result which is of independent interest: in finite player games which admit a (possibly nonlinear) convex potential function, the replicator dynamics (suitably modified to account for nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more material and figures for the case of stochastically fluctuating channels. This version will appear in the IEEE Journal on Selected Areas in Communication, Special Issue on Game Theory in Wireless Communication

Message passing resource allocation for the uplink of multicarrier systems

We propose a novel distributed resource allocation scheme for the up-link of a cellular multi-carrier system based on the message passing (MP) algorithm. In the proposed approach each transmitter iteratively sends and receives information messages to/from the base station with the goal of achieving an optimal resource allocation strategy. The exchanged messages are the solution of small distributed allocation problems. To reduce the computational load, the MP problems at the terminals follow a dynamic programming formulation. The advantage of the proposed scheme is that it distributes the computational effort among all the transmitters in the cell and it does not require the presence of a central controller that takes all the decisions. Numerical results show that the proposed approach is an excellent solution to the resource allocation problem for cellular multi-carrier systems.Comment: 6 pages, 4 figure

Radio resource allocation for multicarrier-low density spreading multiple access

Multicarrier-low density spreading multiple access (MC-LDSMA) is a promising multiple access technique that enables near optimum multiuser detection. In MC-LDSMA, each user’s symbol spread on a small set of subcarriers, and each subcarrier is shared by multiple users. The unique structure of MC-LDSMA makes the radio resource allocation more challenging comparing to some well-known multiple access techniques. In this paper, we study the radio resource allocation for single-cell MC-LDSMA system. Firstly, we consider the single-user case, and derive the optimal power allocation and subcarriers partitioning schemes. Then, by capitalizing on the optimal power allocation of the Gaussian multiple access channel, we provide an optimal solution for MC-LDSMA that maximizes the users’ weighted sum-rate under relaxed constraints. Due to the prohibitive complexity of the optimal solution, suboptimal algorithms are proposed based on the guidelines inferred by the optimal solution. The performance of the proposed algorithms and the effect of subcarrier loading and spreading are evaluated through Monte Carlo simulations. Numerical results show that the proposed algorithms significantly outperform conventional static resource allocation, and MC-LDSMA can improve the system performance in terms of spectral efficiency and fairness in comparison with OFDMA