Section: New Results

Wireless networks

Power and energy considerations in wireless networks have brought to the forefront the need for efficient power allocation and handover policies.

In [13] , we analyze the power allocation problem for orthogonal multiple access channels by means of a non-cooperative potential game in which each user distributes his power over the channels available to him. When the channels are static, we show that this game possesses a unique optimum point; moreover, if the network's users follow a distributed learning scheme based on the replicator dynamics of evolutionary game theory, then they converge to this optimum exponentially fast.

On the other hand, in case the network users have access to multiple-antenna technologies (as most smarphone users do nowadays, we also analyze the problem of finding the optimal signal covariance matrix for MIMO multiple access channels by using an approach based on "exponential learning" – a novel optimization method which applies more generally to (quasi-)convex problems defined over sets of positive-definite matrices (with or without trace constraints) [24] . Furthermore, by using a Riemannian-geometric approach, we devise a distributed optimization algorithm which converges to the optimum signal distribution exponentially fast: users attain an $ϵ$-neighborhood of the system's optimum configuration in time which is at most $𝒪(log(1/ϵ\left)\right)$ (and, in practice, within only a few iterations, even for large numbers of users) [25] .

In the context of heterogeneous wireless networks where vertical handovers are allowed, we also studied a control problem for a new joint admission and resource allocation controller. To account for multi-objective optimization, we considered the maximization of an objective subject to a set of constraints, and we turned this constrained problem into an unconstrained one that we solved numerically using the Semi-Markovian Decision Process (SMDP) framework [19] .