Dynamic robust games in MIMO systems

In this paper, we study dynamic robust power-allocation games in multiple-input-multiple-output systems under the imperfectness of the channel-state information at the transmitters. Using a robust pseudopotential-game approach, we show the existence of robust solutions in both discrete and continuous action spaces under suitable conditions. Considering the imperfectness in terms of the payoff measurement at the transmitters, we propose a COmbined fully DIstributed Payoff and Strategy Reinforcement Learning (CODIPAS-RL) in which each transmitter learns its payoff function, as well as the associated optimal covariance matrix strategies. Under the heterogeneous CODIPAS-RL, the transmitters can use different learning patterns (heterogeneous learning) and different learning rates. We provide sufficient conditions for the almost-sure convergence of the heterogeneous learning to ordinary differential equations. Extensions of the CODIPAS-RL to It's stochastic differential equations are discussed.