Asynchronous Iterative Waterfilling for Gaussian Frequency-Selective Interference Channels: A Unified Framework

In this paper we give an overview of recent results on the rate maximization game in the Gaussian frequency-selective interference channel. We focus on the competitive maximization of information rates, subject to global power and spectral mask constraints. To achieve the so-called Nash equilibrium points of the game Yu, Ginis and Cioffl proposed the sequential Iterative Waterfilling Algorithm (IWFA), where, at each iteration, the users choose, one after the other, their power allocation to maximize their own information rate, treating the interference generated by the others as additive colored Gaussian noise. To overcome the potential slow convergence of the sequential update, specially when the number of users is large, the simultaneous IWFA was proposed by the authors, where, at each iteration, all the users update their power allocations simultaneously, rather than sequentially. Recently, the authors showed that both the sequential and the simultaneous IWFAs are just special cases of a more general unified framework, given by the totally asynchronous IWFA. In this more general algorithm, the users update their power spectral density in a completely distributed and asynchronous way. Furthermore, the asynchronous setup includes another form of lack of synchronism where the transmission by the different users contains time and frequency synchronization offsets. A unified set of convergence conditions were provided for the whole class of algorithms obtained from the asynchronous IWFA. Interestingly, there is a key result used in the proof of convergence of the algorithms: an alternative interpretation of the waterfilling operator as a projector.