Interference networks with local view: A distributed optimization approach

In practice, a node in a network learns the channel through local message passing and obtains a local view of the network. Pure wireless message passing as well as mixed wireless and wireline message passing are considered in this paper. We study the distributed optimization of sum-rate for a class of deterministic interference networks with local view. A connection based utility function is designed for each user to exploit the local knowledge. This utility design turns out to be a potential game with sum-rate as the potential function. For the one-to-many channel with 1.5 wireless rounds of message passing, we show that there is a unique Nash equilibrium and using this strategy, the sum capacity can be achieved. We provide a sufficient condition for which a topology does not have unique Nash equilibrium. Then we consider the scenario that the network size and the users IDs are provided to each user. For various mixed wireless and wireline message passing patterns, including wireline at transmitter/receiver side and sequential/concurrent message passing scheduling, we identify whether a three-user interference network can achieve the sum capacity in a distributed fashion. Compared with the 1.5 pure wireless rounds of message passing, the results show that 2.5 mixed wireless and wireline rounds of message passing can significantly improve the system performance of three-user interference networks. We also derive some sufficient conditions for general K-user interference networks such that the sum capacity can not be achieved based on each user's local view.