Distributed Nonconvex Power Control using Gibbs Sampling

Transmit power control in wireless networks has long been recognized as an effective mechanism to mitigate co-channel interference. Due to the highly non-convex nature, optimal power control is known to be difficult to achieve if a system utility is to be maximized. In our earlier paper , we have proposed a centralized optimal power control algorithm that obtains the global optimal solution for both concave and non-concave system utility functions. A question remained unanswered is whether such global optimal solution can be achieved in a distributed manner. This paper addresses the question by developing a Gibbs Sampling based Asynchronous distributed power control algorithm (referred to as GLAD). The proposed algorithm quickly converges to the global optimal solution regardless of the concavity, differentiability and monotonicity of the utility function. To further enhance the practicality of the algorithm, this paper proposes two variants of the GLAD algorithm, namely I-GLAD and NI-GLAD, to reduce message passing in two dimensions of communication complexity, i.e., time and space. In particular, I-GLAD, where the prefix "I" stands for Infrequent message passing, reduces the "time overhead" of message passing. The convergence of I-GLAD can be proved regardless of the reduction in the message passing rate. Meanwhile, NI-GLAD, where the prefix "N" stands for Neighborhood message passing, restricts the computation overhead related to message passing to a small neighborhood space. Our results show that the optimality of the solution obtained by NI-GLAD depends on the selection of the neighborhood size.