Distributed Non-Autonomous Power Control through Distributed Convex Optimization

Abstract

We consider the uplink power control problem where mobile users in different cells are communicating with their base stations. We formulate the power control problem as the minimization of a sum of convex functions. Each component function depends on the channel coefficients from all the mobile users to a specific base station and is assumed to be known only to that base station (only CSIR). We then view the power control problem as a distributed optimization problem that is to be solved by the base stations and propose convergent, distributed and iterative power control algorithms. These algorithms require each base station to communicate with the base stations in its neighboring cells in each iteration and are hence nonautonomous. Since the base stations are connected through a wired backbone the communication overhead is not an issue. The convergence of the algorithms is shown theoretically and also verified through numerical simulations.

Distributed Bregman-Distance Algorithms for Min-Max Optimization

“…We will keep our discussion brief and refer the readers to [12] for a general discussion on the power allocation problem. We will be using the formulation discussed in [30]. There are m mobile users (MU) in neighboring cells communicating with their respective base stations (BS) using a common wireless channel.…”

Distributed Newton Methods for Strictly Convex Consensus Optimization Problems in Multi-Agent Networks

“…Since each f p is a strictly convex function, both the Hessian matrix H k and its inverse H −1 k are positive definite and block-diagonal for all k. In addition, the matrix A has full row rank as shown in (13). Therefore, the product AH −1 k A is real and symmetric.…”

“…This method makes some improvements in convergence rate over distributed subgradient methods. Compared with conventional centralized methods, the distributed methods have faster computing efficiency and have been widely used in many fields, such as image processing [9,10], computer vision [11], intelligent power grids [12,13], machine learning [14,15], unrelated parallel machine scheduling problems [16], model predictive control (MPC) problems [17], and resource allocation problems in multi-agent communication networks [18,19].…”

Distributed min-max optimization in networks

“…Consider the algorithm as given in (9)-(10). Then, using the notation in (14) and utilizing the non-expansiveness property of the projection operator [10], Proposition 2.2.1, page 88, we have for any z * ∈ X * × {η * }, any k ≥ 0 and i ∈ V ,…”

“…Due to the space limitation we will keep our discussion brief and refer the readers to [13] for a general discussion on the power allocation problem. We will be using the formulation discussed in [14]. There are m mobile users (MU) in neighboring cells communicating with their respective base stations (BS) using a common wireless channel.…”