Joint routing and topology formation in multihop UWB networks

This paper addresses the throughput optimization problem in multihop ultra-wideband (UWB) networks by jointly considering network topology formation and routing. Given a spatial distribution of UWB devices and traffic requirement, we want to form piconets and select paths to maximize the network throughput. Although there have been several works considering the problem of selecting paths to achieve the optimal throughput in multihop wireless networks, to the best of our knowledge, none of them takes the topology formation into the consideration. In this paper, we use Boolean matrices to model role assignment in UWB networks and formulate the throughput optimization problem as a nonlinear programming (NLP) problem. Since the throughput optimization problem is NP-hard, we give an upper bound of the optimal throughput by relaxing some constraints and using pseudo-Boolean optimization to linearize the NLP. We prove that the solution of the upper bound is at most three times of the optimal throughput. Based on the topology formed by solving the upper bound, we formulate a lower bound of the optimal throughput as a linear programming problem and use column generation to solve the lower bound. Numerical results show that the lower bound is very close to the upper bound. Simulation results demonstrate the effectiveness of the scheme.