Congestion & power control of wireless multihop networks over stochastic LTF channels

Network Utility Maximization (NUM) is often applied for the cross-layer design and optimization of wireless networks. In most approaches, the NUM framework is based on the assumption of known or ideal wireless channel conditions. However, realistic wireless channel capacities are stochastic (time-varying and random) bearing time-varying statistics, necessitating the redesign and solution of NUM problems to capture such effects. In this paper, we apply the NUM framework to perform congestion and power control in wireless multihop networks while taking into account the stochastic Long Term Fading (LTF) wireless channels. Specifically, the wireless channel power loss is modeled via the use of Stochastic Differential Equations (SDEs) alleviating several assumptions that exist in state of the art channel modeling within the NUM framework such as the finite number of channel states or the stationarity. Based on that, we initially propose an algorithm for performing congestion control under stochastic LTF wireless channels. Next, the proposed algorithm is enhanced via power control aiming to further increase users´ optimal utility by exploiting the random reductions of the stochastic channel power loss while also considering energy efficiency. Finally, numerical results are presented to evaluate the performance and operation of the proposed approach.