Impact of power control on the performance of ad hoc wireless networks

An ad hoc wireless network with n nodes and m source-destination pairs, using a scheduling based medium access control (MAC) protocol such as time division multiple access (TDMA), and a routing mechanism that may be unicast or multicast based, is considered. Under a given nodal transmit power vector, we define the source-destination throughput vector to be achievable if there exists an associated temporal (based on the channel sharing MAC protocol) and spatial (based on the underlying routing mechanism) joint scheduling-routing scheme that yields the throughput vector. In this paper, we analyze and investigate the effect of nodal transmit power vector on the maximum (or supreme) level of a general (real-valued) function of the source-destination throughput levels. We represent the latter supreme level attained under power vector. We also derive a linear programming (LP) formulation for obtaining the exact solution to the optimization problem that yields the throughput capacity of finite ad hoc wireless networks. Our LP based performance evaluation results identify the magnitude of capacity upgrade that can be realized for networks with random topologies and traffic patterns.