In this paper, we study how to determine concurrent transmissions and the transmission power level of each link to maximize spectrum efficiency and minimize energy consumption in a wireless ad hoc network. The optimal joint transmission packet scheduling and power control strategy are determined when the node density goes to infinity and the network area is unbounded. Based on the asymptotic analysis, we determine the fundamental capacity limits of a wireless network, subject to an energy consumption constraint. We propose a scheduling and transmission power control mechanism to approach the optimal solution to maximize spectrum and energy efficiencies in a practical network. The distributed implementation of the proposed scheduling and transmission power control scheme is presented based on our MAC framework proposed in . Simulation results demonstrate that the proposed scheme achieves 40% higher throughput than existing schemes. Also, the energy consumption using the proposed scheme is about 20% of the energy consumed using existing power saving MAC protocols.