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In this work, we investigate the properties of energy-efficiency (EE) and spectrum-efficiency (SE) for video streaming over mobile ad hoc networks by developing an energy-spectrum-aware scheduling (ESAS) scheme. To describe a practical mobile scenario, we use a random walk mobility model, in which each node can choose its mobility direction and velocity randomly and independently. Through rigorous analysis and extensive simulations, we demonstrate that the node mobility is beneficial to EE but not to SE. The contributions of this work are twofold: 1) We propose an ESAS scheme with a dynamic transmission range, which significantly outperforms the previous minimum-distortion video scheduling in terms of joint EE and SE performance; 2) We derive an achievable EE-SE tradeoff range and a tight upper/lower bound with respect to energy-spectrum efficiency index for various node velocities. We believe that this work helps to shed insights on the fundamental design guidelines on building an energy and spectrum efficient mobile video transmission system.