In this paper, we develop the statistical delay quality-of-service (QoS) provisioning framework for the energy-efficient spectrum sharing\nbased wireless ad hoc sensor network (WAHSN), which is characterized by the delay-bound violation probability. Based on\nthe established delay QoS provisioning framework, we formulate the nonconvex optimization problem which aims at maximizing\nthe average energy efficiency of the sensor node in the WAHSN while meeting PU�s statistical delay QoS requirement as well\nas satisfying sensor node�s average transmission rate, average transmitting power, and peak transmitting power constraints. By\nemploying the theories of fractional programming, convex hull, and probabilistic transmission, we convert the original fractional structured\nnonconvex problem to the additively structured parametric convex problem and obtain the optimal power allocation\nstrategy under the given parameter via Lagrangian method. Finally, we derive the optimal average energy efficiency and\ncorresponding optimal power allocation scheme by employing the Dinkelbach method. Simulation results show that our derived\noptimal power allocation strategy can be dynamically adjusted based on PU�s delay QoS requirement as well as the channel\nconditions. The impact of PU�s delay QoS requirement on sensor node�s energy efficiency is also illustrated.
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