With the overwhelming demand for wireless devices, cognitive radios (CRs) have been envisioned to be applied in the vehicular communications in the near future. In the moving vehicular scenario, reliable detection of the primary user and the interference‐aware power allocation to the vehicular secondary users (VSUs) are amongst the main challenging issues in CR. So, this paper proposes techniques to evaluate the false alarm probability and detection probability on the basis of the spatial correlation among the vehicular users in a soft decision fusion‐based CR vehicular ad hoc network. Further, an attempt has been made to optimize the power allocation to the VSUs. The energy efficiency maximization problem is formulated under the constraints of maximum transmission power limit, interference to the primary receiver and the minimum achievable data rate. For the nonlinear and nonconvex optimization problem to be solved, the parametric transformation is used. The power allocation to the VSUs satisfying the nonlinear constraints is solved by our proposed adaptive scheme on the basis of normalized least mean square algorithm. The relevant simulation results provided show the efficacy of our proposed scheme, and the effect of different network parameters is also studied.