This work investigates a robust energy-efficient solution for multiple-input-multiple-output (MIMO) transmissions in cognitive vehicular networks. Our goal is to design an optimal MIMO beamforming for secondary users (SUs) considering imperfect interference channel state information (CSI). Specifically, we optimize the energy efficiency (EE) of SUs, given that the transmission power constraint, the robust interference power constraint and the minimum transmission rate are satisfied. To solve the optimization problem, we first characterize the uncertainty of CSI by bounding it in a Frobenius-norm-based region and then equivalently convert the robust interference constraint to a linear matrix inequality. Furthermore, a feasible ascent direction approach is proposed to reduce the optimization problem into a sequential linearly constrained semi-definite program, which leads to a distributed iterative optimization algorithm for deriving the robust and optimal beamforming. The feasibility and convergence of the proposed algorithm is theoretically validated, and the final experimental results are also supplemented to show the strength of the proposed algorithm over some conventional schemes in terms of the achieved EE performance and robustness.
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