In this paper, an energy efficient cognitive radio system is proposed. The proposed design optimizes the secondary user transmission power and the sensing duration combined with soft-sensing information to minimize the energy per goodbit. Due to the non-convex nature of the problem we prove its pseudo-convexity to guarantee the optimal solution.
Furthermore, a quantization scheme, that discretize the soft-sensing information, is proposed and analyzed to reduce the overload of the continuously adapted power. Numerical results show that the energy per goodbit performance of the proposed system outperforms the benchmark systems. The impact of the quantization levels and other system parameters is evaluated in the numerical results.