The increased interest in full-duplex communication combined with spectrum utilization enhancements stemming from cognitive radio motivate research activities in full-duplex cognitive radio. Energy detection is among the simplest and most practical methods for spectrum sensing in cognitive radio networks. Energy detection spectrum sensing in full-duplex cognitive radio has been addressed in the literature; however, either due to the lack of experimental verification or for the sake of mathematical simplicity, the residual self-interference (RSI) signal has been conventionally considered as a zero-mean Gaussian signal. In this paper, we establish for the first time an accurate (realistic) mathematical framework and performance analysis for energy detection spectrum sensing in full-duplex cognitive radio under the presence of RSI signal exhibiting Rician statistical nature, as recently proven experimentally. The performance analysis results are derived in the presence of RSI after passive self-interference cancellation (SIC) scenario and after combining passive SIC with active SIC using active analog and digital cancellation (ACDC). Exact expressions for the probabilities of detection and false alarm are derived for the considered RSI cancellation scenarios and verified through simulations. The results show that the previously used conventional zero-mean Gaussian self-interference model was producing pessimistic (lower bound) performance estimates.