Incorporating the effect of residual self-interference, the spectral efficiency (SE) of full-duplex relay channel is analyzed for different relay schemes. The optimal relay power and the corresponding optimal SE have been derived in closed form for decode-forward, compress-forward, and amplify-forward (AF) schemes. In particular, backward decoding is introduced to the AF scheme in the presence of self-interference and it is shown to outperform forward decoding for high relay-destination SNR. Based on the obtained SE, bounds on the relay energy efficiency (REE) are also established. It evaluates how much the cooperation gain can be obtained from unit relay power consumption. We show that time sharing can improve the REE of AF scheme.