In this paper, we consider a full duplex (FD) system using spatial modulation (SM) technique for simultaneous transmission. Despite the recent studies on the combination of these two techniques, nonlinear effects of devices have been ignored. This paper demonstrates, for the first time, the nonlinear power amplifier (PA) effects on a full duplex spatial modulation (FDSM) system. A digital canceller is adopted to deal with the strong selfinterference (SI) in presence of PA nonlinearities. The results are verifying that the considered canceller can suppress SI close to the thermal noise level and has high reliability to ensure the performance of the system.