Abstract : In this paper, a new tensorial modeling is first proposed for nonlinear multiple-input multiple-output (MIMO) direct sequence spread spectrum communication systems. The channel is modeled as an instantaneous MIMO Volterra system. Then, a direct data approach for joint blind channel estimation and data recovery is developed using the parallel factor (PARAFAC) decomposition of a third-order tensor composed of received signals, exploiting space, time and code diversities. A blind channel estimation method based on the PARAFAC decomposition of a fifth-order tensor composed of covariances of the received signals is also proposed, considering phase shift keying (PSK) modulated transmitted signals. The proposed estimation algorithms are evaluated by simulating a nonlinear uplink MIMO radio over fiber (ROF) communication system.