In this letter, we propose an efficient mix source separation algorithm for collision resolution in radio frequency identification (RFID) systems equipped with an antenna array at the reader. We first introduce an approach that exploits the zero constant modulus (ZCM) criterion to separate colliding tags through gradient descent, without using pilot symbols. We show that the ZCM characteristic, considered alone, in the design of the objective function can lead to significant ambiguities in the determination of the beamformers used in the recovery of tag messages. To address this limitation, we propose a more sophisticated approach, relying on a hybrid objective function, incorporating a new ambiguity-raising criterion in addition to the ZCM criterion.