Underlay cognitive radio (CR) permits unlicensed secondary users (SUs) to transmit their own data over the licensed spectrum unless the interference from the SUs on the licensed primary user (PU) exceeds an acceptable level. This paper proposes two interference alignment (IA)-based distributed optimization designs for multiple secondary transceivers in underlay cognitive radio case with channel uncertainty. The precoding and power allocation matrices for each SU are either independently or jointly optimized for imperfect channel knowledge to maximize the secondary rates and to control the secondary interference on the primary receiver to be below the acceptable limit that is determined by the primary receiver. Numerical results prove the ability of the proposed methods to support significant secondary rates and to protect the PU from extra interference, within the acceptable primary range, even in presence of channel uncertainty case. In addition, joint optimization design has higher secondary performance than the independent optimization design.