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 generalized interference alignment (IA)-based distributed optimization designs for multiple secondary transceivers in the underlay CR case with channel uncertainty under assumption that the actual channel error norm is below a certain bound. One of the designs is an extension to an existing method and the other one is a new design. In these methods, 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 hold the secondary interference on the primary receiver under an acceptable limit that is determined by the primary receiver. Numerical results prove the ability of the proposed methods to support significant secondary rates provided that the PU is protected from extra interference from SUs, even in presence of channel uncertainty.