​We study the secondary sum-rate of an underlay cognitive multiple access channel consisting of a primary user and multiple secondary users (SUs) communicating with a common destination. We propose a particular linear precoding and SU selection scheme that maximize the cognitive sum-rate. This scheme is based on space alignment strategy allowing SUs to share the spectrum without interfering with each other. We derive the optimal power allocation for each selected SU after applying perfect or imperfect successive interference cancellation. Numerical results show that the proposed scheme provides a significant sum-rate improvement as the number of SUs increases. In addition, it achieves almost the same performance as an exhaustive search selection, mainly in low and high power ranges.