With the ever increasing interest in multiple-input multiple-output (MIMO) cognitive radio (CR) systems, reducing the costs associated with RF-chains at the radio front end becomes a very important factor. In this paper, we propose two solutions to the problem of joint transmit-receive antenna selection with the objective of maximizing data rates and satisfying interference constraints at the primary user (PU) receiver. In the first method we approximate the original non-convex optimization problem with an iterative way of solving a series of smaller convex problems. Then we present a novel, norm-based transmit receive antenna selection technique that simultaneously improves throughput while maintaining the PU interference constraints. We show that this simple approach yields near optimal results with massive complexity reductions. In addition to making a performance comparison between the proposed approaches and the optimal exhaustive search approach, we establish that antenna selection is a promising option for future MIMO CR devices.