In this paper, we investigate the sensing-throughput tradeoff in multi-antenna cognitive radio (CR) systems. Specifically, we optimize the sensing threshold, sensing time, and transmit power of a multi-input multi-output (MIMO) CR system for maximization of the opportunistic system throughput under transmit power, probability of false alarm, and probability of missed detection constraints. To ... [Show full abstract] this end, we propose a new transmission protocol which allows the CR user to simultaneously perform data transmission and spectrum sensing on different spatial subchannels. We formulate non-convex optimization problems for the optimal choice of the sensing threshold, sensing times, and transmit powers in each spatial subchannel for both single-band and multi-band MIMO CR systems. Since finding the global optimal solution of these problems entails a very high complexity, we develop two iterative algorithms that are based on the concept of alternating optimization and solve only convex subproblems in each iteration. Thus, the complexity of these algorithms is low, and we prove their convergence to a fixed point analytically. Simulation results show that the developed algorithms closely approach the global optimal performance and achieve significant performance gains compared to baseline schemes employing equal powers or equal sensing times in all subchannels.