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This paper addresses the design issues of the multiantenna-based cognitive radio (CR) system that is able to concurrently operate with the licensed primary-radio (PR) system. We propose a practical CR transmission strategy consisting of three major stages, namely, environment learning, channel training, and data transmission. In the environment-learning stage, the CR transceivers both listen to the PR transmission and apply blind algorithms to estimate the spaces that are orthogonal to the channels from the PR. Assuming time-division duplex (TDD)-based transmission for the PR, cognitive beamforming is then designed and applied at CR transceivers to restrict the interference to/from the PR during the subsequent channel-training and data-transmission stages. In the channel-training stage, the CR transmitter sends training signals to the CR receiver, which applies the linear-minimum-mean-square-error (LMMSE)-based estimator to estimate the effective channel. Considering imperfect estimations in both learning and training stages, we derive a lower bound on the ergodic capacity that is achievable for the CR in the data-transmission stage. From this capacity lower bound, we observe a general learning/training/throughput tradeoff associated with the proposed scheme, pertinent to transmit power allocation between the training and transmission stages, as well as time allocation among the learning, training, and transmission stages. We characterize the aforementioned tradeoff by optimizing the associated power and time allocation to maximize the CR ergodic capacity.