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In this paper, we study a multi-antenna-based cognitive radio (CR) system that is able to operate concurrently with the primary radio (PR) system. We propose a novel CR transmission frame structure consisting of three stages, including a new environment learning stage in addition to the conventional channel training and data transmission stages. During the environment learning stage, the CR terminals blindly learn the spatial knowledge of the PR-CR channels, based on which cognitive beamforming is designed at CR transceivers to restrict the interference to and from the PR, respectively, in the subsequent channel training and data transmission stages. Considering the learning and training errors from the first two stages, we derive a lower bound on the ergodic capacity achievable for the CR link subject to a predefined interference-power constraint at the PR and the CR's own transmit power constraint. We then characterize a general learning/training/throughput (LTT) tradeoff associated with the proposed scheme, pertinent to transmit power allocation between training and transmission stages, as well as time allocation among learning, training, and transmission stages.