  This paper addresses the design issues of the multi-antenna-based cognitive
radio (CR) system that is able to operate concurrently with the licensed
primary radio (PR) system. We propose a practical CR transmission strategy
consisting of three major stages: 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
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
training and transmission stages, as well as time allocation among learning,
training, and transmission stages. We characterize the aforementioned tradeoff
by optimizing the associated power and time allocation to maximize the CR
ergodic capacity.
