  In this paper, throughput and energy efficiency of cognitive multiple-input
multiple-output (MIMO) systems operating under quality-of-service (QoS)
constraints, interference limitations, and imperfect channel sensing, are
studied. It is assumed that transmission power and covariance of the input
signal vectors are varied depending on the sensed activities of primary users
(PUs) in the system. Interference constraints are applied on the transmission
power levels of cognitive radios (CRs) to provide protection for the PUs whose
activities are modeled as a Markov chain. Considering the reliability of the
transmissions and channel sensing results, a state-transition model is
provided. Throughput is determined by formulating the effective capacity. First
derivative of the effective capacity is derived in the low-power regime and the
minimum bit energy requirements in the presence of QoS limitations and
imperfect sensing results are identified. Minimum energy per bit is shown to be
achieved by beamforming in the maximal-eigenvalue eigenspace of certain
matrices related to the channel matrix. In a special case, wideband slope is
determined for more refined analysis of energy efficiency. Numerical results
are provided for the throughput for various levels of buffer constraints and
different number of transmit and receive antennas. The impact of interference
constraints and benefits of multiple-antenna transmissions are determined. It
is shown that increasing the number of antennas when the interference power
constraint is stringent is generally beneficial. On the other hand, it is shown
that under relatively loose interference constraints, increasing the number of
antennas beyond a certain level does not lead to much increase in the
throughput.
