  In this paper, the performance of an underlay multiple-input multiple-output
(MIMO) cognitive radio system is analytically studied. In particular, the
secondary transmitter operates in a spatial multiplexing transmission mode,
while a zero-forcing (ZF) detector is employed at the secondary receiver.
Additionally, the secondary system is interfered by multiple randomly
distributed single-antenna primary users (PUs). To enhance the performance of
secondary transmission, optimal power allocation is performed at the secondary
transmitter with a constraint on the interference temperature (IT) specified by
the PUs. The outage probability of the secondary receiver is explicitly derived
in an exact closed-form expression. Also, some special cases of practical
interest, including co-located PUs and massive MIMO, are discussed. Further, to
mitigate instantaneous excessive interference onto PUs caused by the
time-average IT, an iterative antenna reduction algorithm is developed for the
secondary transmitter and, accordingly, the average number of transmit antennas
is analytically computed. Extensive numerical and simulation results
corroborate the effectiveness of our analysis.
