  Unlike point-to-point cognitive radio, where the constraint imposed by the
primary rigidly curbs the secondary throughput, multiple secondary users have
the potential to more efficiently harvest the spectrum and share it among
themselves. This paper analyzes the sum throughput of a multiuser cognitive
radio system with multi-antenna base stations, either in the uplink or downlink
mode. The primary and secondary have $N$ and $n$ users, respectively, and their
base stations have $M$ and $m$ antennas, respectively. We show that an uplink
secondary throughput grows with $\frac{m}{N +1}\log n$ if the primary is a
downlink system, and grows with $\frac{m}{M +1}\log n$ if the primary is an
uplink system. These growth rates are shown to be optimal and can be obtained
with a simple threshold-based user selection rule. Furthermore, we show that
the secondary throughput can grow proportional to $\log n$ while simultaneously
pushing the interference on the primary down to zero, asymptotically.
Furthermore, we show that a downlink secondary throughput grows with $m\log
\log n$ in the presence of either an uplink or downlink primary system. In
addition, the interference on the primary can be made to go to zero
asymptotically while the secondary throughput increases proportionally to $\log
\log n$. Thus, unlike the point-to-point case, multiuser cognitive radios can
achieve non-trivial sum throughput despite stringent primary interference
constraints.
