Capacity Limits of Multiuser Multiantenna Cognitive Networks

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.