This paper considers a spectrum sharing (SS) multiple-input multiple-output (MIMO) system operating in a Rayleigh fading environment. First the capacity of a single-user SS spatial multiplexing system is investigated in two scenarios that assume different receivers. To explicitly show the capacity scaling law of SS MIMO systems, some approximate capacity expressions for the two scenarios are derived. Next, we extend our analysis to a multiple user system with zero-forcing receivers (ZF) under spatially-independent scheduling and analyze the sum-rate. Furthermore, we provide an asymptotic sum-rate analysis to investigate the effects of different parameters on the multiuser diversity gain. Our results show that the secondary system with a smaller number of transmit antennas Nt and a larger number of receive antennas Nr can achieve higher capacity at lower interference temperature Q, but at high Q the capacity follows the scaling law of the conventional MIMO systems. However, for a ZF SS spatial multiplexing system, the secondary system with small Nt and large Nr can achieve the highest capacity throughout the entire region of Q. For a ZF SS spatial multiplexing system with scheduling, the asymptotic sum-rate scales like Ntlog2(Q(KNtNp-1)/Nt), where Np denotes the number of antennas of the primary receiver and K represents the number of secondary transmitters.
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