  Opportunistic scheduling (OS) schemes have been proposed previously by the
authors for multiuser MIMO-SDMA downlink systems with linear combining. In
particular, it has been demonstrated that significant performance improvement
can be achieved by incorporating low-complexity linear combining techniques
into the design of OS schemes for MIMO-SDMA. However, this previous analysis
was performed based on the effective signal-to-interference ratio (SIR),
assuming an interference-limited scenario, which is typically a valid
assumption in SDMA-based systems. It was shown that the limiting distribution
of the effective SIR is of the Frechet type. Surprisingly, the corresponding
scaling laws were found to follow $\epsilon\log K$ with $0<\epsilon<1$, rather
than the conventional $\log\log K$ form.
  Inspired by this difference between the scaling law forms, in this paper a
systematic approach is developed to derive asymptotic throughput and scaling
laws based on signal-to-interference-noise ratio (SINR) by utilizing extreme
value theory. The convergence of the limiting distribution of the effective
SINR to the Gumbel type is established. The resulting scaling law is found to
be governed by the conventional $\log\log K$ form. These novel results are
validated by simulation results. The comparison of SIR and SINR-based analysis
suggests that the SIR-based analysis is more computationally efficient for
SDMA-based systems and it captures the asymptotic system performance with
higher fidelity.
