  The potential benefits of multiple-antenna systems may be limited by two
types of channel degradations rank deficiency and spatial fading correlation of
the channel. In this paper, we assess the effects of these degradations on the
diversity performance of multiple-input multiple-output (MIMO) systems, with an
emphasis on orthogonal space-time block codes, in terms of the symbol error
probability, the effective fading figure (EFF), and the capacity at low
signal-to-noise ratio (SNR). In particular, we consider a general family of
MIMO channels known as double-scattering channels, which encompasses a variety
of propagation environments from independent and identically distributed
Rayleigh to degenerate keyhole or pinhole cases by embracing both
rank-deficient and spatial correlation effects. It is shown that a MIMO system
with $n_T$ transmit and $n_R$ receive antennas achieves the diversity of order
$\frac{\n_T n_S n_R}{\max(n_T,n_S,n_R)}$ in a double-scattering channel with
$n_S$ effective scatterers. We also quantify the combined effect of the spatial
correlation and the lack of scattering richness on the EFF and the low-SNR
capacity in terms of the correlation figures of transmit, receive, and
scatterer correlation matrices. We further show the monotonicity properties of
these performance measures with respect to the strength of spatial correlation,
characterized by the eigenvalue majorization relations of the correlation
matrices.
