  Linear precoding and post-processing schemes are ubiquitous in wireless
multi-input-multi-output (MIMO) settings, due to their reduced complexity with
respect to optimal strategies. Despite their popularity, the performance
analysis of linear MIMO receivers is mostly not available in closed form, apart
for the canonical (uncorrelated Rayleigh fading) case, while for more general
fading conditions only bounds are provided. This lack of results is motivated
by the complex dependence of the output signal-to-interference and noise ratio
(SINR) at each branch of the receiving filter on both the squared singular
values as well as the (typically right) singular vectors of the channel matrix.
While the explicit knowledge of the statistics of the SINR can be circumvented
for some fading types in the analysis of the linear Minimum Mean-Squared Error
(MMSE) receiver, this does not apply to the less complex and widely adopted
Zero-Forcing (ZF) scheme. This work provides the first-to-date closed-form
expression of the probability density function (pdf) of the output ZF and MMSE
SINR, for a wide range of fading laws, encompassing, in particular,
correlations and multiple scattering effects typical of practically relevant
channel models.
