  This paper studies the fluctuations of the signal-to-noise ratio (SNR) of
minimum variance distorsionless response (MVDR) filters implementing diagonal
loading in the estimation of the covariance matrix. Previous results in the
signal processing literature are generalized and extended by considering both
spatially as well as temporarily correlated samples. Specifically, a central
limit theorem (CLT) is established for the fluctuations of the SNR of the
diagonally loaded MVDR filter, under both supervised and unsupervised training
settings in adaptive filtering applications. Our second-order analysis is based
on the Nash-Poincar\'e inequality and the integration by parts formula for
Gaussian functionals, as well as classical tools from statistical asymptotic
theory. Numerical evaluations validating the accuracy of the CLT confirm the
asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.
