  A clear understanding the behavior of the error probability (EP) as a
function of signal-to-noise ratio (SNR) and other system parameters is
fundamental for assessing the design of digital wireless communication
systems.We propose an analytical framework based on the log-concavity property
of the EP which we prove for a wide family of multidimensional modulation
formats in the presence of Gaussian disturbances and fading. Based on this
property, we construct a class of local bounds for the EP that improve known
generic bounds in a given region of the SNR and are invertible, as well as
easily tractable for further analysis. This concept is motivated by the fact
that communication systems often operate with performance in a certain region
of interest (ROI) and, thus, it may be advantageous to have tighter bounds
within this region instead of generic bounds valid for all SNRs. We present a
possible application of these local bounds, but their relevance is beyond the
example made in this paper.
