  In [1], we introduced a new, matrix algebraic, performance analysis framework
for wireless systems with fading channels based on the matrix exponential
distribution. The main idea was to use the compact, powerful, and easy-to-use,
matrix exponential (ME)-distribution for i) modeling the unprocessed channel
signal to noise ratio (SNR), ii) exploiting the closure property of the
ME-distribution for SNR processing operations to give the effective channel
random variable (r.v.) on ME-distribution form, and then to iii) express the
performance measure in a closed-form based on ME-distribution matrix/vector
parameters only. In this work, we aim to more clearly present, formalize,
refine and develop this unified bottom-up analysis framework, show its
versatility to handle important communication cases, performance evaluation
levels, and performance metrics. The bivariate ME-distribution is introduced
here as yet another useful ME-tool, e.g. to account for dependency among two
r.v.s. We propose that the ME-distribution may, in addition to fading, also
characterize the pdf of discrete-time signal r.v.s, thus extending the
ME-distribution matrix form to new generalized 1D/2D-Gaussian-, and Rayleigh-,
distribution-like matrix forms. Our findings here, strengthen the observation
from [1], [2], and indicates that the ME-distribution can be a promising tool
for wireless system modeling and performance analysis.
