  The objective of this article is to propose and statistically validate a more
general additive non-Gaussian noise distribution, which we term McLeish
distribution, whose random nature can model different impulsive noise
environments commonly encountered in practice and provides a robust alternative
to Gaussian noise distribution. In particular, for the first time in the
literature, we establish the laws of McLeish distribution and therefrom derive
the laws of the sum of McLeish distributions by obtaining closed-form
expressions for their PDF, CDF, complementary CDF (C$^2$DF), MGF and
higher-order moments. Further, for certain problems related to the envelope of
complex random signals, we extend McLeish distribution to complex McLeish
distribution and thereby propose circularly/elliptically symmetric (CS/ES)
complex McLeish distributions with closed-form PDF, CDF, MGF and higher-order
moments. For generalization of one-dimensional distribution to
multi-dimensional distribution, we develop and propose both multivariate
McLeish distribution and multivariate complex CS/ES (CCS/CES) McLeish
distribution with analytically tractable and closed-form PDF, CDF, C$^2$DF and
MGF. In addition to the proposed McLeish distribution framework and for its
practical illustration, we theoretically investigate and prove the existence of
McLeish distribution as additive noise in communication systems. Accordingly,
we introduce additive white McLeish noise (AWMN) channels. For
coherent/non-coherent signaling over AWMN channels, we propose novel
expressions for MAP and ML symbol decisions and thereby obtain closed-form
expressions for both BER of binary modulation schemes and SER of various M-ary
modulation schemes. Further, we verify the validity and accuracy of our novel
BER/SER expressions with some selected numerical examples and some
computer-based simulations.
