The objective of this article is to statistically characterize and describe a more general additive noise distribution, termed as McLeish distribution, whose random nature can model different impulsive noise environments often encountered in practice and provides a robust alternative to Gaussian distribution. Accordingly, we develop circularly and elliptically symmetric multivariate McLeish distribution and introduce additive white McLeish noise (AWMN) channels. In particular, we propose novel analytical and closed-form expressions for the symbol error rate (SER) performance of coherent / non-coherent signaling using various digital modulation techniques over AWMN channels. In that context, we illustrate some novel expressions by some selected numerical examples and verify them by some well chosen computer-based simulations.