  Statistical prior channel knowledge, such as the
wide-sense-stationary-uncorrelated-scattering (WSSUS) property, and additional
side information both can be used to enhance physical layer applications in
wireless communication. Generally, the wireless channel's strongly fluctuating
path phases and WSSUS property characterize the channel by a zero mean and
Toeplitz-structured covariance matrices in different domains. In this work, we
derive a framework to comprehensively categorize side information based on
whether it preserves or abandons these statistical features conditioned on the
given side information. To accomplish this, we combine insights from a generic
channel model with the representation of wireless channels as probabilistic
graphs. Additionally, we exemplify several applications, ranging from channel
modeling to estimation and clustering, which demonstrate how the proposed
framework can practically enhance physical layer methods utilizing machine
learning (ML).
