On the correlation and scattering functions of mobile uncorrelated scattering channels

We consider impulse response statistics of the wide sense stationary-uncorrelated scattering (WSSUS) multipath channel that results from a stationary scattering field with either the transmitter or receiver in motion, but not both. Our analysis is based on the theory of generalized stochastic processes. A generalized process is a continuous random linear functional on a topological vector space of test functions. This theory is a direct extension of the well known theory of generalized functions (also known as "distribution theory"). We assume a spatially uncorrelated scattering field with a spatial scattering intensity function.