Sparse multipath channels: Modelling, analysis, and simulation.

A sparse multipath channel is characterized by a small number of randomly distributed scatterers. This study proposes a methodology for the modelling of sparse multipath channels. The new methodology is then used to develop a sparse narrowband multipath channel model by applying the sum-of-cisoids (SOC) principle. The statistical properties of the presented sparse SOC multipath channel model are studied. Analytical expressions are derived for the mean value, variance, autocorrelation function (ACF) and cross-correlation function (CCF) of the complex channel gain, as well as for the probability density function (PDF) of the envelope. Our study shows that mobile radio channels behave in sparse scattering environments completely different from what is known from innumerable studies assuming rich scattering. The derived analytical expressions unfold their full significance if the number of multipath components is small and the path gains are unbalanced, which prevents invoking the central limit theorem.