This paper studies four aspects of multipath propagation with randomly distributed scatterers: (i) Gaussian and hyperbolic time‐of‐arrival (ToA) probability density functions (pdfs); (ii) theoretical bounds on the ToA pdfs; (iii) geometric pdfs in multipath propagation via Gaussian and hyperbolic scattering channels; and (iv) implementation of selective combining diversity as a method to decrease propagation delay, thus improving transmission performance. The Gaussian and hyperbolic scattering channels are employed to model random scatterers between a base station and a user equipment. One‐dimensional and three‐dimensional results of Gaussian and hyperbolic ToA pdfs are reported. Detailed discussions are given. Copyright © 2012 John Wiley & Sons, Ltd.