This paper starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates Lp([0, T]) approximations of the sub-Gaussian random signals. Explicit truncation error upper bounds are established. The obtained rate of convergence provides a constructive algorithm for determining the sampling rate and the sample size in the truncated Whittaker-Kotel'nikovShannon expansions to ensure the approximation of the subGaussian signals with given accuracy and reliability. Some numerical examples are presented.

This paper presents a new trivariate joint and bivariate distributions of a landmobile cellular wireless communication system's uplink multipaths' time-of-arrival (TOA) and two-dimensional (2D) azimuth-elevation direction-of-arrival (DOA). These distributions are rigorously derived via thorough mathematics, based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). Unlike earlier "geometric models" that assume the scatterers to have only a 2D spatial density (for example, uniform density within a disc around the mobile), this present "geometric model" have the scatterer spatial density as uniform within a 3D vertical above ground cylinder whose flat bottom circular base centers at the mobile.

This letter presents the joint/marginal distributions of the uplink (downlink) multipaths' azimuth angles of arrival and times of arrival at the cellular base station (mobile). These closed-form explicit densities are rigorously derived based on a new "geometrical model" wherein omnidirectional scatterers are modeled as spatially distributed at an inverted parabolic spatial distribution on a two-dimensional disc centered at the mobile. This "inverted parabolic" density, in contrast to the uniform disc density or the rim density, indirectly accounts for scattering power loss. This new model better least-squares-fit some empirical data than its competing models can.

This paper presents the open literature's first closed-form explicit expressions of the trivariate joint and marginal distributions of a land mobile cellular wireless communication system's uplink and downlink multipaths' time-of-arrival (TOA) and two-dimensional (2D) direction-of-arrival (DOA), rigorously derived via thorough mathematics based on a "geometrical" model of the three-dimensional (3D) spatial relationships among the mobile-station (MS), the scatterers, and the base-station (BS). The scatterers are herein modeled to have a uniform 3D spatial distribution in an above-ground hemisphere with a flat circular base (or alternatively, within a sphere) centered at the mobile.