On the spatial configuration of scatterers for given delay-angle distributions

Abstract

This paper investigates the distribution of scatterers located around the mobile station (MS) for given delay-angle distributions. The delay-angle distribution function represents the joint probability density function (PDF) of the time-ofarrival (TOA) and angle-of-arrival (AOA). Given such a joint PDF, we first derive a general expression for the distribution of the scatterers in both polar and Cartesian coordinates. We then analyze an important special case in which the TOA and the AOA follow the multiple negative exponential (MNE) and the uniform distributions, respectively. The considered MNE PDF is the sum of several decaying exponential functions, which allows us to describe the TOA in a variety of propagation environments. For the delay profiles specified in COST 207, the scatterer distribution is simulated and visualized in scatter diagrams. The marginal PDF of the distance from the scatterers to the MS is also computed, illustrated, and confirmed by simulations. For the MNE TOA PDF, it is shown that the local scatterers are not symmetrically distributed around the MS even if the AOAs are uniformly distributed. In addition, the obtained scattering area is not confined by firm geometric constraints, which complies with real propagation environments. The importance of the work is to provide a novel approach to channel modelling, in which obtaining the desirable TOA (AOA) PDF is assured.