The Riemann sum method for the design of sum-of-cisoids simulators for Rayleigh fading channels in non-isotropic scattering environments

Abstract

Abstract-In this paper, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-ofcisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We show that the RSM results in an excellent approximation of the channel's autocorrelation function (ACF). Furthermore, we compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and Lp-norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to approximate the channel's ACF, whereas the latter two methods provide better results regarding the emulation of the envelope distribution. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the analysis of mobile communication systems operating in non-isotropic scattering environments.

Novel 3-D Non-Stationary Wideband Models for Massive MIMO Channels

“…3) We provide approximate expressions for the relationship between non-stationary properties of the channel, e.g., spatial-temporal Doppler frequency drifts, and the distances between the transmitting and receiving arrays as well as between these arrays and clusters. 4) We propose a 3D extension of the Riemann sum method (RSM) [29] to compute the amplitude and angular parameters of the 3D simulation model and use the von Mises-Fisher (VMF) distribution to jointly model the azimuth and elevation angles of the scatterers. The rest of this paper is organized as follows.…”

“…random variables uniformly distributed over the interval (0, 2π], the remaining parameters can be obtained using the corresponding equations of the theoretical model, e.g,D SB qp,c,i (t) in (55) can be obtained using (26). In this paper, a 3D extension of the RSM [29] is used to compute the parameters of the small-scale fading processes, and the MEA [33] is used to compute the parameters of the cluster shadowing processes.…”

“…where I E,c and I A,c denote the number of rays used in the simulation model in the elevation and azimuth planes, respectively, so the total number of rays in (55) is I c = I E,c I A,c . In the RSM, the theoretical correlation functions in (41) can be approximated as midpoints Riemann sums of finite number of terms [29]. Then, the angular parameters of the simulation model are assumed equally spaced in both the elevation and azimuth planes asθ…”

“…The parameterΔ SB qp,c,i (δ T , δ R , Δt, t) in (57) can be obtained by pluggingθ ST c,i andφ ST c,i into (11)- (13) and these into (40). Last, the parametersâ c,i in (57) can be obtained as [29]…”

On the autocorrelation function of Rice processes for unsymmetrical doppler power spectral densities

“…In [5], also approximations to the envelope power spectrum are presented for Rayleigh and Nakagami fading channels. Some results dealing with the correlation properties of the envelope with unsymmetrical DPSD (non-isotropic scattering) have been discussed in [6]. However, to the best of our knowledge no results dealing with the envelope power spectrum and ACF in non-isotropic scattering can be found in the literature for Rice fading channels.…”