Carlos A. Gutiérrez

The design of sum-of-cisoids rayleigh fading channel simulators assuming non-isotropic scattering conditions

In this letter, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and the 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 emulate the channels autocorrelation function (ACF), whereas the latter two methods are more precise regarding the approximation of the envelope distribution. The results also show that the benefits of increasing the number of cisoids are more significant in the case of the RSM than in the case of the GMEA and LPNM. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the laboratory analysis of mobile communication systems operating in non-isotropic scattering environments.In this letter, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and the 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 emulate the channel’s autocorrelation function (ACF), whereas the latter two methods are more precise regarding the approximation of the envelope distribution. The results also show that the benefits of increasing the number of cisoids are more significant in the case of the RSM than in the case of the GMEA and LPNM. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the laboratory analysis of mobile communication systems operating in non-isotropic scattering environments.

Level-Crossing Rate and Average Duration of Fades of the Envelope of a Sum-of-Cisoids

For the modelling and simulation of mobile radio channels, one often uses a sum of complex sinusoids (cisoids). This paper analyses in detail the level-crossing rate (LCR), the average duration of the fades (ADF), and the cumulative distribution function (CDF) of the envelope of a sum-of-cisoids (SOC). For these statistical quantities, exact and simple approximate solutions are derived by taking into account that the inphase and quadrature components of SOC models are generally correlated. The correctness of all theoretical results is confirmed by simulations. The results are not only important for getting a better fundamental understanding of the statistical behaviour of SOC models, but also for the performance evaluation of SOC-based mobile radio channel simulators.

Classes of sum-of-cisoids processes and their statistics for the modeling and simulation of mobile fading channels

In this paper, we present a fundamental study on the stationarity and ergodicity of eight classes of sum-of-cisoids (SOC) processes for the modeling and simulation of frequency-nonselective mobile Rayleigh fading channels. The purpose of this study is to determine which classes of SOC models enable the design of channel simulators that accurately reproduce the channel’s statistical properties without demanding information on the time origin or the time-consuming computation of an ensemble average. We investigate the wide-sense stationarity, first-order stationarity of the envelope, mean ergodicity, and autocorrelation ergodicity of the underlying random processes characterizing the different classes of stochastic SOC simulators. The obtained results demonstrate that only the class of SOC models comprising cisoids with constant gains, constant frequencies, and random phases is defined by a set of stationary and ergodic random processes. The analysis presented here can easily be extended with respect to the modeling and simulation of frequency-selective single-input single-output (SISO) and multiple-input multiple-output channels. For the case of frequency-selective SISO channels, we investigate the stationarity and ergodicity in both time and frequency of 16 different classes of SOC simulation models. The findings presented in this paper can be used in the laboratory as guidelines to design efficient simulation platforms for the performance evaluation of modern mobile communication systems.

An Ergodic Sum-of-Cisoids Simulator for Multiple Uncorrelated Rayleigh Fading Channels Under Generalized Scattering Conditions

In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulators for multiple uncorrelated narrowband Rayleigh fading channels. The method, which is intended for a special class of SOS models known as sum-of-cisoids (SOC) models, enables the generation of an unlimited number of mutually uncorrelated Rayleigh fading waveforms with specified autocorrelation properties. This is in contrast to all known methods proposed for SOS simulators, which are restricted to the simulation of multiple uncorrelated Rayleigh fading channels characterized by autocorrelation functions (ACFs) derived under the isotropic scattering assumption. The excellent performance of this new method is exemplarily demonstrated by comparing the correlation properties and the envelope distribution of a set of waveforms generated by the simulator with the corresponding quantities of a reference set of multiple uncorrelated Rayleigh fading channels. The methods performance is evaluated in not only theoretical simulation scenarios, where the lengths of the generated waveforms approach infinity, but also practical scenarios, where the waveform lengths are limited. The simulation approach described in this paper is important to the performance analysis of mobile broadband communication systems using diversity, multicarrier, or multiple-input-multiple-output (MIMO) techniques under generalized scattering conditions.

A Non-Stationary Mobile-to-Mobile Channel Model Allowing for Velocity and Trajectory Variations of the Mobile Stations

In mobile-to-mobile (M2M) communication systems, both the transmitter and the receiver are moving with a certain velocity, which is usually assumed to be constant over time. However, in realistic propagation scenarios, the velocity of the mobile stations (MSs) is subject to changes resulting in a non-stationary fading process. In this paper, we develop a non-stationary narrow-band M2M multipath fading channel model, where the transmitter and the receiver experience changes in their velocities and trajectories. For this model, we derive expressions for the local autocorrelation function (ACF), the Wigner–Ville spectrum, the local average Doppler shift, and the local Doppler spread under isotropic scattering conditions. In addition, we investigate the correlation properties of the proposed model assuming non-isotropic scattering around the MSs. By relaxing the standard assumption of constant velocities of the MSs, this paper shows that the local ACF and the Wigner–Ville spectrum differ completely from known expressions derived for wide-sense stationary M2M channel models. Furthermore, it is shown that our model provides consistent results with respect to the Doppler spread. The proposed channel model is useful for the performance analysis of M2M communication systems under non-stationary conditions caused by velocity variations of the MSs.

Geometry-Based Statistical Modeling of Non-WSSUS Mobile-to-Mobile Rayleigh Fading Channels

In this paper, we present a novel geometry-based statistical model for small-scale non-wide-sense stationary uncorrelated scattering (non-WSSUS) mobile-to-mobile (M2M) Rayleigh fading channels. The proposed model builds on the principles of plane wave propagation to capture the temporal evolution of the propagation delay and Doppler shift of the received multipath signal. This is different from existing non-WSSUS geometry-based statistical channel models, which are based on a spherical wave propagation approach, that in spite of being more realistic is more mathematically intricate. By considering an arbitrary geometrical configuration of the propagation area, we derive general expressions for the most important statistical quantities of nonstationary channels, such as the first-order probability density functions of the envelope and phase, the four-dimensional (4-D) time-frequency correlation function (TF-CF), local scattering function (LSF), and time-frequency-dependent delay and Doppler profiles. We also present an approximate closed-form expression of the channels 4-D TF-CF for the particular case of the geometrical one-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of non-WSSUS M2M Rayleigh fading channels.

A generalized method for the design of ergodic sum-of-cisoids simulators for multiple uncorrelated rayleigh fading channels

In this paper, we present a new method for the design of ergodic sum-of-sinusoids (SOS) simulation models for multiple uncorrelated Rayleigh fading channels. The method, which is intended for a special class of SOS models, known as sum-of-cisoids (SOC) models, can be used to generate an arbitrary number of uncorrelated Rayleigh fading waveforms with specified Doppler power spectral characteristics. This is in contrast to the SOS simulators currently available in the open literature that have been designed under the isotropic scattering assumption, which are limited to the simulation of uncorrelated channels characterized by Clarkes U-shaped Doppler power spectral density (DPSD). The excellent performance of the proposed method is exemplarily demonstrated by comparing the correlation and the spectral characteristics of a set of generated Rayleigh fading waveforms with those of a reference group of uncorrelated Rayleigh fading channels by considering different types of DPSDs. The simulation approach described in this paper can easily be applied to the laboratory performance analysis of mobile broadband communication systems using diversity, multicarrier, or multiple-input multiple-output (MIMO) techniques under generalized scattering conditions.

Analysis of error in the estimation of the temporal ACF of ergodic sum-of-cisoids simulators for mobile fading channels

Mobile fading channel simulators based on ergodic sum-of-cisoids (SOC) processes have been proposed in several papers as a solution to accurately approximate the channels autocorrelation function (ACF) in a single simulation run. However, despite the encouraging results presented in the literature, it is not clear whether the ergodicity of this type of simulators is meaningful in practice, where in contrast to what theory assumes, the waveforms generated by the simulator have finite lengths. To clarifying this issue, we present in this paper a comprehensive analysis of the random error observed when the temporal ACF (TACF) of ergodic SOC processes is estimated from waveforms of finite duration. We start by computing the instantaneous error produced by three different estimators, namely the biased, the unbiased, and the half-interval estimators. We then derive compact expressions for some insightful statistical quantities of the estimation error, such as the mean, the variance, and the mean-squared value. Based on the obtained results, we discuss the conditions under which an ergodic SOC simulator can be considered to perform similarly in theory and practice. The analysis presented in this paper can be used as a framework for testing, calibration, and performance validation of new ergodic SOC channel simulators.

Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications

This paper deals with the modeling of nonstationary time-frequency (TF) dispersive multipath fading channels for vehicle-to-vehicle (V2V) communication systems. As a main contribution, the paper presents a novel geometry-based statistical channel model that facilitates the analysis of the nonstationarities of V2V fading channels arising at a small-scale level due to the time-varying nature of the propagation delays. This new geometrical channel model has been formulated following the principles of plane wave propagation (PWP) and assuming that the transmitted signal reaches the receiver antenna through double interactions with multiple interfering objects (IOs) randomly located in the propagation area. As a consequence of such interactions, the first-order statistics of the channel model’s envelope are shown to follow a worse-than-Rayleigh distribution; specifically, they follow a double-Rayleigh distribution. General expressions are derived for the envelope and phase distributions, four-dimensional (4D) TF correlation function (TF-CF), and TF-dependent delay and Doppler profiles of the proposed channel model. Such expressions are valid regardless of the underlying geometry of the propagation area. Furthermore, a closed-form solution of the 4D TF-CF is presented for the particular case of the geometrical two-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of small-scale nonstationary V2V double-Rayleigh fading channels.

Performance analysis of closed-loop pre-equalisation for multiuser multiple-input multiple-output with multicarrier code division multiple access systems

The use of multiple transmit and receive antennas is widely recognised as an effective technology to boost the capacity of wireless communication systems. Moreover, the combination of multiple-input multiple-output (MIMO) systems with multicarrier code division multiple access (MC-CDMA) offers a strong alternative to satisfy the demand for high data rates with rigorous quality-of-service (QoS) restrictions. In this study, this paper applies a closed-loop pre-equalisation methodology under a unified framework for MIMO and MC-CDMA systems that satisfies the QoS target with a single-user-based detector while minimising the power of the pre-equalisation factors. It is of particular interest to investigate the impact and limitations of combining the robustness of the feedback scheme with the degrees of freedom available in the system, given in terms of the number of subcarriers and multiple antennas. The contribution of this work includes the derivation of the distributed and centralised optimal closed-loop pre-equalisation solutions under the MIMO–MC-CDMA structure. The results and analysis illustrate important gains in the form of power savings, enabled by the spatial diversity of the MIMO scheme.