This paper' deals with the modeling, analysis, and simulation of multiple-input multiple-output (MIMO) narrowband fading channels for mobile-to-mobile communications. A stochastic MIMO mobile-to-mobile reference channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are surrounded by an infinite number of local scatterers. Using a wave propagation model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimensional (3-D) space-time cross-correlation function (CCF). We show that this function can be expressed as the product of two 2D space-time cross-correlation function (CFs), called the transmit and receive CF. From the non-realizable reference model, a stochastic and a deterministic simulation model are derived using a double sum of complex exponential functions. It is shown how the parameters of the simulation model can be determined for any given distribution of the angle of departure (AOD) and angle of arrival (AOA). In case of isotropic scattering, we present a closed-form solution for the parameter computation problem and illustrate some numerical results concerning the transmit CF. The proposed procedure provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts employing MIMO techniques under realistic propagation conditions.

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the deterministic sum-of-sinusoids (SOS) channel modeling principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting deterministic SOS-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, relay fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

In this paper, we propose a multiple-input multiple-output (IMIMO) mobile-to-mobile channel simulation model derived from a non-realizable reference model presented in Part I of our paper. The underlying reference model is based on the geometrical two-ring scattering model, where both the transmitter and the receiver are moving. A closed-form solution is provided for the three dimensional (3-D) space-time cross-correlation function (CCF) of the simulation model. An important result is that this CCF is ergodic. Also, our results show that this 3-D function can be expressed as a product of two 2-D space-time CCF, called the transmit and the receive CCF. It is shown that the parameters of the simulation model can be determined for any given space-time CCF describing the reference model. In case of isotropic scattering, we present a closed-form solution of the model parameters and illustrate some numerical results for the transmit and receive CCF. Finally, simulation results show an excellent correspondence between the statistical and time average of the MIMO channel capacity. This supports the hypothesis that the MIMO capacity is ergodic with respect to the mean

In this paper, we present a reference model for a wideband multiple-input multiple-output (MIMO) channel based on the geometric elliptical scattering model. The model takes into account the exact relationship between the angle of departure (AOD) and the angle of arrival (AOA). Based on this relationship, the statistical properties of the reference model are studied. Analytical solutions are presented for the three- dimensional (3D) space-time cross-correlation function (CCF), the temporal autocorrelation function (ACF), the 2D space CCF, and finally the frequency correlation function (FCF). The correlation properties are studied and visualized under the assumption of isotropic as well as non-isotropic scattering conditions. The proposed reference model can be used as a starting point for the derivation of a frequency-selective space-time MIMO channel simulator enabling the performance evaluation of multi-antenna wideband communication systems. The reference model is also quite useful for studying the MIMO channel capacity under various propagation conditions imposed by the geometry of the underlying scattering model.

This paper introduces a general concept for the design of efficient multi‐input multi‐output (MIMO) narrowband fading channel simulators. The proposed procedure is applied on a reference model for the geometrical one‐ring scattering model consisting of an infinite number of local scatterers laying on a ring around the mobile station (MS). The statistical properties of both the reference model and the simulation model are studied. Closed‐form solutions are presented, for example for the space‐time cross‐correlation function (CCF), the time autocorrelation function (ACF) and the two‐dimensional (2‐D) space CCF. It will be shown, how the parameters of the MIMO channel simulator can be determined for any given space‐time CCF describing the reference model. The excellent performance of the proposed space‐time channel simulator is demonstrated by comparing its temporal and spatial correlation properties with those of the reference model. Moreover, it is demonstrated how the channel simulator can be used to analyze the statistics of the capacity of MIMO channels from time‐domain simulations. Copyright © 2004 John Wiley & Sons, Ltd.