Abstract— In this paper, we characterize the cross-correlation function (CCF) between the time-frequency transfer functions (TF)s of two sub-channels of a multiple-input multiple-output (MIMO) wireless fading channel. The TF of each sub-channel consists of a number of multi-path components caused by propagation of a transmitted signal in random scattering media. The proposed CCF is expressed in terms of several environmental parameters (such as the moment generating function (MGF) of the delay profile (DP) and the pathloss exponent). It is a summation of two terms: the first term is due to the autocorrelation of multi-path components while the second term is due to the cross-correlation of multi-path components. Each term is a product of several correlation functions. Each of these correlation functions represents different dependencies of the wireless channel in terms of time, carrier frequency and the position of the antenna elements around both the transmitter and the receiver site. Interestingly, the last two terms of these functions are η2-order (or η-order) integrations of the MGF of the DP, evaluated at two carrier frequencies (or the difference between carrier frequencies), where η is the pathloss exponent of the environment.
Index Terms— Rayleigh fading, multipath fading channels, multielement antenna communication systems, multiple-input multiple-output (MIMO) systems, MIMO Rayleigh fading channels, antenna arrays, array configurations, electromagnetic wave scattering, radiowave propagation, space-time-frequency channel characterization, Frequency division multiplexing, Multifrequency MIMO channel modeling, propagation path, Delay effects, Time-varying channels, Doppler effect, Doppler spread, isotropic scattering environment, omnidirectional antennas, correlation theory, space-time-frequency cross-correlation function, single-input single-output subchannels, fading correlation, Bessel functions of the first kind, Clark model, direction-of-arrival, direction-of-departure, land mobile radio, angular orientations, antenna separation, microcellular radio, time-delay, path-loss exponent, carrier frequency, channel gain, base station, mobile station, moment generating function, uniform phase change, η-order integration, local scatterer, numerical calculations/simulations, probability density function.