Spatially-Stationary Propagating Random Field Model for Massive MIMO Small-Scale Fading

The spatially uncorrelated Rayleigh small-scale fading model is a useful stochastic tool for analyzing multiple-antenna wireless communication systems, and, as experiments have shown, it often is a good approximation to physical propagation. However, the assumption that the propagating field is uncorrelated from one point in space to another breaks down when, for example, antenna spacings are smaller than one-half wavelength - a model defect typically addressed by assuming some spatial correlation. Spatial correlation can have huge effects even in the absence of close spacing between antennas. While an ad-hoc correlation versus distance, such as exponential, may add an element of realism to the model, in general it does not capture the peculiar “action at a distance” phenomena associated with the wave equation. The very desirable property of spatial stationarity can be retained, provided the spatial autocorrelation is chosen such that the complex Gaussian small-scale fading random field satisfies the homogeneous wave equation. The fading model that is closest to iid Rayleigh fading, and that is still consistent with the wave equation, has an autocorrelation equal to sinc(2πR/λ, corresponding to planewaves arriving uniformly from all directions, and having independent, equal variance complex Gaussian amplitudes. The contribution of this paper is twofold: first, a Fourier planewave representation that provides a computationally efficient way to generate samples of the random field, second, an inverse representation that enables the efficient computation of the joint likelihood of noisy measurements of the field over continuous segments of lines, planes, and volumes.