Fourier Analysis of the Prefaded Signal Synthesis in MPAC Setup

The prefaded signal synthesis (PFS) is a popular channel emulation method used for multiple-input multiple-output over-the-air (MIMO-OTA) testing with the multi-probe anechoic chamber (MPAC) setup. It aims to synthesize the second-order statistics of a target propagation channel in terms of the spatial and temporal correlation. The emulated spatial and temporal correlation is evaluated in a confined volume (test zone) enclosing the device-under-test (DUT). In the industry, it has been often asked about (i) the minimum sufficient spatial sampling density within the test zone when solving probe weights, and (ii) the effect of the antenna radiation pattern of different DUT’s on the emulated channel. In this paper, we aim to address those questions analytically from the perspective of the power spectral density function in the direction and Doppler frequency domain, i.e., the Fourier dual of the spatial and temporal correlation function. Moreover, we use the same Fourier duality to study (i) the root cause of the empirical statistics being different from the statistical expectation for a single channel realization, and (ii) the applicability and effectiveness of two spectral operations, namely the decorrelation and the whitening operation, on improving the empirical statistics for the emulated channel.