Impact of Noisy Measurements With Fourier-Based Evaluation on Condensed Channel Parameters

Condensed channel parameters, such as Root Mean Square (RMS) delay spread and angular spread, are essential ways of representing results from the measurement of wireless propagation channels. However, real-world measurements are invariably affected by noise, which is not inherently reduced by the Fourier processing - in contrast to high-resolution parameter estimation. Even when the signal-to-noise ratio is relatively high, e.g., 20 dB, the impact of the noise on the condensed parameters can be significant and lead to erroneous estimates. This can be explained, e.g., for the computation of the RMS delay spread, where long delays (which often carry noise only) are “up-weighted” by the square of the delay. While techniques like noise thresholding are often applied, the reasons for choosing thresholds are usually not described in detail. This paper systematically analyzes noise thresholding for joint delay-angle measurements and derives equations for the impact of thresholds on the computation of delay and angle RMS spreads and window parameters under various measurement circumstances. The paper provides results based on closed-form equations, as well as MonteCarlo (MC) simulations, and application to real-world measurements in the sub-THz band.