Probability Distribution of the Coherence Bandwidth of a Reverberation Chamber

Abstract

A theoretical probability distribution and associated statistics for the coherence bandwidth of an ideal mode-stirred reverberation chamber are derived. The stochastic model assumes and exploits the ergodicity of a dynamic wave chaotic cavity by expressing the coherence bandwidth in terms of the random effective excitation bandwidth and by replacing spatial averaging of transmitter-receiver locations with stir (ensemble) averaging. The theoretical model is validated through comparison with the empirical cumulative distribution function (cdf) extracted from measured S-parameter data from a real chamber, and through simulation using analytical calculations for a fictitious wall-stirred chamber. The results are particularly relevant to the improvement of transmission quality and uncertainty quantification of wireless multipath propagation.

Pulse Jitter, Delay Spread, and Doppler Shift in Mode-Stirred Reverberation

“…. Unlike in (19) and (20), the coefficients of 2sΩ/λ in (22) and (24) exhibit non-unit amplitudes. This indicates that different maximum Doppler shifts may be expected in stirred 3-D cavities [23,Figs.…”

“…3 and 4] compared to the well-known free-space value D = 2sΩ/λ in continuous-wave radar, from (16). Finally, replacing s with S and multiplying with an sand frequency-dependent scattering cross-section of the facets, followed by an integration as in (17), yields ⟨T d (Ωt)⟩ and ⟨D(f, Ω, t)⟩ as average (effective) values of the random T d (Ωt) and D(f, Ω, t) [24].…”

“…Fig. 2); quantitative discrepancies can be ascribed to the Ωt-dependence of the coefficients of 2sΩ/λ in (20), (22) and (24), as well as the uncertainty of t and the fact that τ refers to threshold crossings of the pulse envelope, as opposed to phase delay in the sinusoidal carrier wave. The threshold crossings exhibit a quasi-periodicity with average period ⟨T τ ⟩.…”

Acoustic detection based on coherence bandwidth

“…The RMS delay spread describes the dispersion in the time domain due to multipath transmission. The RMS delay spread τ rms is the square root of the second central moment of the power delay profile and is defined to be [6] where P ( τ i ) is the power intensity of the i th path and N is the number of multipaths. The mean excess delay E [ τ ] 2 is given as If the definition of the coherence bandwidth B c is stabilised and the frequency correlation function is above 0.5, then the coherence bandwidth is approximately given by This is an experimental relationship and there is no accurate relationship between the coherence bandwidth and the RMS delay spread.…”

“…The RMS delay spread describes the dispersion in the time domain due to multipath transmission. The RMS delay spread τ rms is the square root of the second central moment of the power delay profile and is defined to be [6]…”