Observations and Conclusions from a Three Year Digital Radio Field Experiment in Australia

A statistical characterization of point-to-point microwave links using biased Rayleigh distributions

“…In fact, radio propagation studies often treat dominant interfering rays as the cause of signal distortions that are an inevitable consequence of the multipath propagation phenomenon. However, to conform with common usage [6], [8], [12]- [14], the term "two-ray model" is used where the distribution for the magnitude of the second ray or reflected ray refers to that of the resultant random process caused by the superposition of interfering rays at the microwave receiving antenna.…”

“…The earlier work [16] has shown that delay differences for the two-ray model can be expected to be typically a few nanoseconds. More importantly, the statistical distribution PDF was considered in the model in [8] to incorporate the severity factor to account for the different outage probabilities observed for delays of the same orders. The severity factor in our model is controlled by the percentage of nonminimum phase described in the subsequent paragraphs.…”

“…Since both and are parts of the phase of the second ray in our two-ray model, a knowledge of the aggregate distribution for the second ray's phase would put a constraint on the distribution for , had the delay parameter been predicted to assume a statistical distribution. As for the notch-position parameter authors seem, however, to agree that from physical intuition, it is reasonable to assume a uniform density distribution for the notch-position parameter in most cases [1], [8], [12], [14]. A distribution for the notch-depth parameter is now required that reflects the true mechanism of the two-ray model.…”

“…3), useable for the simulation. However, the Rayleigh PDF's median is biased toward the higher end by the choice of and in the mapping mapped onto (8) Since the second ray's magnitude practically vanishes beyond a certain threshold, an appropriately chosen value for the implementation parameter , while limiting the second ray's magnitude on does not violate the requirement of . Both parameters and determine the percentage of time that the simulation spends in a nonminimum phase condition.…”

“…The Rayleigh cumulative distribution for the received signal level of (6) is closely estimated by the use of a biased Rayleigh density distribution for the second ray in the two-ray model. Deviations from the expected 10 dB/decade slope are accounted for by the biasing constant of (8). In other words, the second ray of the two-ray model exhibits a biased Rayleigh density distribution with biasing values controlling the fading severity.…”