HF direction finding by wave front testing in a fading signal environment

Calculations are reported of the probability of observation of various degrees of phase front nonlinearity, for two and three signals incident from different directions upon a phase‐measuring array. It is assumed that the signals fade independently and that their amplitude probability densities are described by a Rayleigh law. The measure of phase front nonlinearity employed is the rms deviation from the best straight‐line fit to the measured phases along a linear array. The worst‐case condition is that of equal average powers in the incident signals. When there are two such signals present, it is shown that the probability is 0.5 that a single observation of the rms phase deviation will yield a result of 25° or less. When there are three equal‐power signals present, the corresponding probability is 0.2. Experimental measurements over a 911‐km mid‐latitude path and a 2100‐km auroral‐zone path confirm the general behavior predicted by the theory. The experimental program included concurrent measurements using FMCW, CW, and single‐sideband signals from a controlled transmitter. The range resolution capability of the FMCW signals was utilized to provide direction‐of‐arrival statistics on a mode‐separated basis. The standard deviation of the direction of arrival varied from 0.3° for E mode signals to 1.4° for F 2 high‐angle signals. The CW and single‐sideband signals were processed by selecting only those phase fronts with rms phase deviations of 10° or less. For these, direction‐of‐arrival standard deviations were in the range 0.6°–0.9° with slightly smaller deviations being observed for the CW signals.