In considering HF propagation in a random inhomogeneous ionosphere it is necessary to take into account regular and random caustics. Regular caustics connected with regular refraction of radio waves in the ionosphere form a skip zone and determine the maximum usable frequency (MUF) and the maximum of the oblique incidence backscatter sounding (OBS) signal. Random fluctuations of ionospheric radio rays “wash out” field enhancement in the vicinity of MUF and the maximum OBS signal. The presence of random caustics results in strong intensity fluctuations of ionospheric radio waves. The above mentioned problems are considered by the interference integral method. A scintillation index formula for strong fluctuations of oblique ionospheric radio waves is obtained. Average intensity and average pulse signal which form in the vicinity of MUF are investigated. The peculiarities of oblique multihop radio wave propagation, taking into account random ionospheric inhomogeneities, terrestrial surface roughness, and caustics focusing in skip distance are discussed.
The two‐frequency mutual coherence of HF electromagnetic field fluctuations caused by ionospheric irregularities in an oblique radio path is studied. The single scattering approximation is first developed and then extended to stronger field fluctuations by applying Rytov's approximation. Of considerable interest for wideband HF cpmmunication applications is the two‐frequency, two‐time correlation function of the channel 〈u* (ω,t1)u(ω + Ω,t1 + t)〉, where u(ω,t) is the complex amplitude of the radio wave transmitted at a frequency ω, measured by a receiver at time t. Our results show that this particular quantity behaves as though there were no diffraction effects (no Fresnel‐filtering effects). Thus the correlation time τ0 is close to Λ /ν regardless of the ratio between the irregularity size and the Fresnel length. Here Λ is the irregularity size and ν is the component of the drift velocity perpendicular to the ray path. Typical scales for the two‐frequency mutual correlation function are studied, and simple physical interpretations are developed. For example, the correlation bandwidth Ωc is determined by the condition that the rays connecting the transmitter and receiver at ω and ω + Ωc are separated from each other (in the vicinity of the reflection point) by a distance of the order of Λ. A procedure is described which allows the size of irregularities and components of plasma drift to be estimated from one of the mutual correlation functions and from the autocorrelation function. This procedure was applied to measurements from the University of Illinois sounder (transmitter is located in Platteville, Colorado, receiver in Urbana, Illinois). In the examples considered, irregularities with a size of the order of a few hundred meters drifting with a velocity 20–100 m s−1 can explain the fading. The observed magnitude of fading is consistent with an rms irregularity fluctuation of the order of a few tenths of one percent.
An integrated approach is proposed to solve the Constrained Clustering problems which are oriented on taking the opinion of a group of experts into account. A cluster and the objects to be clustered are proposed to be represented as multisets, and the distance between these to be determined by metrics in the Petrovsky multisets space. The approach is implemented within the Constraint Programming paradigm. In so doing, the significant complexity is in organizing effective processing the qualitative constraints, namely, the rules for assigning the objects to one or different clusters. The qualitative constraints are proposed to be represented and processed as table constraints of a new type, i.e., as the smart-tables of D-type. The main attention is confined to the problem of how to reduce the amount of constraints and how to simplify the Constrained Clustering problem. It is proposed to generate constraints for some pairs of objects rather than for all of them, with the generation based on a priori interval estimation of the optimal value of the clustering criterion. To do that, a modified method of multisets hierarchical clustering has been proposed. The approach proposed allows a global optimum to be found for the Constrained Clustering problems considered.
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