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# Estimation of Possible Duration of Coherent Accumulation of Microwave Signals Propagating in Turbulent Atmosphere of the Earth

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M.M. Vildanov, A.G. Vinogradov

In this paper the restrictions imposed by the turbulent atmosphere on the maximum possible duration of the coherent accumulation of radio signals are discussed. Limitations arise from the fact that the large heterogeneity of the environment cause the smooth spatio-temporal changes in signal phase, and small heterogeneity are responsible for small-scale "ripples", which are superimposed on smooth changes. The contribution of large-scale fluctuations is much greater than the contribution of small-scale ones. Therefore, in the random phase shift (t) it is convenient to separate the polynomial with random coefficients (it describes a smooth change of phase): (t) = 0 + t + t2 + (t). Here (t) represents the remainder which appears due to the small-scale fluctuations. Coefficients 0,  and  are chosen to best approximate the true realization. In (t) coefficients  and  specify the random corrections to the Doppler frequency and its change. To determine the maximum time of coherent accumulation it is also necessary to find a structural function. This function characterizes the random signal phase in a turbulent environment within the correlation theory of turbulence. It is defined as the averaged square of the phase difference at two points in time (t and t') and in space (r, r'): D(r, r'; t, t')  D(|r – r'|; t – t') = [(r, t) –(r', t')]2. Knowing the structure function, we can find a coherence time at one point, which is an important characteristic of the medium. Finally, from the fact that the coherence of the signal is preserved when (t) is small relatively to the polynomial part of (t), the maximum time of coherent signal accumulation can be found. The estimates of this time for millimeter wave propagation in the troposphere are given.
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