Two-Frequency Coherence Function for the Field of a Wave Propagating Through a Multiscale Randomly Inhomogeneous Medium

Tinin, M. V.

doi:10.1007/s11141-018-9887-2

Cited by 5 publications

(8 citation statements)

References 34 publications

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“…Thus, the integral representation of the field as DWFT has a combination of the following properties (Tinin, 2018b): It can be employed to describe effects of irregularities of different scales, as inferred from its transformation into results of the methods of GO approximation, smooth perturbations, and phase screen in their areas of applicability. The partial waves used for the field expansion have a relatively simple form of GO wave without amplitude fluctuations (phase GO approximation) up to the second order of permittivity fluctuations. Eikonal fluctuations in these partial waves are independent of source and observer transverse coordinates. …”

Section: Relationship Between the Dwft Methods And Other Approximationsmentioning

confidence: 99%

“…Using DWFT wavefield expression 6, obtain for the two-frequency two-position coherence function (Tinin, 2017(Tinin, , 2018a(Tinin, , 2018b Figure 5. Increments of phase (a) and amplitude (b) after spatial processing 21 when a Gaussian irregularity is at the origin for z b = 0m (blue line), z b = 20km (red line), and z b = 50km (green line).…”

Section: Frequency Coherence Function In the Dwft Approximationmentioning

confidence: 99%

“…When a region with random irregularities is remote from sources and observers, changing variables 14 in 26 yields (Tinin, 2018b):…”

Section: Frequency Coherence Function In the Dwft Approximationmentioning

confidence: 99%

“…Using DWFT wavefield expression , obtain for the two‐frequency two‐position coherence function (Tinin, 2017, 2018a, 2018b)

\begin{matrix} lefttrue \\ {normalΓ}_{E} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}) = 〈E (ρ_{1}, ρ_{01}, normalz, ω_{1}) E * (ρ_{2}, ρ_{02}, normalz, ω_{2})〉 \\ = E_{0} (ρ_{1}, ρ_{01}, z, ω_{1}) E_{0} * (ρ_{2}, ρ_{02}, z, ω_{2}) \overset{⌢}{normalΓ} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}), \end{matrix}

where

\begin{matrix} lefttrue \\ \overset{⌢}{normalΓ} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}) = {([], {\overset{⌢}{k}}_{0} ((), z - z_{0}) / ((), 2 π))}^{2} \exp \{i {\overset{k}{true}}_{0} ({boldρ}_{1} - {boldρ}_{2}) ({boldρ}_{10} - {boldρ}_{20}) / (z - z_{0})\} \\ \times \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} d^{2} {italicsd}^{2} p \exp \{- i {\overset{k}{true}}_{01} [ps (z - {normalz}_{0}) + s ({boldρ}_{10})]\} \end{matrix}

…”

Section: Diffraction Effects In Frequency Coherence Measurements and mentioning

confidence: 99%

“…The same expression for the frequency coherence function can be derived using phase GO approximation . Note (Tinin, 2018a, 2018b) that applicability condition of the GO approximation for the frequency coherence function is weaker than applicability condition of this approximation for certain realizations before averaging, particularly for small frequency separation when X < < 1 .…”

Section: Diffraction Effects In Frequency Coherence Measurements and mentioning

confidence: 99%

See 4 more Smart Citations

Some Possibilities of Spatial Signal Processing in an Inhomogeneous Medium Based on DWFT

Tinin

Knizhin

2020

Radio Science

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The integral representation for the wave field in a multiscale inhomogeneous medium, obtained using the double weighted Fourier transform (DWFT), takes into account different diffraction effects. Spatial radio signal processing based on the DWFT inversion eliminates these effects from received signals. This paper reviews the results of studies on spatial signal processing based on the DWFT inversion. This processing has been shown to reduce amplitude scintillation and improve the resolution in diagnostics of inhomogeneous media. Moreover, elimination of diffraction effects allows us to reduce the residual error in multifrequency global navigation satellite systems. This processing also increases the channel bandwidth and therefore its capacity.

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Section: Relationship Between the Dwft Methods And Other Approximationsmentioning

confidence: 99%

Section: Frequency Coherence Function In the Dwft Approximationmentioning

confidence: 99%

“…When a region with random irregularities is remote from sources and observers, changing variables 14 in 26 yields (Tinin, 2018b):…”

Section: Frequency Coherence Function In the Dwft Approximationmentioning

confidence: 99%

“…Using DWFT wavefield expression , obtain for the two‐frequency two‐position coherence function (Tinin, 2017, 2018a, 2018b)

\begin{matrix} lefttrue \\ {normalΓ}_{E} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}) = 〈E (ρ_{1}, ρ_{01}, normalz, ω_{1}) E * (ρ_{2}, ρ_{02}, normalz, ω_{2})〉 \\ = E_{0} (ρ_{1}, ρ_{01}, z, ω_{1}) E_{0} * (ρ_{2}, ρ_{02}, z, ω_{2}) \overset{⌢}{normalΓ} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}), \end{matrix}

where

\begin{matrix} lefttrue \\ \overset{⌢}{normalΓ} (ρ_{1}, ρ_{2}, ω_{1}, ω_{2}) = {([], {\overset{⌢}{k}}_{0} ((), z - z_{0}) / ((), 2 π))}^{2} \exp \{i {\overset{k}{true}}_{0} ({boldρ}_{1} - {boldρ}_{2}) ({boldρ}_{10} - {boldρ}_{20}) / (z - z_{0})\} \\ \times \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} d^{2} {italicsd}^{2} p \exp \{- i {\overset{k}{true}}_{01} [ps (z - {normalz}_{0}) + s ({boldρ}_{10})]\} \end{matrix}

…”

Section: Diffraction Effects In Frequency Coherence Measurements and mentioning

confidence: 99%

Section: Diffraction Effects In Frequency Coherence Measurements and mentioning

confidence: 99%

See 3 more Smart Citations

Some Possibilities of Spatial Signal Processing in an Inhomogeneous Medium Based on DWFT

Tinin

Knizhin

2020

Radio Science

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show abstract

Wave field in a layer with a linear background profile and multiscale random irregularities

Tinin

2022

Waves in Random and Complex Media

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Statistical Characteristics of a Radiowave Propagating in a Multiscale Randomly Inhomogeneous Plasma

Tinin

Knizhin

2019

2019 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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Two-Frequency Coherence Function for the Field of a Wave Propagating Through a Multiscale Randomly Inhomogeneous Medium

Cited by 5 publications

References 34 publications

Some Possibilities of Spatial Signal Processing in an Inhomogeneous Medium Based on DWFT

Some Possibilities of Spatial Signal Processing in an Inhomogeneous Medium Based on DWFT

Wave field in a layer with a linear background profile and multiscale random irregularities

Statistical Characteristics of a Radiowave Propagating in a Multiscale Randomly Inhomogeneous Plasma

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