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From Equation 11, the delay-Doppler function S v,τ) consisted of the Dirac function in delay-Doppler point (τ q,v q ) which corresponds to reflecting path q and is supposed to be sparse.
When T1 is set as an ultrasound transmitter, the received signal of R1 consists of the signal propagated from a directly transmitted path, a reflecting path from the bubble and the inner pipe wall, and an arc path in the pipe wall.
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The method can account for any number of reflecting paths.
where ({bar {boldsymbol {G}}}_{mathrm {s}}) is a complex deterministic matrix with ([{bar {boldsymbol {G}}}_{mathrm {s}}]_{mj}=c_{mj}), which represents the antenna intra-leakage and inter-coupling coefficients related to the direct path, and ({tilde {boldsymbol {G}}}_{mathrm {s}}) is a complex random matrix that represents the reflection coefficients related to the reflected path.
Hence, six types of CI are valid: 0R0D (direct path), 1R0D (single reflected path), 2R0D, 0R1D, 1R1D and 2R1D.
In this model, j n contains not only the effect of the direct path delay but also that of other reflected path delays.
The first Fresnel zone dimensions are used to determine if the receiving antenna's power pattern, relative to the specularly reflected path, is within the area of the snow-covered prairie grass field.
Assuming that a Lambertian LED is placed at p (r, θ, φ) with a distance of r to the fisheye lens, then, with the channel DC gain on the direct path H d (0) and the reflected path dH ref(0) as defined in [1, 18], the received optical power is defined as {P}_r={P}_tleft[{H}_d(0)+{displaystyle {int}_{mathrm{walls}}d{H}_{mathrm{ref}}(0)}right] (1 where P t is the transmitted optical power.
The acoustic localization/communication is affected by many environmental factors like reflected paths, transmission losses and speed of sound.
Reflected paths result into absorption and scattering of the transmitted signal that reduces the intensity of sound energy.
The calibration consists in extracting relevant multipath components (MPCs), for instance once reflected paths, simultaneously from the model and measurement.
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Justyna Jupowicz-Kozak
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