Case 3: Calculation of polarization measurands

The processing is done in pulse pairs with an optional clutter filter.

RVP10 calculates the following:

Z D R = 10 L O G [\frac{S_{h h}}{S_{v v}}]

Z D R = 10 L O G [\frac{< {| S_{h h} |}^{2} > - N_{h}}{< {| S_{v v} |}^{2} > - N_{v}}] + G D R

P H I D P = \frac{1}{2} \arg [R_{a} R_{b}^{*}]

R H O H V = \frac{| ρ_{h v} (T_{s}) |}{{[ρ_{h v} 2 T_{s}]}^{0.25}}

Using the following definitions:

| ρ_{h v} (T_{s}) | = \frac{| R_{a} | + | R_{b} |}{2 \sqrt{S_{h h} S_{v v}}}

ρ (2 T_{s}) = \frac{\sum_{n = 1}^{\frac{M}{2 - 1}} (S_{h h}^{*} [2_{n} - 1] S_{h h} [2_{n} + 1] + S_{v v}^{*} [2_{n}] S_{v v} [2_{n} + 2])}{(\frac{M}{2 - 1}) (S_{h h} + S_{v v})}

R_{a} = \frac{M}{2} \sum_{n = 1}^{\frac{M}{2}} S_{h h}^{2 n - 1^{*}} S_{v v}^{2 n}

R_{b} = \frac{1}{\frac{M}{2}} \sum_{n = 1}^{\frac{M}{2}} S_{v v}^{2 n^{*}} S_{h h}^{2 n + 1}

The calculation of the channel powers ( $< {| S_{h h} |}^{2} >$ and $< {| S_{v v} |}^{2} >$ ) is done using alternating pulses.

In the calculation of R_b, RVP10 uses the extra M+1 sample. The gain terms cancel in the calculation of r, so in the implementation they are assumed to be 1.