# Step 4-B: Field Strength of the Configuration (Actual Value)

For each antenna, the measured field strength in the point P is determined. The computation is similar to the computation for the isotropic radiator.
• Distance d between P and radiation center of the antenna (xant, yant, zant)
(1) $d=\sqrt{{\left({x}_{1}-{x}_{geo}\right)}^{2}+{\left({y}_{1}-{y}_{geo}\right)}^{2}+{\left({z}_{1}-{z}_{geo}\right)}^{2}}$
• Computation of power density Sant of the direct ray at point P
(2) ${S}_{ant}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{ant}}}{4\pi {d}^{2}}\text{\hspace{0.17em}}$
with Ptant representing the Tx power of the antenna.
• Computation of effective electrical field strength Ean-FSt at P based on power density Sant and impedance of free space ZF0 = 120 πΩ
(3) ${|{\underset{_}{E}}_{iso}|}^{2}\text{\hspace{0.17em}}={S}_{iso}×{Z}_{F0}$
• Computation of penetration / transmission loss LT .
• Subtraction of penetration / transmission loss LT leads to actual received electric field strength at point P (based on direct ray):
(4) ${\underset{_}{E}}_{ant\text{\hspace{0.17em}}0}\text{\hspace{0.17em}}={E}_{ant-FS}-{L}_{T}$

Depending on the path length d and the frequency f, the phase φ of the signal is determined (with wavelength λ and velocity of light c0):

(5) ${\phi }_{i}=\frac{d}{\lambda }×360°=⥂\frac{d}{{c}_{0}}f×360°$

• Additionally, the computation of reflected rays is possible.

For the computation of reflected rays, each object is examined whether a reflection is possible or not.

Additionally, the penetration / transmission must be considered if the reflected ray intersects further.

If the reflected rays exist (point of reflection Q is inside the object), this leads to the power density

(6) ${S}_{ant}\text{\hspace{0.17em}}=\frac{{P}_{{t}_{ant}}}{4\pi {\left({r}_{1}+{r}_{2}\right)}^{2}}\text{\hspace{0.17em}}$
with Ptant representing the transmitter power of the antenna.

• Computation of the effective electric field strength Ean-FSt at point P based on power density Sant and impedance of free space ZF0 = 120 πΩ:
(7) ${|{\underset{_}{E}}_{ant-refl}|}^{2}\text{\hspace{0.17em}}={S}_{ant}×{Z}_{F0}$
• The contributions of the direct and reflected rays are superposed considering their phases:
(8) ${E}_{Ant}=\sum {E}_{i}=\sum {E}_{an{t}_{i}\text{\hspace{0.17em}}}\left(\mathrm{cos}{\phi }_{i}+j\mathrm{sin}{\phi }_{i}\right)$
• Computation of the reflection loss LR of the reflected ray.
• Computation of the transmission/penetration loss LT of the reflected ray.
• Subtracting the transmission loss LT and the reflection loss LR leads to the received field strength at point P (on the basis of the reflected ray):
(9) ${\underset{_}{E}}_{ant\text{​}\text{ }\text{ }i}\text{\hspace{0.17em}}={E}_{ant-refl}-{L}_{T}-{L}_{R}$

Depending on the path length d of the reflected ray and the frequency f (and wavelength λ), the phase j of the reflected ray is determined by the velocity of light c0:

(10) ${\phi }_{i}=\frac{d}{\lambda }×360°+{n}_{R}^{}×180°=⥂\frac{d}{{c}_{0}}f×360°+{n}_{R}×180°$

For each reflection (nR reflections are in the ray), an additional phase shift of 180° is added.

These rays are determined for each antenna, and all rays are superposed with the equation above. The total field strength EAnt is the magnitude of the coherent (including phase) superposed field strengths of the rays of the individual antennas.