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 (x_ant, y_ant, z_ant)
(1) $d = \sqrt{{(x_{1} - x_{g e o})}^{2} + {(y_{1} - y_{g e o})}^{2} + {(z_{1} - z_{g e o})}^{2}}$
Computation of power density S_ant of the direct ray at point P
(2) $S_{a n t} = \frac{P_{t_{a n t}}}{4 π d^{2}}$
with P_tant representing the Tx power of the antenna.
Computation of effective electrical field strength E_an-FSt at P based on power density S_antand impedance of free space Z_F0 = 120 πΩ
(3) ${| {\underline{E}}_{i s o} |}^{2} = S_{i s o} \times Z_{F 0}$
Computation of penetration / transmission loss L_T .
Subtraction of penetration / transmission loss LT leads to actual received electric field strength at point P (based on direct ray):
(4) ${\underline{E}}_{a n t 0} = E_{a n t - F S} - L_{T}$
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) $φ_{i} = \frac{d}{λ} \times 360 ° = ⥂ \frac{d}{c_{0}} f \times 360 °$
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) $S_{a n t} = \frac{P_{t_{a n t}}}{4 π {(r_{1} + r_{2})}^{2}}$
with P_tant representing the transmitter power of the antenna.

Figure 1. Computation of the angle of reflection.
Computation of the effective electric field strength E_an-FSt at point P based on power density S_ant and impedance of free space Z_F0 = 120 πΩ:
(7) ${| {\underline{E}}_{a n t - r e f l} |}^{2} = S_{a n t} \times Z_{F 0}$
The contributions of the direct and reflected rays are superposed considering their phases:
(8) $E_{A n t} = \sum E_{i} = \sum E_{a n t_{i}} (\cos φ_{i} + j \sin φ_{i})$
Computation of the reflection loss L_R of the reflected ray.
Computation of the transmission/penetration loss L_T of the reflected ray.
Subtracting the transmission loss L_T and the reflection loss L_R leads to the received field strength at point P (on the basis of the reflected ray):
(9) ${\underline{E}}_{a n t i} = E_{a n t - r e f l} - L_{T} - L_{R}$
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) $φ_{i} = \frac{d}{λ} \times 360 ° + n_{R}^{} \times 180 ° = ⥂ \frac{d}{c_{0}} f \times 360 ° + n_{R} \times 180 °$

For each reflection (n_R 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 E_Ant is the magnitude of the coherent (including phase) superposed field strengths of the rays of the individual antennas.