Name: Aryan Pund
Reg. ID: 221090054
Expt. ---- 02 Date: 28/07/25
OFDM Experiment No.: 02
AIM: To analyze the Two-Way Ground Reflection Model for wireless signal propagation and
study the effects of various parameters such as distance transmitter height and receiver height
on the path loss using MATLAB.
SOFTWARE USED: MATLAB R2024a
THEORY:
The Two-Way Ground Reflection Model (also known as the Two-Ray Model) is an essential
wireless propagation model that extends Friis' Free Space Model by considering both the direct
line-of-sight (LOS) path and the ground-reflected path between the transmitter and receiver.
This model is widely used in wireless communication, particularly for outdoor and large-scale
environments.
Concept of the Two-Way Ground Reflection Model:
In real-world communication systems, radio waves do not always travel in a straight line from
the transmitter to the receiver. Instead, they may reflect off the ground or other surfaces, leading
to multiple signal components reaching the receiver.
The received signal is the superposition of:
1. Direct LOS Path: The signal travels in a straight line from the transmitter to the receiver.
2. Ground-Reflected Path: The signal reflects off the ground before reaching the receiver,
introducing a phase shift due to the additional path length.
The received power is influenced by interference between these two paths, which can be
constructive (increasing power) or destructive (reducing power), depending on the phase
difference between them.
Mathematical Model
The received power in the Two-Way Ground Reflection Model is given by:
𝑃𝑡 𝐺𝑡 𝐺𝑟 (ℎ𝑡 ℎ𝑟 )2
𝑃𝑟 =
𝑑4 𝐿
where:
• Pr= Received power (W)
• Pt = Transmitted power (W)
• Gt, Gr = Transmitter and receiver antenna gains
• ht, hr = Heights of the transmitter and receiver (m)
• d = Distance between transmitter and receiver (m)
• Ls = System loss factor
Unlike Friis' equation, where received power decreases as 1𝑑2, this model follows a 1𝑑4,
dependence, indicating a higher power loss at longer distances.
Effects of System Parameters
• Distance (d): As distance increases, received power decreases significantly due to the 1𝑑4
relationship. Frequency (f): Higher frequencies result in shorter wavelengths, leading to
higher antenna gains but also increased path loss.
• Antenna Heights (ht , hr): Taller antennas reduce ground reflection losses and improve
signal strength.
• System Loss (L): Represents losses in hardware, propagation medium, and environmental
conditions.
In wireless communication, the electric field strength (E) represents the intensity of the
electromagnetic wave received at a certain distance from the transmitter. It is a key factor in
determining how much power a receiving antenna can extract from the wave. The strength of
the electric field depends on several parameters including the transmitted power, frequency
(or wavelength), the distance between transmitter and receiver, and the heights of the
antennas. As the distance increases, the electric field strength decreases significantly due to
the spreading of the wave and environmental losses. For far-field conditions, especially in the
two-ray ground reflection model, the electric field is also influenced by the constructive or
destructive interference between the direct and reflected paths. Accurate estimation of electric
field strength helps in evaluating coverage, interference, and compliance with safety exposure
limits in wireless systems.
4𝜋𝐸0 𝑑0 ℎ𝑡 ℎ𝑟 𝜆
𝐸=
𝑑2
Where:
• E: Electric field strength at the receiver (in V/m)
• E0: Reference electric field (in V/m)
• d0: Reference distance (in meters)
• ht , hr: Transmitter and receiver antenna heights (in meters)
• λ: Wavelength of the signal (in meters)
• d: Distance between transmitter and receiver (in meters)
BLOCK DIAGRAM:
Start
Initialize Parameters Pt = 1,Gt = 1.5, Gr = 1
ht_fixed = 50 m,hr_fixed = 10 m,d_fixed = 5 km
E0 = 1e-3 V/m, f = 1.5 GHz, c = 3e8 m/s
Vary d,(1 to 10 km)
Pr_d = Pt*Gt*Gr* ht²*hr² / d⁴
Plot Pr vs d (subplot 1)
Vary ht, hr ;(ht: 1–100 m) (hr: 1–50 m)
Pr_ht = Pt*Gt*Gr*ht²*hr² / d_fixed⁴
Plot Pr vs ht (subplot 2)
Pr_hr = Pt*Gt*Gr*ht²* hr² / d_fixed⁴
Plot Pr vs hr (subplot 3)
Compute Electric Field at d_fixed (in m) λ = c / f
E = (4π * E₀ * d₀ * ht * hr * λ) / d²
Print Electric Field Value E
End
ALGORITHM:
1. Start the Program:
• Clear any previous data, close open figures, and reset the workspace.
2. Initialize Parameters:
• Define the transmission power, antenna gains, fixed heights for transmitter and
receiver, and a fixed distance for some calculations.
3. Analyze Path Loss vs Distance:
• Create a range of distances from a small value up to 10 km.
• For each distance, calculate the received power using the two-ray ground reflection
model.
• Compute the corresponding path loss in decibels.
• Plot the path loss against distance to observe how it increases as the receiver moves
farther from the transmitter.
4. Analyze Path Loss vs Transmitter Height:
• Keep the receiver height and distance constant.
• Vary the transmitter height over a defined range.
• For each height, calculate the received power and then compute the path loss.
• Plot the path loss against transmitter height to see how elevation improves signal
strength.
5. Analyze Path Loss vs Receiver Height:
• Keep the transmitter height and distance fixed.
• Vary the receiver height over a defined range.
• For each receiver height, compute the received power and path loss.
• Plot the path loss against receiver height to study its impact on signal reception.
6. Calculate Electric Field Strength:
• Define basic physical parameters like frequency, speed of light, and reference electric
field.
• Use these along with antenna heights and fixed distance to estimate the electric field
strength at the receiver.
• Display the calculated electric field.
7. End of Program:
• The program completes after plotting all three graphs and printing the electric field
value.
MATLAB CODE & OUTPUT:
CODE – clc; clear; close all;
Pt = 10;
Gt = 1.5;
Gr = 1;
ht_fixed = 50;
hr_fixed = 10;
d_fixed = 5;
d_fixed_m = d_fixed * 1000;
d = linspace(0.1, 10, 1000);
Pr_d = Pt * Gt * Gr * (ht_fixed^2) * (hr_fixed^2) ./ (d.^4);
PL_dB_d = 10 * log10(Pt ./ Pr_d);
figure;
subplot(3,1,1);
plot(d, PL_dB_d, 'r', 'LineWidth', 2);
xlabel('Distance d (km)');
ylabel('Path Loss (dB)');
title('Path Loss vs Distance d (ht=50m, hr=10m, Pt=10W)');
grid on;
ht = linspace(1, 100, 1000);
Pr_ht = Pt * Gt * Gr .* (ht.^2) * (hr_fixed^2) / (d_fixed^4);
PL_dB_ht = 10 * log10(Pt ./ Pr_ht);
subplot(3,1,2);
plot(ht, PL_dB_ht, 'b', 'LineWidth', 2);
xlabel('Transmitter Height ht (m)');
ylabel('Path Loss (dB)');
title('Path Loss vs Transmitter Height ht');
grid on;
hr = linspace(1, 50, 1000);
Pr_hr = Pt * Gt * Gr * (ht_fixed^2) .* (hr.^2) / (d_fixed^4);
PL_dB_hr = 10 * log10(Pt ./ Pr_hr);
subplot(3,1,3);
plot(hr, PL_dB_hr, 'g', 'LineWidth', 2);
xlabel('Receiver Height hr (m)');
ylabel('Path Loss (dB)');
title('Path Loss vs Receiver Height hr');
grid on;
E0 = 1e-3;
f = 1.5e9;
c = 3e8;
lambda = c / f;
d0 = 1000;
ht = ht_fixed;
hr = hr_fixed;
E = (4 * pi * E0 * d0 * ht * hr * lambda) / (d_fixed_m^2);
fprintf('Electric Field E = %.4e V/m\n', E);
OUTPUT –
CONCLUSION:
