OFDM-MIMO Lab
Veermata Jijabai Technological Institute
(An Autonomous Institute of Government of Maharashtra)
Department: Electronics and Telecommunication Engineering
(OFDM-MIMO Lab)
Experiment No. 3
Aim: 1. To calculate path loss, received power and electric field using two ray ground reflection
model.
2. To plot various graph of received power by varying parameters.
Name of Students: 1. Suraj Sonawane (221090904)
2. Mukta Pathak (221091905)
3. Namrata Gadhe (221091907)
4. Sakshi Kalchavkar (221091908)
5. Purva Yeshi (221091909)
Year & Semester: Third year seventh semester
Branch: Electronics and Telecommunication
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OFDM-MIMO Lab
EXPERIMENT NO. 3
Aim: 1. To calculate path loss, received power and electric field using two ray ground reflection
model.
2. To plot various graph of received power by varying parameters.
Theory: Propagation models that predict the mean signal strength for an arbitrary transmitter-
receiver (T-R) separation distance are useful in estimating the radio coverage area of a transmitter
and are called large-scale propagation models, since they characterize signal strength over large T-R
separation distances (several hundreds or thousands of meters).
2-Ray Model:
Figure: Two-ray ground reflection model
The 2-ray ground reflection model is a simplified radio wave propagation model that considers two
main paths: a direct path from transmitter to receiver and a ground-reflected path where the signal
bounces off the ground before reaching the receiver.
The 2-ray ground reflection model used in mobile communication systems considers two paths: one
direct and one reflected off the ground, between the transmitter and receiver. In most cases, the
maximum distance between them is only a few tens of kilometers, and the Earth's surface is assumed
to be flat. The total received electric field (ETOT) is the sum of the direct line-of-sight component
(ELOS) and the ground-reflected component (Eg). The transmitter's height is represented as ht, the
receiver's height as hr, and E0 is the free space electric field at a reference distance d0 from the
transmitter, measured in volts per meter (V/m).
The resultant total E-field envelope is given by,
| ETOT |=| ELOS + Eg |
The electric field ETOT (d,t)
E0 is free space E-field in V/m at reference distance d0 from transmitter then for d>d0.
ETOT(d,t)
E0d0 d′ E0d0 d′′
ETOT(d, t) = cos (𝜔c (𝑡 − )) + (-1) cos (𝜔c (𝑡 − ))
d′ 𝑐 d′′ 𝑐
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OFDM-MIMO Lab
Figure: The method of images is used to find the path difference between the-of-sight and the
ground reflected paths.
The path difference (delta), between the line-of-sight and the ground reflected paths can be
expressed as,
∆= d′′- d′ = √(ht + hr)2 + d2 - √(ht- hr)2 + d2
The received E-field can be approximated as,2E d 2πh h k
𝐸𝑇𝑂𝑇(d) ≈ 0 0 t r ≈ V/m
d dλ d2
As long as d satisfied following equation,
( d ≫ √hrht ),
The received power at a distance d from the transmitter can be expressed as,
√hr2ht2
Pr = PtGtGr
d4
PL(dB) = 40logd – (10logGt + 10logGr +20loght + 20loghr)
Algorithm:
1. Define parameters like Power transmitted, d, ht, hr, frequency, effective aperture of antenna and
E-field from the transmitter.
2. Calculate the path loss, received power and electric filed.
3. Vary distance from 1m to 100 Km and plot the variations in received power.
4. Vary ht from 1m to 100m and plot the variations in recevied power.
5. Vary hr from 1m to 100m and plot the variations in recevied power.
Calculations:
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OFDM-MIMO Lab
Block Diagram:
Input Parameters
Pt, d, do, ht, hr, freq,
apperture, Eo, c
Calculate Wavelength
λ = c / freq
Calculate Antenna Gain Gt, Gr
Gt = 4 * pi * apperture/ λ^2
Calculate Electric Field E
E = (2 * Eo * do *2 * pi * hr * ht) /(λ * (d^2))
Calculate Received Power Pr
Pr = (Pt * Gt * Gr * ((ht * hr)^2)) /(d^4)
Calculate Path Loss PL
PL = 40 * log10(d) - (10 * log10(Gt) +10 *
log10(Gr) +20 * log10(hr) + 20 * log10(ht))
Generate d_values
ht_values, hr_values
Calculate Pr_d,
Pr_ht, Pr_hr Arrays
Plot Results
(Pr vs d, ht, hr)
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OFDM-MIMO Lab
Code:
Pt = 50;
d = 10*10^3;
do = 10^3;
ht = 50;
hr = 1.5;
freq = 900*10^6;
apperture = 0.012;
Eo = 10^-3;
c = 3*10^8;
lambda = c/freq;
Gt = 4*pi*apperture/lambda^2;
Gr = Gt;
E = (2*Eo*do*2*pi*hr*ht)/(lambda*(d^2));
Pr = (Pt*Gt*Gr*((ht*hr)^2))/(d^4);
PL = 40*log10(d) - (10*log10(Gt) + 10*log10(Gr) + 20*log10(hr) + 20*log10(ht));
display(E);
display(Gt);
display(Pr);
display(PL);
d_values = 1:10000:100000;
Pr_d = (Pt*Gt*Gr*((ht*hr)^2))./(d_values.^4);
if (d_values(end)^2) > (ht*hr)
display(Pr_d);
else
printf('The distance does not exceed the threshold. No output displayed.');
end
ht_values = 1:100;
Pr_ht = (Pt*Gt*Gr.*((ht_values.*hr).^2))/(do^4);
hr_values = 1:100;
Pr_hr = (Pt*Gt*Gr.*((ht.*hr_values).^2))/(do^4);
figure;
subplot(3, 1, 1);
plot(d_values, Pr_d);
xlabel('Distance (m)');
ylabel('Received Power');
title('Received Power vs Distance');
subplot(3, 1, 2);
plot(ht_values, Pr_ht);
xlabel('ht (m)');
ylabel('Received Power');
title('Received Power vs ht');
subplot(3, 1, 3);
plot(hr_values, Pr_hr);
xlabel('hr (m)');
ylabel('Received Power');
title('Received Power vs hr');
Output:
Part A: Calculate path loss, received power and electric field for given data.
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OFDM-MIMO Lab
Part B:
1. Vary distance from 1m to 100 Km.
2. Vary ht from 1m to 100m.
3. Vary hr from 1m to 100m.
Conclusion:
