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Laboratory Experiment #2
Investigation of non-linear distortion in FDMA systems
Objective:
By performing this lab, the student will be able to visualise how non-linear distortion affects the
communication system in operation and other systems operating in other frequency bands as well.
Tool:
MATLAB program.
Introduction:
This is a practical demonstration of non-linear distortion in FDMA systems, which was studied
theoretically in lectures. This effect is known as inter-modulation distortion (IMD). In this
experiment, the band from 5 MHz to 6 MHz is multiple accessed using the FDMA technique,
where the band is divided into 5 FDMA channels of 200 KHz each. Before transmission, the BS
amplifies all signals on the band using a power amplifier operating near saturation. As a result the
input-output relationship is written as:
𝑦(𝑡) = 10𝑥(𝑡) + 0.01𝑥2(𝑡) + 0.001𝑥3(𝑡) ……………...(1)
We will use MATLAB to find the effect of IMD on signal output. For simplicity, we assume that only
carriers are transmitted (no data). i.e.
𝑥(𝑡) = 10{cos 2𝜋𝑓1𝑡 + cos 2𝜋𝑓2𝑡 + ⋯ + cos 2𝜋𝑓5𝑡}……..(2)
Procedure:
Open a new Matlab script files and execute the following tasks.
Task (1): Set initial parameters
Write your code heading by setting your initial parameters such that the maximum displayed
frequency is 20 MHz with frequency resolution of 1 KHz. Note Nyquist rate sampling is applied.
Task (2): Synthesize input signal 𝒙(𝒕) and plot its PSD
Write the appropriate code to model the signal 𝑥(𝑡) according to Eq. (1) and plot its single-sided
PSD.
Task (3): Calculate output signal 𝒚(𝒕) and plot its PSD
Write the appropriate code to model the signal 𝑦(𝑡) according to Eq. (2) and plot its single-sided
PSD.
Electrical & Communications Engineering Department
Module Code: 22ECE36H
Module Title: Wireless Communication Technologies
Semester: 1 ‒ 2022/2023
Module Leader: Dr. Mohammad Abdellatif
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Task (4): Calculate Carriers generated by non-linear effect and plot their PSD
Plot the PSD of the IMD-generated signals and list the frequency bands at which IMD is observed
in the table below.
Bands 1 2 3 4
Frequency range
Homework:
Let a GSM base station be transmitting over the entire GSM-900 DL band (935.1−959.9 MHz), i.e.
124 channels of 200KHz each were active. Apply the above procedure to the whole GSM system
and regenerate the PSD plots for this case. Your model should account for the following
1) Maximum observation frquency 𝑓𝑚𝑎𝑥 = 2 GHz.
2) You need a way to construct 𝑥(𝑡) for all users in a short code segment.
3) Due to the application of power control mechanism, the base station transmits lower power
levels to nearby mobile stations, while it transmits higher power levels to users on the cell
edge. Transmitted power can vary between 5 dBm to 40 dBm with a step of 2 dBm. Use an
appropriate probability distribution function to model the randomised transmitted power
levels.
Electrical & Communications Engineering Department
Module Code: 22ECE36H
Module Title: Wireless Communication Technologies
Semester: 1 ‒ 2022/2023
Module Leader: Dr. Mohammad Abdellatif
