The Papua New Guinea University of Technology
Department of Electrical and Communications Engineering
EE321 Communications Systems
MATLAB Assignment #1 - Noise, SNR, and Power Spectral Density
Type: Independent
Total Marks: 100
Learning Objectives:
The learning objectives that this assessment covers include:
1. Apply mathematical signals & systems theories to advanced communication
systems
2. Evaluate and critique common modern communication systems in terms of their
properties, advantages and disadvantages
3. Simulate the operation of communication systems to predict their performance
Report guidelines
For the lab report, you will create a PowerPoint presentation (or use a similar presentation
program), save it as a PDF, and submit it in Google Classroom on or before 10PM on the
23rd August 2023. You will also submit your MATLAB code as a PDF. All submitted Matlab
code should be well organized and commented with clear comments for easy readability. All
submitted plots should be easy to see and well-labelled.
You are to work independently. This is not a team assignment. Feel free to help your
fellow classmates understand principles and concepts, but please do not directly
share significant portions of your MATLAB code.
Your presentation will have 8 slides. Please include a slide number in the footer of each
slide. To earn full credit your presentation must contain the slides in the order asked for in
this lab. If you miss a slide, please leave a blank slide in its place so that you have still have
exactly 8 slides total. Your first slide should be:
•
Slide 1: Title slide with your name, student ID number, date, lab name, subject name
and Code.
Procedure
You will be asked to create a noisy sinusoid in MATLAB It will be helpful for you to review
the following material before you begin this assignment: Tutorial: PSD, Autocorrelation, and
Noise in MATLAB.
1. Create some noise
a. Consider white Gaussian noise 𝑋𝑛𝑜𝑖𝑠𝑒 (𝑡). Create a sampled, discrete-time
representation of this noise in MATLAB using the "randn" function. The sample
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rate is 𝑓𝑠 = 150𝐻𝑧 and the total time-duration of the noisy signal is 𝑇 =
10 𝑠𝑒𝑐𝑜𝑛𝑑𝑠. The noise should be created such that it has a nominal power
spectral density (PSD) of 0.25 𝑊 ⁄𝐻𝑧. Calculate the average power 𝑃𝑔 , the
average PSD, and plot the PSD in 𝑾⁄𝑯𝒛 over frequency. The title of your plot
should be descriptive and include your full name. Label the 𝑦 − 𝑎𝑥𝑖𝑠 "PSD
(𝑾⁄𝑯𝒛)". Label the 𝑥 − 𝑎𝑥𝑖𝑠 "Frequency (𝐻𝑧)". The font size for labels, titles,
and axis ticks should be set to be size 14 or larger, so it's easy to read. Present
your results in Slide 2.
b. Generate and plot a histogram of the noise in MATLAB using the "histogram"
function. The number of bins should be in the 20 − 50 range. Choose a value
that results in a bell-shaped histogram. The title of your plot should be
descriptive and include your full name. Clearly label the 𝑥 − and 𝑦 − 𝑎𝑥𝑒𝑠 with
descriptive names. The font size for labels, titles, and axis ticks should be set
to be size 14 or larger, so it's easy to read. Present your plot in Slide 3.
2. Create a clean sinusoid
a. Consider a clean, continuous-time sinusoid 𝑥(𝑡) = 𝐴0 cos(2𝜋𝑓0 𝑡). Create a
sampled, discrete-time representation of this signal in MATLAB. As before, the
sample rate is 𝑓𝑠 = 150𝐻𝑧 and the total time-duration of the signal is 𝑇 =
10 𝑠𝑒𝑐𝑜𝑛𝑑𝑠. The frequency of the sinusoid is 25𝐻𝑧 and the amplitude of the
sinusoid should be set such that the average power of the sinusoid is 𝑃𝑔 =
20𝑊. In MATLAB calculate the average power 𝑃𝑔 and plot the PSD
in 𝑾⁄𝑯𝒛 over frequency. The title of your plot should be descriptive and
include your full name. Label the 𝑦 − 𝑎𝑥𝑖𝑠 "PSD (𝑾⁄𝑯𝒛)". Label the 𝑥 − 𝑎𝑥𝑖𝑠
"Frequency (𝐻𝑧)". The font size for labels, titles, and axis ticks should be set
to be size 14 or larger, so it's easy to read. Present your plot in Slide 4.
3. Create a noisy sinusoid
a. Add together the noise and the clean sinusoid from the previous steps to
create a noisy sinusoid: 𝑥(𝑡) = 𝐴0 cos(2𝜋𝑓0 𝑡) + 𝑋𝑛𝑜𝑖𝑠𝑒 (𝑡). The sampling
frequency, time-duration, signal amplitude, and noise are the same as defined
in the previous steps. Use MATLAB to calculate the signal-to-noise ratio (SNR)
and plot the PSD in 𝒅𝑩⁄𝑯𝒛 over frequency. The title of your plot should be
descriptive and include your full name. Label the 𝑦 − 𝑎𝑥𝑖𝑠 "PSD (𝒅𝑩⁄𝑯𝒛)".
Label the 𝑥 − 𝑎𝑥𝑖𝑠 "Frequency (𝐻𝑧)". The font size for labels, titles, and axis
ticks should be set to be size 14 or larger, so it's easy to read.
What is the carrier-to-noise ratio (CNR)? The CNR is discussed here: Carrierto-noise ratio in cable networks. Present your results and the plot in Slide 5.
b. Generate a time-domain plot of the noisy sinusoid using MATLAB. Zoom in to
the plot, so that two or three periods of the sinusoid are visible. The title of your
plot should be descriptive and include your full name. Label the 𝑦 − 𝑎𝑥𝑖𝑠
"Amplitude". Label the 𝑥 − 𝑎𝑥𝑖𝑠 "Time (𝑠)". The font size for labels, titles, and
𝑎𝑥𝑖𝑠 ticks should be set to be size 14 or larger, so it is easy to read. Present
your plot in Slide 6.
4. Clean the noise with a bandpass filter
a. Use MATLAB to create and apply an FIR bandpass-filter to the noisy sinusoid.
The bandpass filter should have a narrow bandwidth and pass the sinusoid
while filtering out the majority of the white noise. This should significantly
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improve the SNR. For the filtered sinusoid, use MATLAB to calculate the new
signal-to-noise ratio (SNR) and plot the PSD in 𝒅𝑩⁄𝑯𝒛 over frequency. The
title of your plot should be descriptive and include your full name. Label the
𝑦 − 𝑎𝑥𝑖𝑠 "PSD (𝒅𝑩⁄𝑯𝒛)". Label the 𝑥 − 𝑎𝑥𝑖𝑠 "Frequency (𝐻𝑧)". The font size
for labels, titles, and axis ticks should be set to be size 14 or larger, so it's easy
to read. Present your results and the plot in Slide 7.
b. Generate a time-domain plot of the filtered noisy sinusoid using MATLAB.
Zoom in to the plot, so that two or three periods of the sinusoid are visible. The
title of your plot should be descriptive and include your full name. Label the
𝑦 − 𝑎𝑥𝑖𝑠 "Amplitude". Label the 𝑥 − 𝑎𝑥𝑖𝑠 "Time (𝑠)". The fontsize for labels,
titles, and axis ticks should be set to be size 14 or larger, so it's easy to read.
Present your plot in Slide 8.
Marking Scheme:
The milestones and allocated marks as shown in the able below. This assessment item is
worth 100 marks which is 7.5% of overall subject assessment. Details marking criteria will
be posted online.
Particular
Marks Allocated
Slide 1: Title slide with your name, student ID number, date, lab name, subject
name and Code.
5 marks
Slide 2 & 3: Noise creation
a. Calculate:
i) the average power 𝑃𝑔
ii) the average Power Spectral density (PSD)
iii) Power Spectral Density (PSD) plot
5 marks
5 marks
5 marks
b. Generate and plot the Histogram of the noise
10 marks
Slide 4: A clean sinusoid creation
a. Calculate:
i) the average power 𝑃𝑔
ii) Power Spectral Density (PSD) plot
5 marks
5 marks
Slide 5 & 6: a noisy sinusoid creation
a. Calculate:
i) the Signal-to-Noise Ratio (SNR)
ii) Power Spectral Density (PSD) plot
5 marks
5 marks
b. Generate a time-domain plot of the noisy sinusoid
10 marks
Slide 7 & 8: Clean the noise with a bandpass filter
a. Calculate:
i) the New Signal-to-Noise Ratio (SNR)
ii) Power Spectral Density (PSD) plot
5 marks
5 marks
b. Generate a time-domain plot of the filtered noisy sinusoid
10 marks
MATLAB code
EE321 Communication Systems
20 marks
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