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Experiment 4A & 4B: Digital Modulation & Channel Coding
June 11, 2024
1. Introduction
Modern wireless communication systems involve many well-coordinated steps and compo- nents to deliver a message from a transmitter to a receiver. A simplified system diagram of such a wireless communication system can be found in Figure. 1.1.
On the transmitter side, the process begins with the information source, which generates the data to be transmitted. This data is converted into an electrical signal by the input transducer. The base-band processor then conditions the signal, making it ready for encod- ing. The encoder applies error correction codes, and the modulator combines the encoded signal with a carrier frequency for transmission. The up converter shifts this modulated signal to a higher frequency, and the power amplifier boosts its strength. Finally, the radio transmitter sends the amplified signal through the antenna into the air.
The transmission medium, typically air, allows the electromagnetic waves to travel from the transmitter to the receiver. The receiver’s antenna captures these waves and passes them to the radio receiver, which converts them into a form suitable for further processing. The down converter shifts the frequency of the received signal to a lower frequency, making it ready for demodulation. The demodulator extracts the base-band signal from the carrier, effectively reversing the modulation process. The decoder then applies error correction to recover the original data format.
On the receiver side, the base-band processor conditions the decoded signal for out- put. The output transducer converts this processed electrical signal back into a human- understandable form, such as sound through a speaker or an image on a screen. The infor- mation receiver presents the final information to the user, completing the communication process. This system demonstrates the essential components and steps involved in modern wireless communication, highlighting the transformation of data from its original form to a transmitted signal and back to its original form at the receiver’s end.
This lab manual is designed for students to gain hands-on experience with different digital modulation schemes and channel coding techniques using MATLAB. By performing
Figure 1.1: A simplified system diagram of modern wireless communication systems.
the experiments outlined in this manual, students will:
• Develop an understanding of the digital modulation techniques such as Binary Phase Shift Keying (BPSK) and Quadrature Amplitude Modulation (QAM) in modern wire- less communication systems.
• Learn to implement and analyse the performance of these modulation schemes over an Additive White Gaussian Noise (AWGN) channel.
• Explore various channel coding techniques ranging from old-fashioned Hamming codes to state-of-the-art codes.
• Evaluate the effectiveness of these techniques with the well-known metric — the Bit Error Rate (BER).
By the end of this lab, students should be able to:
• Understand the principles and applications of different digital modulation and channel coding schemes.
• Improve the MATLAB skills for their future careers.
• Improve analytical skills and critical thinking strategies.
2. Crashcourse on MATLAB
MATLAB’s user-friendly interface and straightforward syntax make it an excellent choice for you while learning science and engineering concepts throughout their courses. Specifically for this course, MATLAB allows you to focus on understanding telecommunications concepts without getting bogged down by complex programming constructs (such as C/C++). This section will be a preliminary for MATLAB programming, but you are welcome to seek external sources if you wish to learn about this useful skill. Besides, feel free to have a look at the official tutorial about the fundamentals of MATLAB programming via this link: https: //au.mathworks.com/help/matlab/language-fundamentals.html?s_tid=CRUX_lftnav.
2.1. MATLAB Environment
Familiarise yourself with the MATLAB desktop environment, which includes:
• Command Window. This window normally sits at the bottom of your screen. You can type in any commands/functions/scripts that you wish to run in this window. This is where you can search the documentation of a function of your interest.
• Workspace. It is at the right side of your screen. Initially it is empty but you will see a list of variables stored in the memory of MATLAB. You can double click the variable of your interest to examine its value when the script. stops running (i.e. when the script finishes, paused due to a breakpoint or terminates due to some errors).
• Current Folder. This section will show your current working directory.
• Editor. The place to write your MATLAB script. After clicking anywhere in the editor, the menu bar at the top automatically changes to show the buttons about different ways of running the current script. You can click "Run" to run the whole script or select some parts of the script and then click "Run selection".
2.2. MATLAB Variables and Operations
Start with basic commands such as arithmetic operations, creating variables, and using built-in functions. For example:
a = 5;
b = 10;
c = a + b;
disp(c); % This will display the result of a + b
Variables can be a vector or a matrix and you can apply all the matrix operations to these variables. However, it is your job to make sure the dimensions of your operants are right for the operation. For example, you can add 2 vectors with the same dimension together:
v = [1, 2, 3, 4]; M = [5, 6, 7, 8];
result = M + v % will give you the correct result .
However, you cannot perform matrix multiplication on the two vectors due to the wrong dimensions of v and M :
v = [1, 2, 3, 4]; M = [5, 6, 7, 8];
result = M * v % will give you an error .
There is a short-hand syntax in MATLAB if you wish to perform element-to-element oper- ations (mostly multiplication and division) by add a "." (period) before the operation you wish to perform. For example, you can calculate the element-to-element division of v and M , you can do the following:
v = [1, 2, 3, 4]; M = [5, 6, 7, 8];
result = M ./ v % will give you the correct result .
However, if you miss the "." in the front of "./", it means that you are trying to perform the matrix division, which will give you an error in the last example.
2.3. The “end”
You may find that your codes stop working after you move your loops/if-else branches to someplace else. If this happens, the first thing you should check is whether you move the correct “end” together with your loops/if-else branches. The MATLAB keyword, “end”, marks the end of a code block, where the code block could be your loop body or your if-else statements, just like the close curly braces ("}") in many programming languages such as C/C++.
2.4. Scripts and Functions
Code Modularisation is always a good practice in programming. The benefit of the modu- larisation may lead to the following advantages:
• Reuse your code. Modularisation allows for the reuse of code across parts of scripts. Once a module is created and tested, it can be reused without modification, saving time and reducing the likelihood of introducing errors. This is particularly beneficial in MATLAB, where complex algorithms and functions can be encapsulated into reusable scripts or functions.
• Easier Testing and Debugging. Testing individual functions independently is more straightforward than testing a length MATLAB script. By modularising your codes, you can test your implementation separately, which will significantly help you identify and fix bugs while working on the lab tasks.
Before working on this experiment, you are recommended to read through the tutorial pages about defining and using your own functions in MATLAB via this link: https://au. mathworks.com/help/matlab/functions.html?s_tid=CRUX_lftnav.
Creating your own function(s) can be very useful when you are required to complete tasks (e.g. Task 2 of Part A) from scratch. The recommended practice is to define your own function(s) in separate files and call your defined function(s) wherever you need them. This can be done by clicking the downward triangle under the button “New” and selecting “function”. However, there are a few things to keep in mind:
• Keep the files containing your own functions under the same directory of your Lab 4 files.
• Ensure that the name of your function is exactly the same as the name of the function file.
For example, as shown below, I created a function named “addNumbers” in an empty .m file:
% Example of a function
function output = addNumbers(x, y) output = x + y;
end
When I save this file, I need to make sure that the saved file is named “addNumbers.m”. Now, if I would like to call this “addNumbers” function, I can simply do the following:
% Example of calling a function % . . . . . some Matlab codes
a = 1; b = 2;
c = addNumbers(a,b);
% . . . . . some Matlab codes
2.5. Debugging in MATLAB
Debugging is an essential part of the programming process. Debugging your codes allows you to understand how the codes work and identify the source of your error. Fortunately, due to its own feature, MATLAB will always run your code until an error is generated. MATLAB provides robust (more importantly, easy-to-use) debugging tools that help you detect and correct issues. Here’s a brief example of a typical debugging workflow in MATLAB:
• Set a Breakpoint: Set a breakpoint at the beginning of a suspicious code section by clicking the line number in the Editor.
• Run the Program: Run your program. MATLAB will pause execution at the break- point, allowing you to inspect the program’s current state. Now it is time to examine your values of all the variables in the workspace.
• Step Through Code: Use step-by-step execution commands to move through your code, examining the changes in the variable values and the execution flow and see if the execution matches what you expect.
• Analyze Errors: If an error occurs, read the error message carefully to understand the nature of the problem. Use the information provided to make necessary corrections.
• Modify and Continue: Make any necessary changes to your code and restart the program. Repeat the debugging process as needed until all issues are resolved.
Debugging can be very helpful when you have your own functions defined.
2.6. MATLAB Tips
Some additional tips might be useful to you:
• Remove the semicolon at the end of a statement to show you the execution result of that statement. For example, in the codes below, the value of d will be shown in the command window, but the value of c will be hidden from you. Note that both c and d are executed.
% Example of calling a function % . . . . . some Matlab codes
a = 1; b = 2; e = 3;
c = addNumbers(a,b); d = addNumbers(e,b)
% . . . . . some Matlab codes
• Pause the execution of your script just before an error is generated. Clicking the downward triangle under the button "Run" will show you additional ways of running your script. By selecting "pause on error", MATLAB will pause just before an error is generated and enter the debugging mode. This can help you identify where your code will go wrong and make it easier for you to fix it.
2.7. Additional Reading on Channel codes and digital modulation
in MATLAB
With the MATLAB communication toolbox, you can simulate all the critical components of a modern communication system. Additional reading closely related to Part A of this experi-ment can be found here: https://au.mathworks.com/help/comm/error-detection-and-correction. html. For Part B, additional reading can be found here: https://au.mathworks.com/help/comm/modulation.html.
3. Part A: Channel Codes
In this part, you will investigate the different types of channel codes and observe how these codes can improve the overall performance of a simulated communication system. To com- plete this lab, you may use your own laptop during the lab session or the computers provided in the lab. You are highly recommended to install and use MATLAB Communication Tool- box throughout this lab.
3.1. Procedure
1. Download the Lab 4 package from TELE4652 pages on Moodle and extract the down- loaded file to any directory you prefer.
2. Start MATLAB and navigate to the extracted Lab 4 package.
3. Go through the file "Lab4AcodesForStudents.m".
4. Follow the instructions in this file and complete all the tasks described.
5. Once you complete the last step of the procedure, run your simulation and wait until it finishes.
3.2. Questions
1. Briefly introduce the channel codes that you used in your simulation.
2. Configure all the channel codes in your simulation so that they have similar code rates. Run your simulation and compare their BER vs. Eb /No performance. Explain your findings.
3. Configure all the channel codes in your simulation to a different code rate and run your simulation again. How did your codes perform compare to the simulation results in Question 2?
4. What will you observe if your channel codes cannot correct all the bit errors?
5. Time the encoding and decoding process separately for each codes in your simulation. Do you think the encoding/decoding time is a critical factor to consider for practical system? Justify your answer based on your measured processing time.
6. In this simulation, we essentially transmitted the red, green and blue value of each pixel to the receiver. Is this a good way to transmit messages such as pictures?
4. Part B: Modulation
In this experiment, we will delve into the principles and practical applications of different dig- ital modulation techniques. We will mainly focus on several key digital modulation schemes, including Amplitude-based modulatiom and Phase Shift Keying (PSK). These techniques are fundamental to various communication systems, from cellular networks to satellite com- munications, and play a critical role in ensuring reliable and efficient data transmission.
NOTE: You are not required to complete Part A before working on this part.
4.1. Procedure
1. Download the Lab 4 package from the TELE4652 pages on Moodle and extract the downloaded file to any directory you prefer.
2. Start MATLAB and navigate to the extracted Lab 4 package.
3. Go through the file "Lab4BcodesForStudents.m".
4. Follow the instructions in this file and complete all the tasks described.
5. Once you complete the last step of the procedure, run your simulation and wait until it finishes.
4.2. Questions
1. Run your simulation and compare the BER vs. Eb /No performance between the two types of the modulation with the following parameters:
• M-ary PSK: M = 4, Gray labelling, 0 phase shifts.
• M-ary QAM: M = 4, Gray labelling, 0 phase shifts.
• No pulse-shaping filter applied.
2. Change the Gray labelling to natural bit labelling in the configuration in Question 1 and explain whether Gray labelling can improve the overall BER performance.
3. Explain how the eye diagram is plotted. What information we can obtain from the eye diagram?
4. Why pulse-shaping filters are applied? Apply the pulse-shaping filter while keeping the rest of the modulation configuration the same as in Q1. Explain your findings, particularly in the eye diagram.
5. Why a fixed phase offset can be introduced for PSK? What are the benefits of intro- ducing such a phase offset? Answer this question by setting the phase shift of your PSK modulation function to π/4.
6. Increase the value of M to 16 and then 64 for both PSK modulation and QAM while keeping other parameters the same as in Question 1. Will your BER performance improve?