(Solved): Problem 3 - Quadrature Amplitude Modulation A quadrature amplitude modulation (QAM) signal s(t) can ...

Problem 3 - Quadrature Amplitude Modulation A quadrature amplitude modulation (QAM) signal $s(t)$ can be mathematically expressed as $\begin{array}{rl}s(t)& =\underset{n=??}{\overset{?}{?}}a[n]p(t?nT)\cos \left({?}_{c}t+?[n]\right)\\ & =\underset{n=??}{\overset{?}{?}}a[n]p(t?nT)\left[\cos \left({?}_{c}t\right)\cos (?[n])?\sin \left({?}_{c}t\right)\sin (?[n])\right]\\ & =\underset{n=??}{\overset{?}{?}}a[n]p(t?nT)\cos (?[n])\cos \left({?}_{c}t\right)?\underset{n=??}{\overset{?}{?}}a[n]p(t?nT)\sin (?[n])\sin \left({?}_{c}t\right)\\ & =I(t)\cos \left({?}_{c}t\right)?Q(t)\sin \left({?}_{c}t\right)\end{array}$ 2 ELEC301 Fall 2023 MATLAB Project \# 2 Due Date: $19/11/2023$ where $I(t)={?}_{n=??}^{?}a[n]p(t?nT)\cos (?[n])\text{ and }Q(t)={?}_{n=??}^{?}a[n]p(t?nT)\sin (?[n])$ The values that $a[n]$ can take depend on the constellation size $M$ of PAM, and should contain positive and negative values. For the following questions, assume that $p(t?nT)$ 's are rectangular pulses. 1. Apply 16-QAM modulation and demodulation by following the steps: (a) Create a uniformly distributed random bit sequence with length 120 . (b) Draw the constellation diagram for 16-QAM. What are the amplitude values that in-phase component $I(t)$ and quadrature component $Q(t)$ can take? How did you choose those values? Don't forget to name the axes. PS: You don't have to consider Gray coding. (c) Take baud rate $f_b=50\mathrm{Hz}$, carrier frequency $f_c=1\mathrm{kHz}$, and sampling rate for QAM-modulated signal $f_s=5\mathrm{kHz}$. Modulate the signal with $16?\mathrm{QAM}$. What is the duration of a single symbol? How many symbols do you expect to see in the modulated signal? What is the duration of the total modulated signal? Explain the details of how you modulated the signal. Plot the modulated signal. (d) Demodulate the signal applying the steps below: - Multiply the modulated signal with in-phase and quadrature components separately. Should there be any constant in front of them? - Take the integral of branches over each symbol interval $[nT,(n+1)T]$, where $n$ is an integer and $T$ is symbol duration (you calculated it in part c). Remember that the result of integration should be a single number since it is a definite integral. - Find the closest symbols to the resultant amplitudes. - Convert them to the bit sequence. Did you get the original sequence? 2. Repeat question 1 for $10\mathrm{dB}$ SNR white-Gaussian noise added onto the modulated signal. You can use the same message sequence in part 1(a), and you don't have to re-draw the constellation diagram asked in part 1(b).