This document reports on a Matlab project experimenting with a digital communication chain using M-QAM modulation. It describes tasks performed including plotting transmitted 16-QAM symbols, analyzing the effects of varying SNR and multipath channels on the received signal spectrum. It also examines the received constellation for different modulation orders, SNR levels, and multipath channels to analyze the impact on the receiver's ability to detect and decode symbols. Effects of adding phase noise to the receiver oscillator are also explored. The general conclusion is that transmission parameters and channel conditions affect the receiver's performance.

1. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
1/14
ELT-41308 Communication Theory
Report of Matlab Project Work
Submitted by NCHANG TITA MARTIN (# 050497919)
Project Work: Experimenting an Elementary Single-Carrier M-QAM-based Digital Communication Chain
The basic system model is shown below, where baseband equivalent approach is taken (i.e. I/Q
modulation and I/Q demodulation are not explicitly considered).
Tasks 1:
Plot the relevant responses and explain what you observe.
Figure 1: Transmitted symbols for 16-QAM

2. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
2/14
Explanation:
The alphabet size 16 = 24
, each symbol represents 4 bits.
Information is in both the amplitude and phase of the carrier-modulated waveform, which is a
superposition of the carrier modulated I and Q component waveforms. These latter contain both
amplitude and phase modulation. The negative values of the baseband I and Q waveforms correspond to
180deg phase shift, relative to the unmodulated cosine and sine.
Figure 2: Time domain response of the Transmit root-raised cosine (RRC) filter g(t)
Explanation:
RRC pulses are used to control the effective length of an ideal sinc-pulse using a window function. The
effective pulse duration is decreased by increasing the excess bandwidth 𝛼, so that the oscillation of the
pulse attenuates faster the bandwidth increases.

3. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
3/14
Figure 3: Amplitude response of the Transmitter filter
Tasks 2
1. Vary the SNRdB value e.g. few values between 0 ... 50, and see how that impacts the RX signal
spectrum. Provide relevant spectral examples and explain what you observe.
i) For SNRdB = 0

4. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
4/14
ii) For SNRdB = 15
iii) For SNRdB = 30

5. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
5/14
iv) For SNRdB = 45
v) For SNRdB = 50
Remarks: The smaller the SNRdB value, the more the distortion in the Rx amplitude spectrum
Explanation: Smaller SNR means noise power is more than signal power. Distortions reflect the ISI
2. Explain also the effects of multipath, why does the RX signal spectrum have clear fading
notches inside the passband?

6. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
6/14
Without a frequency-selective channel, the pulse-shape at the RX filter output would be a beautiful
raised-cosine Nyquist pulse. However, the frequency-selective channel due to multipath, will distort
the pulse-shape badly and create inter symbol interference, ISI. Also, the fading response is non-
symmetric around the zero frequency. The Rx signal is no longer bandlimited though the transmitted
signal was.
3. Vary also the multipath channel profile between the channels b1, b2, b3 and explain what you
observe (in terms of the RX signal spectrum).
i) For b = b1 (means no multipath at all), there’s no distortion trivially.

7. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
7/14
ii) For b = b2
iii) For b = b3
Remark: For more additional propagation paths, the more the distortion. The spectrum becomes
more and more non-symmetric about the zero frequency and also becomes less bandlimited.
Task 3
1. First momentarily omit the multipath (i.e. use the channel b1) and set SNR to 35dB. Plot the
RX signal constellation and explain what you see.

8. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
8/14
Remark:
With high SNR and channel b1 (no multipath), the received signal nearly matches the
constellation points. Higher SNR means more signal strength than noise power, thus the
receiver will be able to detect/decode the received signal.
2. Then repeat by changing the SNR to 10 dB and 20 dB and plot and comment again the RX signal
constellation. Would the RX still be able to reliably decode/detect the received signal?
SNR 20dB, channel b1 SNR 10dB, channel b1
Remarks: The smaller the SNR, the more the received signal mismatches the constellation
points, because of greater noise power. Thus, the receiver won’t be able to reliably decode
/detect the received signal.
3. Then repeat by setting SNR back to 35 dB but now turning on the multipath channel. Experi-
ment with both multipath channels b2 and b3. Plot always the RX signal constellation and try
to explain what you see.

9. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
9/14
SNR 35dB, multipath channel b2 SNR 35dB, multipath channel b3
Remarks: Despite the relatively high SNR, the received constellation will not match the original
constellation if there are more additional paths to the direct propagation path. Receiver won’t
be able to reliably decode/detect the received signal without equalisation.
4. Then lower the SNR down to 10 dB. Again plot the RX signal constellations with all (multipath)
channels b1, b2 and b3 and explain what you see.
SNR 10dB, channel b1 SNR 10dB, channel b2
SNR 10dB, channel b3 Remarks:
With low SNR, the noise power is more than
signal power in such a way that the multipath
effect is not that pronounced.

10. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
10/14
5. Next, change the modulation order to M = 4, and repeat the above steps shortly. Comment on
the differences.
Original constellation SNR 35dB, channel b1
Remarks:
SNR 20dB, channel b1 SNR 10dB, channel b1
Remarks:
SNR 35dB, channel b2 SNR 35dB, channel b3
Remarks:

11. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
11/14
SNR 10dB, channel b1 SNR 10dB, channel b2 SNR 10dB, channel b3
Remarks:

12. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
12/14
6. Finally, change the modulation order to M = 64, and repeat the above steps shortly. Comment
on the differences.
Original constellation SNR 35dB, channel b1
Remarks: The received symbols still match the original constellation at SNR 35dB (more signal
power than noise)
SNR 20dB, channel b1 SNR 10dB, channel b1
Remarks: For low SNR even without multipath, ISI is observed
SNR 35dB, channel b2 SNR 35dB, channel b3
Remarks: With high SNR ie more signal power than noise, there is still much ISI due to
multipath.

13. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
13/14
SNR 10dB, channel b1 SNR 10dB, channel b2 SNR 10dB, channel b3
Remarks: At very low SNR, there will always be ISI whether its direct path or multipath channel.

14. ELT-41308 Communication Theory Project Work Report of Matlab Project Work
14/14
Tasks 4 Modeling a phase noise in receiver
• First set Beta = 100 and plot the RX signal constellation and explain what you see.
Remark: The oscillator introduces phase noise of positive and negative phases. However, for beta = 100,
the received symbols match the original symbols but with some small positive and negative phases.
• Then repeat by changing the Beta = 5000 and plot and comment again the RX signal constellation. Would
the RX still be able to reliably decode/detect the received signal?
Remark:
For higher values of beta (ie the extra bandwidth introduced by the oscillator), a greater phase noise is
created and I think the receiver will not reliably detect/decode the transmitted symbols.
General Conclusion:
The models show that a communication chain is affected by the Tx, Rx and channel parameters (AGWN,
multipath, phase noise) which affect the ability of Rx to detect/decode the transmitted symbols from the
received constellation.