TELE4653 - ASSIGNMENT 1 (DEADLINE: 4/4/2022) 0
Assignment 1 - TELE4653 Digital Modulation & Coding
Publication Date: 18 March 2022.
Notes:
• Total Marks: 10.
• Total pages: 3 (including this page).
• Deadline of the report submission: 4 April 2022.
• Late submission will suffer a penalty of 2 marks per day late.
• The assignment report (PDF file) must be sent to w.zhang@unsw.edu.au before/on the
deadline.
• Every student must work on the assignment independently.
• The assignment report should include following:
(a) Title page: Student name & ID, email address, affiliation, etc.
(b) Main part: your solutions with detailed derivations.
(c) Simulation results (figures and discussions of the results).
(d) Appendix: Program code for producing the figures in the report.
TELE4653 - ASSIGNMENT 1 (DEADLINE: 4/4/2022) 1
I. ASSIGNMENT 1 - TELE4653, 2022
Consider the two 8-point QAM signal constellations shown in Fig. 1. The min-
imum distance between adjacent points is 2.
(a) (b)
Fig. 1. Two 8-point QAM signal constellations.
1) (4 marks)
Determine the average transmitted power for each constellation, assuming
that the signal points are equally probable. Which constellation is more power
efficient?
2) (6 marks)
Suppose at time instant k a signal point ak randomly selected from the
constellation A is transmitted and corrupted by additive zero-mean white
Gaussian noise zk. The received signal can be expressed as
rk = ak + zk.
The detection of signal ak is performed by finding
aˆk = arg min∀ak∈A
|rk − ak|2,
i.e., the one which has the minimum Euclidean distance between the received
signal rk and the possible transmitted signal point in the constellation A. Plot
TELE4653 - ASSIGNMENT 1 (DEADLINE: 4/4/2022) 2
the average probability of the detection error (aˆ 6= a) as a function of signal
to noise ratio (SNR) from 0 dB to 10 dB for each constellation in Fig. 1
(attach the program code of plotting).