Assignment 1 - Simulation of an 8-ary Digital

Communication System

Digital Communications, 2020/2021

You are required to write, in MATLAB, a simulation of a digital communication system

which uses 8-ary modulation (there are M = 8 equiprobable transmit symbols). The system

model is shown on the left-hand side of Figure 1. Transmission is over the additive white

Gaussian noise (AWGN) channel. The signal space diagram for the modulation scheme is

shown on the right-hand side of Figure 1. Note that it is sufficient to simulate the

equivalent vector channel (you do not need to simulate the waveforms).

SYMBOL TO BIT

MAPPING DEMODULATOR

BIT TO SYMBOL MODULATOR MAPPING

Figure 1: Left: Block diagram of the 8-ary digital communication system to be simulated.

Right: Signal-space diagram for the 8-ary modulation scheme.

The following are the requirements:

? Use your simulation to plot the symbol error rate (SER) versus Es/N0 curve for the

system. Plot SER on a log scale and Es/N0 in dB.

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? Then, on the same graph, plot the theoretical SER curve for the system. To do this,

you will need to derive an expression for the probability of symbol error for this system

as a function of Es/N0.

? Choose a bit to symbol mapping for the transmitter. Describe your mapping clearly,

and explain why you chose this particular mapping.

? On a new graph, plot the bit error rate (BER) versus Eb/N0 curve for the system.

Plot BER on a log scale and Eb/N0 in dB.

? From this curve, estimate the value of Eb/N0 above which the system BER lies below

10?4

(or, if this takes too long a time, 10?3

).

? Your program should consist of a single m-file script, and should be appropriately

annotated with comments. You should not use any procedures from the MATLAB

communications toolbox.

? Your assignment should be submitted via Brightspace, and should contain two files:

(a) Your MATLAB simulation m-file, and

(b) A short report (in PDF format) containing the derivation of the theoretical

SER as well as the two system performance graphs mentioned above. A brief

commentary about the methods you used and the results you obtained should

also be included in this report. The answers to the specific questions asked above

should also be stated clearly in your report.

? The deadline is 11:30 pm Dublin Time on Friday 30th October 2020.

? And most importantly: The program you submit should be your own work.

Programs will be scrutinized for evidence of copying. Programs in which copying is

found will NOT be awarded a pass grade.

You may find the following MATLAB tips useful:

? The function rand generates a random number which is uniformly distributed between

0 and 1. Thus for example, b = rand < 0.5 generates a random bit b.

? The function randn generates a Gaussian-distributed random number with mean 0

and variance 1. Thus, multiplying this number by σ produces a Gaussian-distributed

random number with mean 0 and variance σ

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.

? The function semilogy(x,y) plots x against y, rather like plot(x,y), except that it

uses a log scale for the y-axis.

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