COMS4105/7410 Communication Systems
Practical 2: Channel Coding, Bit Error Rate and
Frequency Synchronisation
1 Introduction
This practical is the second of three practicals which will run in this course. Each practical
will be run over a fortnight. Work for the practical can be either done at home or during
the practical sessions. Your preparation and lab work for the practical needs to bemarked
off during the practical sesssions.
Practical work for this course will take place in the 78-212 laboratory as well as in an
online Zoom session. For those participating in the practical session in the lab, you should
note that this location is classified as an engineering laboratory and workplace health
and safety regulations apply. You should read the “Occupational Health and Safety in
the Laboratory” guidelines and fill out the declaration. Failure to sign the declaration
and/or abide by the guidelines will result in your exclusion from the laboratories. In par-
ticular, if you fail to wear covered footwear, you will be excluded from your prac session.
Additionally, this year, as this session may involve close range teaching (i.e. staff helping
students in close range at a computer screen) we have the following additonal guidelines
that we should follow:
• Physical distancing (1.5m is encouraged but may not be possible at all times)
• Use of a face mask is required during close range teaching.
• Use hand sanitiser on your way in and out of the lab
• Use sanitising wipes to wipe down equipment / surfaces - before and after use.
• If you feel unwell, please stay how and get tested - you may also join the online
zoom session of the practical.
Bring your RTL-SDR device (including antenna) to each practical session. For each
prac, you need to have attempted the pre-lab questions for each practical before attending
the practical session. All code that is marked must be checked into your own private Git
repository on GitHub (NOTE: must be logged in!). Also, see the private GitHub wiki for
additional hints.
NOTE: this year, due to the dual offerings, you should be able to capture all recordings
using the online tool.
2 Learning Objectives
In this lab you will be evaluating different channel coding methods within a communica-
tion system which operates in a additive white Gaussian noise environment. In addition,
due to the importance of frequency synchronisation, a simple method used to perform
coarse frequency synchronisation will be introduced.
In the first part of this practical you will be simulating three different channel coding
methods, Hamming coding, Convolutional coding and Reed-Solomon coding. As you
will have direct control over the effects of the channel, you will be be able to adjust the
signal-to-noise ratio (SNR) and find the bit error rate of the system as a whole.
3 Preparation 2
The next two parts of the practical will experimentally test these coding techniques.
For over-the-air (OTA) signals before applying any demodulation, there is a need to per-
form both time and frequency synchronisation. In practical 1 we studied time synchro-
nisation in detail. This practical introduces a simple method to perform frequency syn-
chronisation. The transmitted signal from the demonstration computer in the lab will be
used to test the channel coding methods under varying signal to noise ratio.
The learning objectives are as follows:
1. Understand how a software defined radio (SDR) based communication system op-
erates including its block diagram and process,
2. Be able to apply channel coding (and decoding) to various parts of data, implement-
ing error detection and/or correction,
3. Be able to perform basic frequency synchronisation,
4. Read relevant sections of a communication standard (DAB – ETSI EN 300 401)
5. Using the knowledge obtained from the previous parts of this practical becomemore
familiar with the DAB signal, by understandingwhere the different coding schemes
apply in practice,
6. Experience designing a structured communication system by usingmodular system
blocks which are connected with-in a top-level design.
3 Preparation
To help you test your code in the practical, the preparation questions will ask you to
perform some channel coding and decoding by hand. Also you will need to research the
available channel coding methods present in DAB.
Question 1 Design a Hamming (7,4) block code via a generator matrix G. Encode a mes-
sage with a single ‘1’ in the first bit position and the remaining bits set to ‘0’s.
Find the corresponding parity check matricesH. After applying an error in the fourth
bit of each of the code words, calculate the syndrome for this and explain which received
bit the algorithm would correct.
What is the code rate? How many errors can be detected, and corrected?
Question 2 The cyclic-redundancy-check (CRC), is a code used to apply a checksum to a
block of data. DAB uses a CRC-16 code to apply checksums on many of the packet struc-
tures. What is the polynomial used in DAB’s CRC-16 calculations? Find the checksum
for the data 1001 0000 0000 1001. In DAB (ETSI EN 300 401) in the FIC – on how many
bytes of data is the CRC-16 performed on?
Similarly, in theDAB standard specification (ETSI EN 300 401), find the structure of the
Reed-Solomon code, including both the code generator polynomial and field polynomial.
Explain the process of encoding using this RS code. (Hint: there are some similarities
between CRC and RS)
Question 3 In the DAB standard specification (ETSI EN 300 401), find the structure of the
Convolutional encoder used. Encode the bits 101, and pad the message with ‘0’s until the
three original bits are no longer in the state variables.
As this convolutional code is quite large in terms of its state space, in this practical we
will also consider a smaller code – so that it is feasible to check the code by hand. The
4 Method 3
convolutional code has the following output polynomials
x0 =1 + p
x1 =1
x2 =1 + p+ p
2
Draw the trellis diagram for this simpler code, and decode the received bits ‘101 001
110 011 001’.
Question 4 Prepare your Git repository for the practical. For this practical, place a file
to describe the practical in it (e.g. README.md). Make sure you are using a Git client,
rather than uploading files manually. Your existing work for the other practicals should
be stored in their own places.
Question 5 Consider a simple frequency synchroniser packet structure which repeats the
preamble twice. If the received signal is a assumed to be a frequency shifted version of the
transmitted signal, with an unknown complex channel, h, then the following expression
holds.
y[t] = ej2pifcthx[t] + n[t]
This means that if we compare the first preamble to the second, and ignore the noise
terms, we notice the following
y[t+Npre] = ej2pifcNprey[t]
or, each sample of the second preamble is a constantmultiple of the corresponding sample
in the first preamble. Hence, we devise a way to estimate the frequency offset via a ‘best
fit’.
This problem can be formulated by means of Npre simultaneous equations, and one
unknown. Being an overdetermined system of equations, it means that we should use
the least squares (LS) method to solve it.
In Matlab/Octave, least square problems can be solved using the ‘\’ operator, also
known as the pseudo-inverse. This provides a “line of best fit” between two sets of vari-
ables. Whereas in Python you can use the linalg.lstsq function in numpy.
For example, consider the following vectors: x =(1 3 4 9)T , and y =(2 5.5 9 17)T ,
and we would like to map this to a function y = mx. We put the values into two column
vectors, giving the equation y = xm, with y ∈ R4×1, x ∈ R4×1, and m ∈ R1×1. So
m = x+y.
After the value of best fit is found between the two copies of the preamble, find a way
to convert this value to the frequency shift.
Unfortunately there are some limitations as to how large a frequency shift can be
solved for. Find the maximum frequency shift which can be solved when the sample
rate is fs =2 MS/s and the training sequence has 8 symbols (16 after repetition). There
are 8 samples per symbol.
4 Method
In this practical we will be using most significant bit (MSB) first ordering just like in
Practical 1. The guide on Github (available at https://github.com/UQ-Communication-
Systems/public/wiki/Guide-Converting-Data) shows you how to convert ASCII data to
bits. Of course in the receiver you will need to reverse this process.
4 Method 4
Next, to avoid non-linear distortion on your RTL-SDR, you should avoid using auto-
gain, and instead capture signals with a ‘gain’ value set (via -g). If you are close to the
transmitter use lower levels of gain.
rtl_sdr dump.bin -s 2e6 -f 110.9e6 -n 2e6 -g 35
4.1 Evaluating the Performance of Channel Coding
For channel coding there are a large number of different channel codes available to the
designer. Each scheme has different characteristics in terms of code rate, error detection
capability, error correction capability, and complexity.
In lectures we grouped channel coding into two main categories, block and contin-
uous. The Hamming code, and polynomial (CRC) are block codes. Convolutional en-
coding is a continuous code. We also considered a multi-level block code known as the
Reed-Solomon code. In this practical we will evaluate the bit error rate performance of
the different channel coding methods as well as the improvement (if any) over not using
channel coding at all.
Input
Modulate
Demodulate
Output
1010101
1010101
+ Noise
Channel
Channel
Encode
Channel
Decode
Figure 1: Recommended block diagram in Practical 2
The basic block diagram that you will need to implement is shown in Figure 1. You
can interchange the various channel coding blocks for the different parts of the practical.
As we are considering a single carrier communication system, you may assume that the
baseband modulation occurs on a centre frequency fc = 0Hz. Also, implement your sys-
tem to have a symbol duration of 8 samples. The dotted lines in the diagram are drawn to
remind you that you can test your system without the full implementation. For example,
you can put the channel encoder output into the channel decoder input – this way you
test your channel coding process without relying on the rest of your system. In addition,
when testing under real data, you should look at the input and output of each block to
see if the data looks correct – the I&Q values being demodulated should look like the
constellation they are for (QPSK, BPSK, 16QAM). For each part you will need to send a
significant number of bits through the communication system and then calculate the bit
error rate.
4 Method 5
Exercise 4.1.1 In this exercise you will be using two different Hamming codes: the
(7, 4) and (15, 11) hamming code. To do this you should write a number of functions:
1. Implement a block which takes one block of message bits and outputs one block
of coded bits.
2. Implement the corresponding block which is used at the receiver. That is – a
block which performs the syndrome calculation and corrects the bit error(s) (if
they exist).
3. Put these two blocks into your BER testing system and generate the BER vs SNR
graph for the two hamming codes. Compare the result to when no channel cod-
ing is used.
What are the improvements and penalties for using the channel code at various
SNRs?
Hint: Your design should include a top-level design which is structured similarly
to the figure presented at the beginning of this section. You do not need to process
all the bits in one go, in fact it might make sense to send smaller batches of bits and
accumulate the results. ■
Exercise 4.1.2 Another block based channel code is the cyclic redundancy check (CRC).
We will be using the CRC-16 polynomial used in DAB (refer to the preparation ques-
tion). It will be used to add 16-bits of checksum to every block of 16 message bits.
This time, instead of performing error correction at the receiver, only error detection
will be performed.
Using statistics of how many error frames occur and are detected for each value of
SNR plot a graph of actual and un-detected errors per block as a function of SNR. ■
Exercise 4.1.3 Repeat 4.1.1 by using the simple Convolutional encoder presented in
the preparation questions. ■
Exercise 4.1.4 Repeat 4.1.1 by using the RS encoder which is used in DAB.
Hint: Reed Solomon encoding is codewhich already implemented inMatlab/Octave
(rsenc, rsdec). In Python check out GitHub for a compatible RS encoder. ■
4.2 FEC, Error detection and frequency synchronisation
In this part of the practical we testing the channel coding receivers using over-the-air trans-
mitted signals.
With real received signals, we have noticed that in addition to time synchronisation,
we must also obtain good frequency synchronisation. So before decoding the data we
will first perform an exercise on frequency synchronisation.
Like the previous practical, transmissions will occur on four frequencies (A-D) and
these will be referred to in the corresponding exercises of the practical. The actual fre-
quencies will be posted on the whiteboard during each practical.
You will need to use your signal detection methods from Practical 1 including both
energy detection and preamble detection.
Exercise 4.2.1 To help with both frequency and time synchronisation the sequence
introduced previously will be transmitted twice using QPSK modulation 11110011
4 Method 6
10100000 (This is labelled as ‘training’ in the diagram below), and a new sync word
will be used provide an even better way of detecting the frame, 10101011 – which is la-
belled as ‘sync’ in the diagram below. The same packet structure is used in most of the
following examples. You can use your frequency offset estimator from the preparation
question, and your packet detectors from practical 1.
Tune into frequency A, to see if your frequency estimator works correctly. Note,
that if your frequency offset is more than the limit, the estimator may not work (refer
to the preparation question).
The structure of the signal in frequency A is as follows:
YNCS DATA DATA
...
0.064 ms 0.128 ms
BPSK
YNCSNULL NULL
BPSK
0.4 ms
QPSK
TRAININGTRAINING
QPSK
800 128 Samples @ 2MS/s128x2 160+
0.08 ms+ 0.064 ms 0.064 ms0.4 ms
161616
The data and training are encoded using QPSK modulation. The data part of the
transmission is a text message which will be decoded in the next exercise. ■
Exercise 4.2.2 The data transmitted in 4.2.1 is a text message which has been encoding
using a Hamming (7,4) code.
The same packet structure applies, but here we need to find the original text, rather
than the coded message. The data part of the packet has been encoded using a Ham-
ming (7,4) code. Make sure your Hamming decoder can correct for the required num-
ber of errors.
Find the word being transmitted. ■
Exercise 4.2.3 If more errors occur than the channel code can correct or even detect we
may not be able to receive our signal correctly.
In this exercise you will receive a signal encoded using a Hamming (15,11) code,
but in addition each frame will have a CRC-16 checksum.
YNCS DATA DATA
...
0.064 ms 0.128 ms
BPSK
YNCSNULL NULL
BPSK
0.4 ms
QPSK
TRAININGTRAINING
QPSK
800 128 Samples @ 2MS/s128x2 160+
0.08 ms+
C
R
C
128
0.064 ms
16 16 16
For this you will need to detect both the start and end of each frame. As you will
need to detect where the CRC-16 finishes.
Tune into frequency B, and use a one second recording (for offline processing).
Find the words being transmitted in a few consecutive packets. ■
4.3 Convolutional, Reed Solomon and Concatenated Codes
In a system such as DAB, two different channel coding methods are used. The first is
convolutional coding, which is also known as an inner code. The second is Reed-Solomon
coding, a block code, which is the outer code. The two codes are used together to produce
a concatenated code which achieves superior channel coding gain.
Here we will study Convolutional and Reed-Solomon codes individually and then
together as one concatenated code.
To study the error performance the signal power will be decreased for frequency C
and D and hence the effect of using the channel codes will be visible – error correction
should occur.
4 Method 7
Exercise 4.3.1 Here we will have two different types of packets transmitted on the
same frequency. The way you will distinguish themwill be via different ‘frame types’.
Tune into frequency C, find the messages prefixed with the same (double) training
sequence as previously: 11110011 10100000. Following this, the next 4 bits (or 2 sym-
bols) are encoded with a frame type. For this exercise - frames with the frame type ‘0
0 0 1’ are present. Next decode the data which has been encoded using the simpler
convolutional code specified in the preparation questions.
YNCS DATA DATA
...
0.064 ms 0.128 ms
BPSK
YNCSNULL NULL
BPSK
0.4 ms
QPSK
TRAININGTRAINING
QPSK
Fr
a
m
e
T
y
p
e
800 128 Samples @ 2MS/s128x2 160+
0.08 ms+
C
R
C
128
0.064 ms
16 16 16
Take a 1 second recording for offline processing. ■
Exercise 4.3.2 The second type of packet will be a Reed-Solomon encoded packet. The
packet structure is similar to the previous example, and this time the frame type is ‘0
0 1 0’.
YNCS DATA DATA
...
0.064 ms 0.128 ms
BPSK
YNCSNULL NULL
BPSK
0.4 ms
QPSK
TRAININGTRAINING
QPSK
Fr
a
m
e
T
y
p
e
800 128 Samples @ 2MS/s128x2 160+
0.08 ms+
C
R
C
128
0.064 ms
16 16 16
Tune into frequency C, find the messages with the stated frame type and decode
the RS encoded data.
■
Exercise 4.3.3 In this exercise we will combine the different features from the various
coding methods presented above. That is all data will be first encoded using Reed-
Solomon coding followed by a convolutional code. This is the same encodings as used
in the previous exercises, but this time together as a concatenated code.
Modulation will be done using a 16-QAMmodulation in both the training and the
data, with 8 samples bit symbol. The training sequence will be improved by creating
two pairs of training sequences. Decoding should be done in the opposite order.
Training A will be the 16-QAM modulation of the previous sequence 11110011
10100000 (4 Symbols), and training Bwill be same symbols butwith +1 on each symbol,
giving 00000100 10110001. Because of the reduced samples per bit, the total number
of symbols of the training remains the same. However note that the symbol duration
is half of the previous questions.
Finally to ease the detection of the end of the packet, the first 16 bits of each packet
will contain the length of the remaining parts of the packet (coded data + CRC16).
YNCS DATA DATA
...
0.064 ms 0.064 ms
BPSK
YNCSNULL NULL
BPSK
0.4 ms
16-QAM
Le
n
g
th
TRAININGTRAINING
800 128 Samples @ 2MS/s32x4 160+
0.08 ms+
C
R
C
32
0.016 ms
16-QAM
Le
n
g
th16 8 8
Tune into frequency D to try to decode this message.
■

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