BEST gr-bertool

University of Messina - DIECII

The gr-bertool
Supervisors
Candidate
Prof. Salvatore Serrano

Arturo Rinaldi

Prof. Giuseppe Campobello

Department of Electronics Engineering, Chemistry and Electrical Engineering
BEST School - Messina, September 2013

Goal of the thesis work
• The making of a learning tool for the analysis of the digital modulations

in diﬀerent communication channels

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Arturo Rinaldi - The gr-bertool


• The simulated channels were :

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◦ Wired : AWGN

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◦ Wired : AWGN
◦ Wireless : Rayleigh and Rician

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◦ Wired : AWGN
• Verify the correspondence between the theoretical and experimental

results of the BER (Bit Error Rate)

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◦ Wired : AWGN

• Provide complementary tools to show how audio and video files are

modified under the effect of the transmission channels

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◦ Wired : AWGN

• Provide complementary tools to show how audio and video files are

modified under the effect of the transmission channels
• The gr-bertool was built by using the open-source DSP platform GNU

Radio

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GNU Radio
• GNU Radio is an open-source software

toolkit providing a huge library of
blocks for Digital Signal Processing
(DSP) written in C++ which can be
combined together in order to build and
develop radio applications

Gnu Radio Companion (GRC), XML
Python Flow Graph
(Created using the processing blocks)
SWIG (Port C++ blocks to Python)
GNU Radio Signal Processing Blocks
(C++)

USB Interface / Gigabit Ethernet
Generic RF Front End
( USRP / USRP 2 )

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GNU Radio
• GNU Radio is an open-source software

toolkit providing a huge library of
blocks for Digital Signal Processing
(DSP) written in C++ which can be
combined together in order to build and
develop radio applications
• It is provided with a graphical interface

to ease its learning curve (GRC : GNU
Radio Companion)

Gnu Radio Companion (GRC), XML
Python Flow Graph
(Created using the processing blocks)
SWIG (Port C++ blocks to Python)
GNU Radio Signal Processing Blocks
(C++)

USB Interface / Gigabit Ethernet
Generic RF Front End
( USRP / USRP 2 )

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Software-Deﬁned Radio : an introduction
• GNU Radio was developed to be in use of Software-Deﬁned Radio

(SDR), a new “paradigm” of communication systems

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• A receiver is an SDR device if its communication functions are made as

reconﬁgurable software working on ad hoc hardware

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• So it’s possible to implement diﬀerent software transmission standards

by using only one device

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• So it’s possible to implement diﬀerent software transmission standards

by using only one device
• An SDR sytem is also able to recognize and avoid possible interferences

with other transmission channels

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A general overview on the main
GNU Radio blocks

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Signal Source
The block generates diﬀerent kind of waveforms to
be used as the main signal to transmit or as a
reference one.
The block is only not able to generate Sinusoidal or
Costant kind of waveforms but also Square,
Triangle and Saw Tooth ones.
Type : complex, ﬂoat, int, short

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Noise Source
The block is able to generate noise according to the
Uniform, Gaussian, Laplacian and Impulse
models.
Please also note that the Amplitude parameter fed
to the Gaussian kind of noise is the standard
deviation σ of the Gaussian Noise, given by :
σ=

N0
2

where N0 /2 is the power spectral density of white
noise (i.e. its variance).

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Operators

These blocks perform the four basic arithmetical
functions over the signal sources they are fed with
(sum, subtraction, multiplication and division).
Please also note that they perform the operation
element by element (i.e. ﬁrst element of the row ﬁrst element of the column) so the rule of thumb is
to feed the inputs with equal amounts of data.

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Random Source 2
The block generates a random array of unsigned
integer data with values spanning from 0 to 255 (we
are working with 1-byte elements !).
We use it because is a more reliable source of
random data compared to the one provided with the
GNU Radio platform.
The only parameter fed to the block is the number
of samples (i.e. the length of the generated list of
elements).
Type : complex, ﬂoat, byte
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Random Source 2
1
2
3
4
5
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7
8
9
10
11
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14
15
16
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18
19
20
21
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23
24

from g n u r a d i o i m p o r t g r
i m p o r t random
d e f OnDataSource random ( s a m p l e s ) :
src1 = [ ]
f o r i in range ( samples ) :
d a t a = random . r a n d i n t ( 0 , 2 5 5 )
s r c 1 . append ( d a t a )
return src1
c l a s s randomsource b ( gr . h i e r b l o c k 2 ) :
def

init

( s e l f , number samples ) :
gr . h i e r b l o c k 2 .
init
( s e l f , ” randomsource b ” ,
gr . i o s i g n a t u r e (0 , 0 , 0) ,
gr . i o s i g n a t u r e (1 , 1 , gr . s i z e o f c h a r ) )
d a t a s a m p l e s = OnDataSource random ( n u m b e r s a m p l e s )
s e l f . v e c t o r = g r . v e c t o r s o u r c e b ( d a t a s a m p l e s , True , 1 )
s e l f . connect ( s e l f . vector , s e l f )

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Random Source - The easy way
The block generates a random array of unsigned
integer data.
It is a more direct implementation compared to the
one we have just seen.
We feed it with the data list (of unsigned integer of
course) and we also set to Yes the repeat option
since we need a constant stream of data.
Let’s see how to build the data array this time....

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Random Source - The easy way
1
2
3
4
5
6
7

from g n u r a d i o i m p o r t g r
i m p o r t numpy
d a t a = map ( i n t , numpy . random . r a n d i n t ( 0 , 2 5 6 , 6 e5 ) )
v e c t o r = g r . v e c t o r s o u r c e b ( d at a , True , 1 )

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Packed to Unpacked
The block returns sequences of packed bytes
according to the integer number we set to the Bits
per Chunk argument.
It is possible to set the Endianness of the output
sequences according to Big (MSB) or Little (LSB)a .
So let’s assume we have this binary sequence
11100001. If we feed it to the block we’ll get four
binary sequences, speciﬁcally :
•
•
•
•

00000011
00000010
00000000
00000001

Type : int, short, byte
a Johathan Swift, “Gulliver’s Travels”
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Map
We usually exploit this block every time we want to
perform Gray Coding on the symbols of a digital
modulation.
For a 2-bit symbols modulation :
•
•

Binary to Gray sequence : [0,1,3,2]
Gray to Binary sequence : [0,1,3,2]

For a 3-bit symbols modulation :
•
•

Binary to Gray sequence : [0,1,3,2,7,6,4,5]
Gray to Binary sequence : [0,1,3,2,6,7,5,4]

Type : byte

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Constellation Decoder - 1
It could be seem strange feeding the same coding
numeric sequence when un-gray a constellation.
However, this is due to how GNU Radio works and in
particular how the Constellation Decoder block
operates over the signal points.
So, once you have assigned the correct Symbol
Value Out (i.e. for a QPSK constellation is
[0,1,2,3]), you have to scramble the Symbol
Position values again to perform a correct decoding.
You can take care of this by using a cascading link to
the Map block again and feeding it with the
originary coding sequence.
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Constellation Decoder - 2
Please also note that all our work is based on the ”old” version of the
gr constellation decoder block. In fact, the version we have just dealt
with is the one taken from the GNU Radio 3.4.2 tarball and built again as a
custom block with the cmake custom wrapper you can usually ﬁnd inside a
tarball1 .
This however is nowadays considered an old-school method since the latest
tarballs provide the “Swiss-army knife” tool called gr-modtool, which will
generate the skeleton of your new custom package.

1 This is true for tarball version ranging from 3.5.0 to 3.6.5.1

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Chunks to Symbols
Once we have set the coding on our binary sequences
(the ones from the Packed to Unpacked block) we
can assign the points of the constellation to them.
So for example, if we want to build a BPSK
constellation we will assign the points [-1,1] to the
Symbols Table.
Otherwise if we want to build a QPSK constellation
we will assign these other points :
[1+1j,-1+1j,-1-1j,1-1j]
Input type : int, short, byte
Output type : complex, ﬂoat
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Throttle
We usually use this block to limit the cpu load when
operating with non-audio or non-usrp sources/sinks.
This means that our system won’t freeze or be
overloaded by the GNU Radio engine.
If by any chance we forget it to put it in our ﬂow
graph, we will be warned about it runtime.
Type : complex, ﬂoat, int, short, byte

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WX GUI Slider
It’s a simple slider making part of the GNU Radio
GUIs. We can use to vary at runtime the value of
certain variable we have previously set.
We will mostly use this slider to set the Eb /N0 value
in our simulations.
We are also able to set the Default Value (it is
usually a ﬂoat one), and the number of steps
between the Maximum and Minimum value of the
variable itself.

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WX GUI Scope Sink
The WX GUI Scope Sink is a simple graphical sink
to show our generated waveforms or digital
constellations as well.
At runtime, you will notice that is provided with
buttons to set the X and Y axis divisions and their
oﬀset as well.
Be sure to set XY Mode to On when working with
digital constellations or any complex stream of data
to show both the orthogonal components in the
correct way.
Type : complex, ﬂoat
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Unpacked to Packed
Basically, this block exactly works in the reverse way
of the Packed to Unpacked block we saw a couple
of slides ago.
Remembering the four binary sequences, which were
“splitted” from the original one :
•
•
•
•

00000011
00000010
00000000
00000001

they will be reverted to the original transmitted
binary sequence 11100001.
Type : int, short, byte
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Import
The Import block allows us to import the installed
python libraries or even some custom code residing
in your PYTHONPATH(s).
Some common examples of imports into the block
are :
• Import: numpy
• Import:

scipy

• Import:

<my-code>

and so on.

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WX GUI Number Sink
The WX GUI Number Sink is a simple graphical
sink to display the result of a numeric calculation of
a GNU Radio ﬂow graph.
We also might feed it,for example, with a constant
source (depending on a variable) to have a numeric
reference to compare with a real-time result.
You can also set the number of the decimal digits so
to get more accuracy in the displayed result.
Type : complex, ﬂoat

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BER and SER calculation
These ones are the blocks for the BER and SER
calculation of the digital modulation. We usually
feed their inputs with the reference and the decoded
stream of data.
Please note that we have only to specify the number
of Bits per Symbol only in the BER block.
It is also recommended to set number of samples of
Window Size to 600k or 1M (and of the input data
streams as well) to get an accurate measure of the
error rates.
Input type : byte
Output Type : ﬂoat
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Now let’s build a QPSK
constellation together ! ! !

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Click on the GRC icon in your menu bar

or just type from your local shell :

$ gnuradio-companion &

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map(int, numpy.random.randint(0, 256, 6e5))
1+1j, -1+1j, -1-1j, 1-1j

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The developed tool :
gr-bertool

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The developed tool : gr-bertool
• The tool main GUI

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• BER experimental veriﬁcation

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• Real-Time BER experimental veriﬁcation

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• Complementary tools

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The BER Calculation

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BER experimental veriﬁcation
• The Bit Error Rate (BER) of a digital modulation, is the number of bit

errors divided by the total number of transferred bits during a studied
time interval

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time interval
• Let’s verify the BER theoretical values with the experimental ones by

varying the signal-to-noise ratio Eb /N0

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time interval
• Let’s verify the BER theoretical values with the experimental ones by

varying the signal-to-noise ratio Eb /N0
• From digital communications theory is well known that for a Q-PSK

modulation the Bit Error Rate is given by :
Pb = Q

2Eb
N0

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• This set of tools calculates the BER in

a range of Eb /N0 values given by min
and max with the opportunity to
choose the increase step size

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• We can enable or disable the Gray

Coding

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• We can enable or disable the Gray

Coding
• By clicking on the Plot button the BER

curves are showed in a simple BER vs
Eb /N0 diagram

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We can see a perfect agreement between the theoretical results and the
experimental ones :

(a) BER AWGN BPSK

(b) BER AWGN Q-PSK

(c) BER AWGN 8-PSK

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Let’s try it together ! ! !

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The Real-Time BER Calculation

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Real-Time BER and signal constellation evolution
• This tool allow us to show the real-time

BER and signal constellation evolution
in the three diﬀerent types of
examinated transmission channels

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• In the following example we’ll show the

BER evolution in the Rician Channel in
the range of Eb /N0 values going from
−15 dB to 0 dB

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−15 dB to 0 dB
• Once started the BER value settles to

the BER value corresponding to
Eb /N0 = 0 dB about equal to ≈ 0.11

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−15 dB to 0 dB

• Ch1 Experimental Value ; Ch2

Theoretical Value
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−15 dB to 0 dB

• Ch1 Experimental Value ; Ch2

Theoretical Value
• Let’s see the evolution....

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Real-Time BER evolution

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The signal constellation
• Let’s consider a generic transmission scheme for a TLC system.
m(t)
S

s(t)
Tx

r(t)
Tx Channel

d(t)
Rx

D

Figure : Generic block diagram for a TLC system

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• Let’s consider a generic transmission scheme for a TLC system.
m(t)
S

s(t)

r(t)

Tx

d(t)
Rx

Tx Channel

D

Figure : Generic block diagram for a TLC system
• In the absence fo any noise in the channel the generci transmitted

symbol si will be correctly received. The plot of the received symbols is
¯
knows as “Constellation” of the digital modulation.
ℑ
s3 (‘01’)
¯

s0 (‘11’)
¯

ℜ

s2 (‘00’)
¯

s1 (‘10’)
¯

Figure : Constellation of a QPSK modulation
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• The presence of noise in the channel modiﬁes phase and amplitude of

the transmitted symbols and so the received symbol ri is not one
¯
belonging to the constellation showed before
ℑ
s3 (‘01’)
¯

s0 (‘11’)
¯

The transmitted si symbol is not
¯
correctly received

ri
¯

ℜ

s2 (‘00’)
¯

s1 (‘10’)
¯
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Evolution of the Signal Constellation

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Real-Time BER Evolution


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Image Transmission

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Image Transmission
• This tool allow us to observe how the

most common image formats are
aﬀected by digital modulations

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Image Transmission

• We studied the eﬀects over the

simulated channels (AWGN, Rayleigh e
Rician) for a ﬁxed value of
Eb /N0 = 0 dB and Q-PSK digital
modulation for a Jpeg image

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Image Transmission


modulation for a Jpeg image
• Let’s see the results......

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Image Transmission : AWGN Channel

(a) Original

(b) AWGN
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Image Transmission : Rician Channel

(c) Original

(d) Rician
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Image Transmission : Rayleigh Channel

(e) Original

(f) Rayleigh
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Image Transmission


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Audio Transmission

most common audio formats are

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Audio Transmission


modulation

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Audio Transmission


modulation
• We took as sample the wav ﬁle

play it sam.wav with the following
speciﬁcations :

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Audio Transmission
Speciﬁcations of the sample ﬁle
play_it_sam.wav :
File Size: 1.76M
Bit Rate: 1.41M
Encoding: Signed PCM
Channels: 2 @ 16-bit
Samplerate: 44100Hz
Replaygain: off
Duration: 00:00:10.00
• Let’s see the results....
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Audio Transmission

(g) Original

(h) AWGN Channel

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Audio Transmission

(i) Rician

(j) Rayleigh

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Conclusions

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Conclusions
Why using gr-bertool ? Advantages
It’s an helpful tool for the teacher to use in TLC courses

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Conclusions
The student can ﬁnd a quick veriﬁcation with the learnt notions during
classes

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Conclusions
classes
It has an ”user-friendly” GUI

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Conclusions
classes
It has an ”user-friendly” GUI
It’s open-source !

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Contact Information
Arturo Rinaldi
Freelance Collaborator @ DIECII
Address : Dep. of Electronics Engineering (DIECII) C.da di Dio, 98166 Messina (Italy)
E-mail : arty.net2@gmail.com
Fixed : +39-090-3977376 ; Mobile : +39-340-5795584 (Whatsapp)
Skype : arty.net ; Facebook : arty.net
Twitter : artynet2 ; LinkedIn : Arturo Rinaldi
Prof. Giuseppe Campobello, Ph.D.
Researcher in Telecommmunications
Address : Dep. of Electronics Engineering (DIECII) C.da di Dio, 98166 Messina (Italy) - Room: 636
(block B, 6th ﬂoor)
E-mail : gcampobello@unime.it
Fixed : +39-090-3977378
Prof. Salvatore Serrano, Ph.D.
Researcher in Telecommmunications
Address : Dep. of Electronics Engineering (DIECII) C.da di Dio, 98166 Messina (Italy)
E-mail : sserrano@unime.it
Fixed : +39-090-3977522
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