Communications and Network, 2013, 5, 57-64
http://dx.doi.org/10.4236/cn.2013.53B2012 Published Online September 2013 (http://www.scirp.org/journal/cn)
Modulation for Digital Radio Broadcasting Using
Amplitude Autocorrelation of Pseudo Random Noise Codes
to Carry Information
Fabrício de Araújo Carvalho, Fernando Walter
Departamento de Telecomunicações, Instituto Tecnológico de Aeronáutica, São José dos Campos, Brazil
Received June, 2013
ABSTRACT
The frequency bands used in mobile communications are allocated according to the type of application. With the need
for more channels, the frequency spectrum has become a scarce natural resource. This study shows the results of a pro-
posed modulation using a variation of the autocorrelation of pseudo-random codes to carry information. The work also
presents the generation of multiple orthogonal axes to increase the bit rate thus improving the channel efficiency.
Keywords: Digital Radio Broadcasting; Spectral Efficiency; Pseudo Random Codes; CDMA; SDR
1. Introduction
The perception of the environment that surrounds us and
information generated from this perception are rational-
ized to form our knowledge. This knowledge is vital to
the survival of the individuals and the society in which
they live. This knowledge is the result of lived and ra-
tionalized experiences, but the ability to communicate
allows its transfer among members of different groups,
so that this knowledge is incorporated into the experi-
ences of others.
The transfer of knowledge ensures its elaboration, its
improvement, as well as its maintenance over the years.
No person aware of a common problem fails to share it
with a neighbor or warn him/her of a danger. The diffi-
culties and the existing obstacles in our way of living
sharpen our thinking and responses to problems to be
communicated to the others.
The knowledge spreads through verbal and visual
communication, and perpetuates in books, drawings and
paintings, as well as in the memory of individuals. It is
therefore a cumulative process, the result of the senses,
reasoning and communication.
Over the centuries, technological advances have al-
lowed the expansion of the media. In the media today,
the information is propagated mainly by electromagnetic
waves and digital files. Today, the state of the art elec-
tronic systems also allow the machines to communicate
among themselves. Relatively traditional systems, such
as phone systems, cell phones, computer networks, vi-
deogames, PDAs (Personal Digital Assistants), TVs (to-
day, smart TVs) go through a period of convergence and
interactivity forming a large communication network.
In this context, the frequency spectrum used by all
these agents of communication has become a scarce nat-
ural resource.
The communication frequencies are allocated accord-
ing to the type of application and transmission medium.
We particularly observed a useful spectrum for AM and
FM radio transmission (Figure 1), where we note scar-
city of ranges in relation to the demand for new services.
Figure 1. Allocation of Frequencies: 54.0 - 117.975 MHz (Source: National Telecommunications and Information Admini-
stration, http://www.ntia.doc.gov/osmhome/allochrt.html).
C
opyright © 2013 SciRes. CN

F. de A. CARVALHO, F. WALTER
58
This demand requires a continuous search for new
technologies. Since 2005, the Brazilian government has
opened a public call for submission of new proposals and
assessments of the existing digital radio. Meanwhile,
some universities and federal institutes are developing
studies with the same purpose.
2. Digital Radio
Having the goal of developing a communication system
capable of operating with existing systems and with a
power close to the thermal noise, we adopted, as a start-
ing point, the CDMA DS technique, widely used in mo-
bile communication systems. In the CDMA technique
pseudo-random codes are used (Pseudo Random Noise -
PRN) allowing access several channels to the environ-
ment using the same carrier frequency.
With the development of the first prototype of broad-
cast radio (transmitter and receiver) using only the BPSK
modulation, we found a low bit rate for audio/video ap-
plications. Because of this, the work has been directed to
increase the number of bits per symbol, thus resulting in
the proposed modulation for better transmission of the
audio signal.
The proposed modulation shows a method of adding
more information per code period by exploring the am-
plitude of autocorrelation of the PRN code. The signals
are generated and processed using baseband processing
techniques with digital signals.
2.1. PRN Codes
The used PRN codes are called Gold codes. They are
almost orthogonal to each other. They are formed by a
binary sequence of “0`s” and “1`s”. In the pseudo- ran-
dom sequences, the bits are called “chips”. The term chip
is used to distinguish the bit of a code from a bit of the
information. In Equation 1, we can see the representation
of the PRN code ci (t) of the i-th transmitter.

1
0
,0
Nchip
iil il
lchip
tlT
ctcc ou
T


 




1 (1)
where () represents a rectangular pulse of Tchip; cil
duration corresponding to the value of the chip (“0” and
“1”) for a given l; l being a counter from 0 to N-1; N is
the number of chips of the code. The sequence ci(t) is
periodic (Equation 2), period TC (N x Tchip).


1
00
Nchip C
iil
kl chip
tlT kT
ct cT
 






  (2)
The sequence can be converted to Ci(t) of “1`s” and
“-1`s” if the multiply operation is used to modulate the
signal (Equation 3):

 
cos .
ii
Ct ct


 (3)
The used sequence is generated from two registers of
maximum length, denominated as G1 and G2 Figure 2,
for sequence with length of 511 (29 - 1) registration chips
are used with 9 cells or elements. Both records are ini-
tialized with 1`s to operate with module 2 (

). Each
record has its values shifted according to a time reference,
which determines the rate of the chip and hence the code
period.
Table 1 presents the G1(t) and G2(t) polynomials used
to match the value in each element of G1 and G2 registers.
Figure 3 shows the sequence of chips provided by
PRN code generator (Figure 2).
Figure 2. Generator of gold codes.
Table 1. PRN code generator polynomials.
Reg. Polynomial Initialization
G1(t) 94
1xx  111111111
G2(t) 9
1xxxx  643 111111111
Figure 3. PRN sequence of 511 chips of Gold code genera-
tor.

F. de A. CARVALHO, F. WALTER 59
The PRN sequence identifies what the tuned radio sta-
tion is. The distinction by the receiver between the
transmitters is made through a correlation process. The
correlation occurs between the code contained in the re-
ceived signal and its replica generated in the receiver and
measurement of the degree of similarity between these
signals by amplitude of correlation. The amplitude of
correlation between distinct PRN`s and orthogonals is
approximately equal to zero, Rij (τ) (cross-correlation) for
a delay τ (Equation 4).
  
0
10; /
chip
NT
iji j
RCt Ctdtpqualquer
NT

 


(4)
In this equation, Ci(t) and Cj(t) are the PRN codes for
the i-th and j-th transmitter, respectively.
For the autocorrelation, Rii (τ), the amplitude is non-
zero for delays τ less than a chip; 0 ≤ |τ| ≤ T
chip,
and are approximately zero for delays, τ, larger than the
chip (Equation 5).
  
2
0
1;
1
0;
chip
NT chip
c
iii i
chip
chip
Apara T
T
RCtCtdt
NT para T










 (5)
As noted, the autocorrelation peak has the width of
two chips and repeats every period (N x Tchip) of the code.
The amplitude increases linearly from a prior chip to
maximum alignment and drops to approximately zero
one chip after the maximum (Figure 4).
N
A2

chip
TN )1( 
chip
TN )1( 
chip
TN )1(

chip
TN )1( 
2
A
)(

R
chip
NT
chip
T
chip
T
chip
NT
chip
T
Figure 4. Process of autocorrelation of a PRN sequence.
The autocorrelation for this code is shown in Figure 5.
In it the maximum values of non standard amplitudes can
be observed [511, 31, -1, -33]. The sequence was delayed
250 chips to center the maximum amplitude.
2.2. PWM
In the existing modulations, three parameters of the car-
rier are modified to transmit information: the phase, the
frequency and its amplitude.
In this proposal, in order to increase the number of bits
per symbol by exploring the dynamic range of the auto-
correlation amplitude of a given PRN sequence, we varied
the width of the chip via a modified PWM called CWM,
where the letter C represents the initial chip (with ampli-
tude values +1 and -1), Figure 6.
In this example, with four bits we can obtain 16 levels
of the cyclic variation of the CWM, which is equivalent
to dividing the maximum amplitude of autocorrelation
into 16 levels. Therefore, the transport of the information
on the correlation amplitude can transmit more than one
bit per code; in this case four bits. To further increase the
bit rate, new orthogonal axes were created.
2.3. Dimensional Generator
The different PRN codes can be viewed as orthogonal or
approximately orthogonal subcarriers (as in OFDM
modulation). The number of distinct codes of the same
length is, however, limited.
The ideal for the initial design of the system is that
each station is characterized by only one PRN code.
A good solution found and used so far, is working with
the same code for all axes, but with fixed displacement of
n chips between them. This solution intends to save the
number of PRN codes for a given geographic area and
50 100 150 200250 300350 400450 500
0
50
100
150
200
250
300
350
400
450
500
X: 148
Y: 31
Correla ção
Am plitude
Chi p s
X: 251
Y: 511
Figure 5. Autocorrelation of pseudo-random codes.
Chip period
(Tc)
0000
0001
0010
0011
0100
Word: 4 bits
PWM
1
-1
1
-1
1
-1
1
-1
1
-1
Figure 6. Control of the width of the chip. The width is a
function of the binary word from the A/D converter of au-
dio.
thus enables more channels to be used, therefore, more

F. de A. CARVALHO, F. WALTER
60
stations, and more community radios.
Figure 7 shows 3 axes with maximum amplitude. It
means in this case that all three axes called X, Y and Z,
are transmitting the same sequence of bits. In this case:
X= 0000; Y= 0000; Z= 0000.
From the point of view of the receiver, this solution is
desirable because it facilitates the generation of internal
signals by using only a code generator for tracking and
demodulation.
Another feature which will be seen later on is the iden-
tification of the axes. The identification of only two axes
is enough to locate the others. We need to remember that
the relative displacement between the codes (axes) is
fixed.
We observed that all three axes are at the same value
of maximum amplitude. But it is important to say that the
value of maximum amplitude is not obtained for any rel-
ative displacement between the axes. There are only a
few points where we can achieve this balance. The iden-
tification of these points and location of new axes com-
poses this study. The modulation of chip width of direct
sequences (DSCWM) resulted in the development of
transmitter and its dual receiver.
3. DSCWM Transmitter
The binary information coming from the A/D audio con-
verter operates on the CWM (PWM chip), which deter-
mines the width of the chip, and consequently the value
of amplitude of autocorrelation obtained by the receiver
during the correlation process between the signals. The
CWM exists only in the transmitter. The signal generated
internally by the receiver does not change the width of
the chip, this way the amplitude obtained in the correla-
tion is only a function of the transmitted information.
A pilot channel containing the same code is needed to
correctly decode the amplitude. It serves as a reference
for the received power, in addition to synchronization
and correction of Doppler shift on the carrier and the
code.
The block diagram, Figure 8, presents an overview for
the DSCWM transmitter encoded on a digital baseband
and digital intermediate frequency (IF). In this diagram,
the voice signal is digitized by an A/D converter. The
binary sequence provided by the converter controls the
width of the code chip that carries the information. This
signal is subsequently multiplied by the digital carrier
and elevated to an intermediate frequency. The transmis-
sion rate can increase with the addition of new orthogo-
nal axes, with the component carrier in the quadrature.
The oscillator serves as a time reference for the A/D
converter and the frequency synthesizer, which is re-
sponsible for determining the frequency for the other
transmitter circuits: DSCWM modulator, PRN code gen-
erator and CWM.
The PRNs code generator provides pseudo-random
sequence for the dimensional generator (code shifter) and
the DSCWM modulator. The orthogonal axes generated
by the dimensional generator, are modulated by CWM.
Figure 9 shows the result of the digitalization of axis
and the application of the duty cycle on each of them.
Figure 7. The same pseudo-random code for the new axes is
used.
Frequency
synthesi zer
DSCWM modulator
PRN code
generator
Compression of
the data
/N1
/N2
f0 = 10 MHz
Broadcast
signal
Information
Data Mapper
A/D converter
Local
oscillator
CWM1 CWM2 CWM3 CWM4

PRN
Code Shifter
CX CY CZ CW

mixer
Figure 8. Block diagram of the DSCWM transmitter in the
baseband and digital IF.
1000 2000 3000 4000 5000 6000 7000 8000
0
1000
2000
3000
4000
5000
6000
7000
8000
X: 4320
Y: 7678
Correlação em X,Y,Z
A mpli t ude
Chips
X: 5768
Y: 4866
X: 2408
Y: 5314
X: 189
Y: 6494
Figure 9. The same pseudo-random code is used for the new
axes.

F. de A. CARVALHO, F. WALTER 61
The binary sequence coming directly from the A/D
converter or compression of the data is distributed to the
various orthogonal axes through the data mapper. Each
axis is modulated by a duty cycle determined by the out-
put of the data mapper. The signals of the axes coming
from dimensional generator are multiplied by the respec-
tive duty cycle and subsequently summed.
Afterwards, the result is used to modulate the in-phase
component of the carrier. The signal is stored in a binary
file to be read by the software of the receiver.
3.1. DSCWM Receptor
At the receiver, the broadcast stations are identified by an
autocorrelation process. The amplitude correlation is
used to identify propagation delay, the presence of the
signal transmitter, and a likely Doppler shift on the car-
rier. Figure 10 illustrates a DSCWM receiver in a block
diagram.
After downconverter stage, the analog IF is sampled,
quantized and encoded by an AD converter. Figure 11
illustrates the sampling by fs (16 points per chip).
Preamp Downconverter A/D
Converter
CAG
Refe re n ce
Oscillator
DSCWM
Demodulation
D/A Converter
Frequency
Synthesizer
Analog
IF
Digital IF
Antenna
Broadcast 1
Broadcast 2
Correlator
Binary Sequence
axis N axis 1...
Pilot
Ch.
Figure 10. Community radio broadcasting receiver CDMA.
2
s
fs
f
f
Output
frequency
Input frequency
Figure 11. Process of bandpas s sampling.
The converter output is a digital IF that is processed by
the correlator.
The station's signal must be weak enough not to harm
the other communication systems, Figure 12. In this
proposal, it is transmitted with power close to the thermal
noise.
In a block diagram Figure 13 shows the process of
tracking and demodulation of the signal at the DSCWM
receiver [1,3-4].
The axis used to track a signal for correction of carrier
and code frequency is also used as a reference of maxi-
mum amplitude. This axis (pilot signal) does not undergo
modulation by PWM circuit and is therefore used as a
reference for all other axes.
The dimensional generator of the receptor shows the
same axis as the ones existing at the transmitter, there-
fore the correlation process is immediate, because the
relative delays are maintained. For the synchronism and
further demodulation, it is enough to identify two or
more correlation peaks for the receiver to use the refer-
ence axis. The amplitude values for each axis are nor-
malized by the amplitude of the reference axis. For the
-50 -10 010 50
-180
-160
-140
-120
-100
-80
Frequency [ M H z]
Power [dBm]

-n dB m
(> -1 03 ,98 d Bm )
PRN
Noise f loor , 20 M Hz BW
RF filter
Figure 12. Signal of interest below the thermal noise.
Integrate
&dump
Code loop
discriminator
Integrate
&dump
Integrate
&dump
Integrate
&dump
Integrate
&dump
Integrate
&dump
E P L
Code Generator
Carrier loop
discriminator
Code loop
filter
Code
DCO
90º
E
E
P
P
L
L
Carrier
DCO Carrier
loop filter
Digital
IF
Si(m)
Dimensional
Generator
word
Pilot signal
Decompression
of data
D/A
conveter
CosSin
Transducer
Demodulador Multidimensional
Integrate
&dump
Integrate
&dump
Integrate
&dump
axis
1axis 2axis 3
P
decoder
decoder
decoder
Integrate
&dump decoder
axis
4
mixer
mixer
Figure 13. Phase of tracking and demodulation.

F. de A. CARVALHO, F. WALTER
62
amplitudes of the axes in the demodulation process, the
FFT method can be used.
One of the processing stages in the receiver is the
identification of the beginning of the word, or synchro-
nization of the bit for a correct representation of the sam-
ple. When the DSCWM modulation symbol shows the
number of entire multiple bits of the word (16-bit word),
16, 32 and 48 bits, the synchronization process is done
by modulation. For example, a signal transmitting three
orthogonal axes, where each axis carries a 16-bit word,
three words are sent per symbol. The receiver knows that
each axis contains a word with 16 bits, making unneces-
sary the preamble for synchronization. The PRN code
itself makes this function. The following example was
simulated using a submultiple of the 16-bit word. In this
case four orthogonal axes were adopted, each with four
bits of information. At the receiver, the four axes rebuilt
a 16-bit word, with no need of the preamble to synchro-
nize.
Another important fact is that the bits used for the
correction of parity can be allocated to a specific axis,
which facilitates the decoding of the message.
3.2. Results
To test the transmission and reception of the signal, an
audio signal captured by a computer microphone was
used (Figure 14). This signal was sampled at a rate of 8
kHz, quantized and encoded into 16-bit words.
The message “RECORDING AUDIO” is displayed
(Figures 1 5 and 16) in the time and frequency domain.
For more than three axes other nomenclature could be
used: eg A1, A2, ... AN, B1, ..., C1, ..., and the represen-
tation of the constellation would not be as we are accus-
tomed to. One suggestion might be representation in
multiple plans or multiple cubes.
Observing the constellation in three dimensions (Fig-
ure 17) and then the same for the XY plane, using the
zoom tool (Figure 18), we can see a portion of a vacant
space.
This leads us to the conclusion that there is a possibil-
ity of a larger number of bits per symbol to be transmit-
ted without the need for an increase of the space to more
than four dimensions (the fifth axis).
With this multiplicity of axes, it is possible to obtain a
much higher than intended number of bits per symbol.
Figure 14. Block diagram of the prototype.
Figure 15. Original audio signal in the time domain.
Figure 16. Original audio signal in the frequency domain.
Figure 17. The X, Y and Z axes generated by the dimen-
sional generator form the three-dimensional space that
composes the constellation plot in 3D. Each of the colored
dots represents a symbol containing 12 bits. The fourth axis
has not been traced.

F. de A. CARVALHO, F. WALTER 63
X = 2048
Y = -2022
Z = -5135
Figure 18. A view in XY.
Figure 19. Recovered signal in the time domain.
Figure 20. Recovered signal in the frequency domain.
The retrieved message (Figures 19 and 20) was plotted
in red to differentiate the transmitted signal. The differ-
ence of the spectrum is small in relation to the original
information, and depends on the instant of observation
used to calculate the FFT.
3.3. Conclusions
The increasing demand for new communication channels
requires a continuous search for new technologies. In
research of software-defined receivers and transmitters,
there is a fertile field for new works which are strategic
for the present society.
A new proposal of modulation of digital radio broad-
cast capable of operating on the same frequency of the
AM and FM radio with signal near the thermal noise was
presented. The modulation allows a greater number of
bits per symbol (as compared with BPSK) by using: 1)
the extent of autocorrelation and 2) the number of or-
thogonal axes. The data transmitted by each of the axes
were concatenated in the receiver after demodulation to
compose the final message. However, it is worth noting
that each axis can be treated as a different channel and
with different types of data (axis 1: channel 1, axis 2:
Channel 2,...). The PWM used in our proposal is bipolar
and acts on the code chip width and therefore is denomi-
nated as CWM (“C” initial chip), so that by reducing the
duty cycle, the positive period of the chip is reduced
while the negative suffers equivalent increase in modulus.
Signal reception from radio stations broadcasted with
distinct pseudo-random codes (PRN), in addition to se-
cure communication, allows offering services of precise
positioning complementing the global positioning sys-
tems GNSS (GPS, GLONASS and Galileo). The need for
positioning is a reality for current transport systems (ur-
ban, road and rail, providing estimates of position and
time of arriving) and for agriculture (eg autonomous
harvesters).
Being a complete communication system (transmitter
and receiver) many further studies should be made. Study
of multipath and fading are some examples, but due to
the inherent characteristics of the PRN codes, should
address these issues and good results are expected during
retesting.
4. Acknowledgements
The NavCon Navigation and Control Company, partner
of the Instituto Tecnológico de Aeronáutica by allowing
the continuous training of its engineers.
REFERENCES
[1] J. B. Y. Tsui, Fundamentals of Global Positioning System
Receivers, A software approach. Wiley Interscience Pub-
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[2] Carvalho, F. A. Alexandre B. V. Oliveira and F. Walter:
“Receptor GPS em Software. In: 25th Brazilian Sympo-
sium on Telecommunications – XXV SBrT 2007, Recife,
PE, Brasil, set, 03 a 07.

F. de A. CARVALHO, F. WALTER
64
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