of so much upside many communication applications

of Differential Chaos Shift Keying (DCSK) in Security Design

Authors: Tyler Lisnock and Aaron

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It all started back around the 1990 when the amount of
chaos-based communication systems started expanding and began to exploit the
properties of chaotic waveforms. The amount of positive outcomes discovered by
non-linear signals was amazing. Due to so much upside many communication
applications have been specifically designed when energy, data transfer rate,
and synchronization are important parameters. A major focus took place with
non-coherent chaos-based systems being able to implement the advantages of
chaotic signals and noncoherent detection and to avoid needing chaotic
synchronization, which in the presence of additive noise exhibits a weak
performance. This paper will describe the application of Chaos engineering for
wireless communication systems explaining their pros, and cons to society and
explain exactly how chaos engineering can be implemented to ensure a more
protected and secure communication channel where data is still efficiently
transmitted. In order to really understand what chaos engineering is you must
first understand the meaning of the  each
term. Synchronization in schemes are based on coherent detection, it also  enables and allows timing as well as recovery
. Carrier recovery refers to the reproduction or recovery, at the receiver’s
end of the carrier signal produced in the transmitter. Once both transmitter
and receiver oscillators are matched, coherent demodulation of the modulated
baseband signal is possible. On its turn, timing recovery refers to the need
that both coherent and noncoherent receivers have to know the exact time and
duration of each received symbol in a stream, in order to be able to assign
decision times and reset the initial conditions of the correlator6. Simply
speaking chaos synchronization means we a specific form of carrier recovery
will be utilized and implemented in order to fully recover the carrier’s

Previous Work

In the last twenty-five years cell phones and more
specifically wireless communication have seen a rise in usage and demand. With
this increase in services Multi carrier (MC) transmission has become basically
a necessity. MC transmission happens when the signal being sent is divided into
different “sub” signals which are sent in a parallel manner over the channel to
be transmitted and then received by the receiver. This allows for information
to transfer at a faster rate than if it were to have the same sample rate
serially. Chaos Shift Keying (CSK) is a digital modulation where each symbol to
be transmitted is encoded as coefficients of a linear combination of signals
generated by different chaotic attractors 3. Transmission and reception of
the signal relies basically upon the transmitter and receiver of the system
being synchronized. However, this is not always the case as in a non-coherent
system. Which leads to the introduction of the two types of system detection;
coherent and non-coherent. For a coherent system after synchronization the
receiver has the ability to implement both recovery of the carrier and the
timer. In essence, the systems carrier recovery is the capability for the
receiver to duplicate the signal that has been sent from the transmitter. This
specific signal decoding method is called chaos-pass filtering which use the
property of synchronous systems to discard the non-chaotic part of the signal,
which allows the message to be separated from the chaotic carrier signal
3.  A non-coherent receiver doesn’t
need the carrier signals phase information which is beneficial in the fact that
it doesn’t require complex/expensive carrier recovery circuit2.  A proposed system with a non-coherent
receiver, named differential chaos shift keying (DCSK) system, in which chaotic
synchronization is not used or needed on the receiver side, delivers a good
performance in multipath channels. Furthermore, differential non-coherent
systems are better suited than coherent ones for time and frequency selective
channels 1. DCSK is a variant of CSK with two maps whose basis sequences
consist of repeated segments of chaotic waveforms. To transmit a “1” two
identical segments of length N/2 integer are sent. To transmit a “0” the second
segment is multiplied by (?1). The decision on the transmitted bit is based on
the correlation between these two segments and the decision threshold is zero,
independently of the channel noise 2. One major problem with using DCSK and a
non-coherent CSK is the need to use aperiodic signals, which means that the
energy per signal is distinct at each symbol and non-uniform. Essentially
because we’re using an aperiodic and have different energy values the receiver
can have errors that will occur even when the channel is ideal and noiseless
which is obviously troublesome. The major weakness of the DCSK system is an
infiltrator is able to realize the chaotic sequence. a number of recent studies
have proved that an intruder can recover chaotic sequences by blind estimation
methods and use the sequences to detect symbol period, which will result in the
original data being exposed. To overcome this security weakness, this paper
proposes a novel chaotic DSSS technique, where the symbol period is varied
according to the nature of the chaotic spreading sequence in the communication
procedure. The data with variable symbol period is multiplied with the chaotic
sequence to perform the spread-spectrum process. Discrete-time models for the
spreading scheme with variable symbol period and the despreading scheme with
sequence synchronization are presented and analyzed. Multiple-access
performance of the proposed technique in the presence of the additional white
Gaussian noise (AWGN) is calculated by means of both theoretical derivation and
numerical computation5.  With this
knowledge an intruder is no longer able to identify the symbol period, even
with adequate data of the chaotic sequence applied.


Example of Signal Sequences below:



A common method used in chaos engineering is  direct-sequence spread-spectrum (DSSS)
technique which require good  periodic
variation properties ,good correlation,a 
wideband spectrum, initial condition must be sensitive to improve the
security at physical layer. Studies show that 
if an intruder may possibly recover a 
chaotic sequences by a method called blind estimation which will use the
data given from the different sequences to identify the symbols period given
from the this information from your 
original data. We can enhance this security issue by creating using a
varied period according to the behavior of the chaotic spread in the communication
system. How this works exactly is the information given from  the system is given in a variable symbol
period and is  multiplied with a chaotic
sequence to perform the spread-spectrum process. Below are different examples
of different  discrete-time models that
show the synchronization , and analyzation 
for a spreading scheme with variable symbol periods  as well as a despreading scheme with
sequence. We cover a series of Multi-access performance of white Gaussian noise
(AWGN) which  is calculated by both  numerical computation and theoretical
derivation . After this we compare and contrast the computer and actual
simulations to verify that received data is correct our obtained results point
out that our proposed technique can protect the DSSS systems against the
detection of symbol period from the intruder, even if he has full information
on the used chaotic sequence

 Spreading scheme with variable bit period

Block diagram demonstrates a spreading scheme with a pulse
chain that has a variable inter-pulse intervals. We used  {pl}, as the variable interval pulse
generator (VIPG) The input we used is the 
{xk} to stand for the chaotic sequence. Which is sampled at each
triggered input pulse.  (1)pl=P(t?tl),
with  (2)P(t)={10?t??,0 Then the  tl is the when you generate the lth pulse and  the 
output sample xl is then converted into a positive integer ?l.This
happens by using a  transformation
function example (?l=f(xl)).Once  f( · )
is determined the sequence {xl} varies 
range is discovered and the  xmin
& xmax, {?l} is then in direct 
correlation to the range 
?min=f(xmin)=0,?max=f(xmax)=?m.So in order to determine the function
f( · ), we had to usea fixed value for ?m. After we choose the value the  xmin, xmax of the function is then divided
into (?m+1) value intervals, xmin+j?,xmin+(j+1)?,with j varying from 0 to ?m
and ? being a constant defined by(3)?=(xmax?xmin)/(?m+1).Once the input number
xl falls in the range of xmin+j?,xmin+(j+1)?, the value for the other
source  value  ?l can finally be determined for example:
(4)?l=f(xl)=?xl?xmin??,Depending on the value of ?l,  will determine  (l+1)after that the pulse is created at the
output of the VIPG at the tl+1 given by (5)tl+1=tl+(?+?l)?,? is the chip period
of the chaotic sequence {xk} and ? is a fixed integer and the value is fixed.

Figure 1: Spreading Scheme below:


Figure 1 7


Figure 2: PC Simulated image for DSSS system below


Figure 2 7


All together you should get Figure 3 below:


Figure 37


Despreading scheme
chaotic sequence synchronization

 The local chaotic
sequence is regenerated and synchronized with the incoming called a
synchronized chaotic generator (SCG)

Figure 4 7


This synchronization scheme in figure 4 is used for a conventional
chaotic DSSS technique. The SCG is a synchronization process in which there is
two phases separated acquisition and tracking. Looking into the acquisition
phase, we use the correlator to calculate the value between the  local chaotic sequence and the  received signal. As soon as the correlator is
triggered by the pulses {pl} then eventually stops on it own after a certain
period depending on the applications duration, Ts = ?? . The correlators output
is then squared,with the square value at a fixed threshold. What is important
and people usually don’t know is that the local chaotic sequence is shifted and
advance by one chip period, if the threshold does not exceed past. This process
is repeated until the threshold exceeds. The acquisition phase is then put to
aa halt as the synchronization process continues  to track 
the signal and  phase. What the
tracking maintains is the  local chaotic
sequence in synchronism  mode with the
incoming signal. The  noted  signal received is fed  to two correlators, where the two outputs
from the chaotic generator with either a early or late  sequences is delayed by the other signal by a
interval always less than ?.In order to get the correlation value you must  square the value before being subtracted from
each other. Once this value is discovered and there is a difference in value we
input the loop filter  that drives the
(VCO). Here, the VCO as a clock for a chaotic generator. Although if the
synchronization is not precisely exact, the squared output from one of the
two  correlators overrides  the other and once this happens the VCO will
either be  advanced or delayed depending
on the situation . In order to find the exact synchronism completely you must
have to have two squared outputs that are would equally displaced from the
peaks value. As for a synchronized chaotic sequence is used for the despreading
process and data recovery. The received signal is the sum of the transmitted
signal and the noise of AWGN channel.


Figure 5: Despreading scheme below:

Figure 5 7


Figure 6: Despreading simulation below:

Figure 6 7


All together you should get figure 7 below:

Figure 7 7



Similar to almost all engineering tools the application of
Differential Chaos Shift keying has both benefits and drawbacks. By introducing
the direct-sequence spread spectrum modulation technique our system is better
equipped to handle intruders trying to intercept the signal. The DSSS technique
varies the symbol period based on the spread sequence that is being utilized.

The systems numerous access performance will be enhanced when the initial
spreading factor (?) is increased which leads to a degradation in the symbol
rate. Increasing the initial spread factor will decline the performance of the
system, but also heighten its security and encryption by obscuring the symbol rate.

This is crucial because even with the chaotic sequence known an intruder is
unable to infiltrate and intercept the signal. This being said the major
concern now is obtaining the proper ? value while considering the trade offs
between the system’s overall performance, speed, and most applicable it’s
encryption and security. This illustrates the effectiveness of the DCSK DSSS
technique by applying a variant period allowing for an improvement in the
systems physical layer of security.