It all started back around the 1990 when the amount of chaos
type communication systems started expanding and began to exploit the
properties of chaotic waveforms. The amount of potential non-linear signals had
was virtually unimaginable. 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 signal.

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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 demand 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. Synchronization of the coherent system allows
recovery of both the carrier and timer. Basically 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 signal’s phase information which
is beneficial in the fact that it doesn’t require complex/expensive carrier
recovery circuit 2.  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 equivalent sections of length N/2 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 computation 5.  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 a
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  o two correlators, where the two outputs from
the chaotic generator with either an early or late  sequences is delayed by the other signal which
is less than the time period ? . 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.





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