IntroductionIt all started back around the 1990 when the amount of chaostype communication systems started expanding and began to exploit theproperties of chaotic waveforms.

The amount of potential non-linear signals hadwas virtually unimaginable. Due to so much upside many communicationapplications have been specifically designed when energy, data transfer rate,and synchronization are important parameters. A major focus took place withnon-coherent chaos-based systems being able to implement the advantages ofchaotic signals and noncoherent detection and to avoid needing chaoticsynchronization, which in the presence of additive noise exhibits a weakperformance. This paper will describe the application of Chaos engineering forwireless communication systems explaining their pros, and cons to society andexplain exactly how chaos engineering can be implemented to ensure a moreprotected and secure communication channel where data is still efficientlytransmitted. In order to really understand what chaos engineering is you mustfirst understand the meaning of the  eachterm.

Synchronization in schemes are based on coherent detection, it also enablesand allows timing as well as recovery. Carrier recovery refers to thereproduction or recovery, at the receiver’s end of the carrier signal producedin the transmitter. Once both transmitter and receiver oscillators are matched,coherent demodulation of the modulated baseband signal is possible. On itsturn, timing recovery refers to the need that both coherent and noncoherentreceivers have to know the exact time and duration of each received symbol in astream, in order to be able to assign decision times and reset the initialconditions of the correlator6. Simply speaking chaos synchronization means wea specific form of carrier recovery will be utilized and implemented in orderto fully recover the carrier’s signal.Previous WorkIn the last twenty-five years cell phones and morespecifically wireless communication have seen a rise in usage and demand. Withthis increase in demand Multi carrier (MC) transmission has become basically anecessity.

MC transmission happens when the signal being sent is divided intodifferent “sub” signals which are sent in a parallel manner over the channel tobe transmitted and then received by the receiver. This allows for informationto transfer at a faster rate than if it were to have the same sample rateserially. Chaos Shift Keying (CSK) is a digital modulation where each symbol tobe transmitted is encoded as coefficients of a linear combination of signalsgenerated by different chaotic attractors 3.

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Transmission and reception ofthe signal relies basically upon the transmitter and receiver of the systembeing synchronized. However, this is not always the case as in a non-coherentsystem. Which leads to the introduction of the two types of system detection,coherent and non-coherent. Synchronization of the coherent system allowsrecovery of both the carrier and timer. Basically the systems carrier recoveryis the capability for the receiver to duplicate the signal that has been sentfrom the transmitter. This specific signal decoding method is called chaos-passfiltering which use the property of synchronous systems to discard thenon-chaotic part of the signal, which allows the message to be separated fromthe chaotic carrier signal 3.  Anon-coherent receiver doesn’t need the carrier signal’s phase information whichis beneficial in the fact that it doesn’t require complex/expensive carrierrecovery circuit 2.  A proposed systemwith a non-coherent receiver, named differential chaos shift keying (DCSK)system, in which chaotic synchronization is not used or needed on the receiverside, delivers a good performance in multipath channels.

Furthermore,differential non-coherent systems are better suited than coherent ones for timeand frequency selective channels 1. DCSK is a variant of CSK with two mapswhose basis sequences consist of repeated segments of chaotic waveforms. Totransmit 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 transmittedbit is based on the correlation between these two segments and the decisionthreshold is zero, independently of the channel noise 2. One major problemwith 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 andnon-uniform. Essentially because we’re using an aperiodic and have differentenergy values the receiver can have errors that will occur even when thechannel is ideal and noiseless which is obviously troublesome.

The major weaknessof the DCSK system is an infiltrator is able to realize the chaotic sequence. Anumber of recent studies have proved that an intruder can recover chaoticsequences by blind estimation methods and use the sequences to detect symbolperiod, which will result in the original data being exposed. To overcome thissecurity weakness, this paper proposes a novel chaotic DSSS technique, wherethe symbol period is varied according to the nature of the chaotic spreadingsequence in the communication procedure. The data with variable symbol periodis multiplied with the chaotic sequence to perform the spread-spectrum process.

Discrete-time models for the spreading scheme with variable symbol period andthe despreading scheme with sequence synchronization are presented andanalyzed. Multiple-access performance of the proposed technique in the presenceof the additional white Gaussian noise (AWGN) is calculated by means of boththeoretical derivation and numerical computation 5.  With this knowledge an intruder is no longerable to identify the symbol period, even with adequate data of the chaoticsequence applied. Example of Signal Sequences below: Figure 17 MethodA common method used in chaos engineering is  direct-sequence spread-spectrum (DSSS)technique which require good  periodicvariation properties ,good correlation,a wideband spectrum, initial condition must be sensitive to improve thesecurity at physical layer. Studies show that if an intruder may possibly recover a chaotic sequences by a method called blind estimation which will use thedata given from the different sequences to identify the symbols period givenfrom the this information from your original data.

We can enhance this security issue by creating using avaried period according to the behavior of the chaotic spread in thecommunication system. How this works exactly is the information given from thesystem is given in a variable symbol period and is  multiplied with a chaotic sequence to performthe spread-spectrum process. Below are different examples of different discrete-timemodels that show the synchronization, and analyzation  for a spreading scheme with variable symbolperiods  as well as a despreading schemewith sequence. We cover a series of Multi-access performance of white Gaussiannoise (AWGN) which  is calculated byboth  numerical computation andtheoretical derivation . After this we compare and contrast the computer andactual simulations to verify that received data is correct our obtained resultspoint out that our proposed technique can protect the DSSS systems against thedetection of symbol period from the intruder, even if he has full informationon the used chaotic sequence Spreading scheme with variable bit periodBlock diagram demonstrates a spreading scheme with a pulsechain that has a variable inter-pulse intervals.

We used  {pl}, as the variable interval pulsegenerator (VIPG) The input we used is the {xk} to stand for the chaotic sequence. Which is sampled at eachtriggered input pulse.  (1)pl=P(t?tl),with  (2)P(t)={10?t??,0 Then the  tl is the when you generate the lth pulseand  the output sample xl is then converted into a positive integer ?l.Thishappens by using a  transformationfunction 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 functionf( · ), we had to usea fixed value for ?m. After we choose the value the  xmin, xmax of the function is then dividedinto (?m+1) value intervals, xmin+j?,xmin+(j+1)?,with j varying from 0 to ?mand ? being a constant defined by(3)?=(xmax?xmin)/(?m+1).

Once the input numberxl falls in the range of xmin+j?,xmin+(j+1)?, the value for the othersource  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 theoutput of the VIPG at the tl+1 given by (5)tl+1=tl+(?+?l)?,? is the chip periodof the chaotic sequence {xk} and ? is a fixed integer and the value is fixed. Figure 2: Spreading Scheme below: Figure 2 7 Figure 3: PC Simulated image for DSSS system below Figure 3 7 All together you should get Figure 4 below: Figure 4 7 Despreading schemechaotic sequence synchronization The local chaoticsequence is regenerated and synchronized with the incoming called asynchronized chaotic generator (SCG) Figure 5 7 This synchronization scheme in figure 4 is used for a conventionalchaotic DSSS technique. The SCG is a synchronization process in which there istwo phases separated acquisition and tracking. Looking into the acquisitionphase, we use the correlator to calculate the value between the local chaoticsequence and the received signal. As soon as the correlator is triggered by thepulses {pl} then eventually stops on it own after a certain period depending onthe applications duration, Ts = ?? .

The correlators output is thensquared,with the square value at a fixed threshold. What is important andpeople usually don’t know is that the local chaotic sequence is shifted andadvance by one chip period, if the threshold does not exceed past. This processis repeated until the threshold exceeds. The acquisition phase is then put to ahalt as the synchronization process continues to track the signal and phase.What the tracking maintains is the local chaotic sequence in synchronism modewith the incoming signal. The noted signal received is fed  o two correlators, where the two outputs fromthe chaotic generator with either an early or late  sequences is delayed by the other signal whichis less than the time period ? . In order to get the correlation value you mustsquare the value before being subtracted from each other.

Once this value isdiscovered and there is a difference in value we input the loop filter thatdrives the (VCO). Here, the VCO as a clock for a chaotic generator. Although ifthe synchronization is not precisely exact, the squared output from one of thetwo correlators overrides the other and once this happens the VCO will eitherbe  advanced or delayed depending on thesituation . In order to find the exact synchronism completely you must have tohave two squared outputs that are would equally displaced from the peaks value.As for a synchronized chaotic sequence is used for the despreading process anddata recovery. The received signal is the sum of the transmitted signal and thenoise of AWGN channel.  Figure 6: Despreading scheme below:Figure 6 7 Figure 7: Despreading simulation below:Figure 7 7 All together you should get figure 8 below:Figure 8 7 ConclusionSimilar to almost all engineering tools the application ofDifferential Chaos Shift keying has both benefits and drawbacks.

By introducingthe direct-sequence spread spectrum modulation technique our system is betterequipped to handle intruders trying to intercept the signal. The DSSS techniquevaries the symbol period based on the spread sequence that is being utilized.The systems numerous access performance will be enhanced when the initialspreading factor (?) is increased which leads to a degradation in the symbolrate. Increasing the initial spread factor will decline the performance of thesystem, but also heighten its security and encryption by obscuring the symbol rate.This is crucial because even with the chaotic sequence known an intruder isunable to infiltrate and intercept the signal. This being said the majorconcern now is obtaining the proper ? value while considering the trade offsbetween the system’s overall performance, speed, and most applicable it’sencryption and security.

This illustrates the effectiveness of the DCSK DSSStechnique by applying a variant period allowing for an improvement in thesystems physical layer of security.