IntroductionIt 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 haveto know the exact time and duration of each received symbol in a stream, in order tobe able to assign decision times and reset the initial conditions of the correlator 6.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.Previous WorkIn 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 attractors3. 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 : MethodA 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 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 periodBlock 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 2 PC Simulated image for DSSS system below: All together you should get : Despreading scheme chaotic sequence synchronization The local chaotic sequence is regenerated and synchronized with the incoming called a synchronized chaotic generator (SCG) This synchronization scheme 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 3 despreading scheme :Figure 4 despreading simulation below:All together you should get : ConclusionSimilar 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.Reference1 Kaddoum, Georges, and Francois-Dominique Richardson. “Multi-User Multi-Carrier Differential Chaos Shift Keying Communication System.” Ieeeexplorer.com, 2013, ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6583829.2Chen, Sheng. “Coherent and Non-Coherent Receivers.” 2014.3Grzybowski, Jose, and Marcio Eisencraft. 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