Introduction know the exact time and duration of


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.

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.

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