1.1
SYSTEM INITIAL DESIGN
In the Fig1 shows the block diagram of the chaos based modulation and demodulation scheme
known as Enhancement COOK. E-COOK is a special case of non-coherent CSK
In this scheme only chaotic based signal is needed the binary symbol “+1” and “0” are simply
represented by transmission of the signal and null transmission respectively.
Chaos
Data
Permutation
Matrix F(.)
Interleave
genera
Closed or opened depending on +1 or 0 being sent
Inverse
Permutation
Matrix
inverse
De
Interleave
Channel
Bit energy estimator
⬚
⦁ 𝑑𝑡
Recovered symbol
𝑇𝑏
Threshold detector
Tb
Fig1: Cook Modulation and Demodulation
1.1.1 Modulation:
Chaos On-Off Keying is only one chaotic signal is used in transmission of message signal. When
the message signal is bit 1, the chaotic signal is transmitted, but when the message signal is bit 0
no signal is transmitted. The modulation part contains chaos generator its shown in the fig2
below.
Data
Chaos
Permutation
Matrix F(.)
interleave
Closed or opened depending on +1 or 0
being sent
1.1.1.1
Channel
DATA TRANSMISSION:
Data bits are sent as a frame. Each data d k can be written as
Assume That :
Fig 2: Cook Modulation
X1 X2 X3 X4 X5 X6 X7 X8 X9
Bit 2
Bit1
X1
X2
X3
X4 X5 X6
Bit3
X7 X8 X 9
12
Fig 3: DATA TRANSMISSION
This is the original signal which is transimitted and received.
The data in which is to be transmiited is fig4 show below, here the modulation signal is
transmitted using chaotic on off keying modulation scheme chaotic generator will genertate the
data which is to be transmitted. This data is then passed to the interleave part.
X1
X4
X7
X2 X5 X8
X3 X6 X 9
12
Fig 4: Data In Modulation
1.1.2 INTERLEAVER WITH PERMUTATION UNIT AND DEINTERLEAVER
WITH DE PERMUTATION UNIT
Interleave
De
Interleave
Inverse
Permutation
Matrix
inverse
Permutation
Matrix F(.)
Channel
Fig 4: Interleave With permutation Unit and DE interleave with De
permutation
Interleaving is basically taking a block of samples from your signal and shuffling (interleaving)
them around before sending them, This is so that if a short 'burst' interferer causes errors in a
number of bits in the channel, the errors affect bits that were not actually next to one another
when the signal was created. So when the data is 'unstuffed' (de-interleaved) then the error
control code can work on the errors more easily, because the errors are spread though the
message, not obliterating any particular spot .The interleaved signal is then passed to the
permutation block in order to provide effective signal and easy decoding we use the permutation
using permutation we can easily decode the signal in the demodulation part. The signal is then
transmitted which is to be transmitted this is called channel.
X1
X2
X3
X4
X5
X6
X7
X8
X9
1.1.2.1
PART:
This is the original signal.
INTERLEAVER WITH PERMUTATION UNIT IN THE MODULATION
X1
X4
X7
0
0
1
X2
X5
X8
0
1
0
X3
X6
X9
1
0
0
=
X7
X4
X1
X8
X5
X2
X9
X6 X3
This signal will transmit in modulation part;
X7
X4
X1
X8
X5
X2
X9
X6 X3
1.1.2.2
DEINTERLEAVER WITH DE PERMUTATION UNIT IN
DEMODELATION PART:
In the demodulation part reverse process of interleave and inverse permutation takes place on
the received signal.
X7
X4
X1
0
0
1
X8
X5
X2
0
1
0
X9
X6 X3
1
0
0
=
X1
X4
X2
X5
X8
X3
X6
X9
This signal will receive demodulation part;
X1
X2
X3
X4
X5
X6
X7
X8
X9
X7
1.1.3 NON COHERENT DEMODULATION BASED ON BIT ENERGY ESTIMATION
After the de interleave signal passed to the non-coherent chaotic on-off keying demodulation. In
non-coherent csk demodulation the chaotic carriers are not recovered at the receiver .Detection
has to be done based on some distinguishable property of the transmitted signals. One such
property is the bit energy which can be deliberately made deferent for deferent symbols in the
modulation process.
At the receiving end, the bit energy can be estimated by squaring and integrating the cipher
signal. Since additive noise corrupts the transmitted signal and the noise power is limited,
therefore we have:
𝑟 𝑡 =𝑠 𝑡 +ξ t
Where:
ξ t = noise signal
s t = Encrypted message signal(message signal sent)
r t = cipher text (encrypted message signal)
Then we square the received signal r t followed by integrating the 𝑟 𝑡
calculate the energy bit
𝑟 𝑡
2
= 𝑠 𝑡 +𝜉 𝑡
2
= (𝑠 𝑡 + 𝜉 𝑡 )( 𝑠 𝑡 + 𝜉 𝑡 )
= 𝑠2 𝑡 + 𝑠 𝑡 𝜉 𝑡 + 𝑠 𝑡 𝜉 𝑡 + 𝜉2 𝑡
= 𝑠 2 𝑡 + 2𝑠 𝑡 𝜉 𝑡 + 𝜉 2 𝑡
Therefore
= 𝑠 2 𝑡 + 2𝑠 𝑡 𝜉 𝑡 + 𝜉 2 𝑡
2
signal in order to
So we integrate 𝑟 𝑡
2
Let energy per bit is = 𝑦 𝑙𝑇𝑏
𝐼𝑇𝑏
[ 𝑠 2 𝑡 + 2𝑠 𝑡 𝜉 𝑡 + 𝜉 2 𝑡 ]𝑑𝑡
𝑦 𝑙𝑇𝑏 =
𝑙−1 𝑇𝑏
𝐼𝑇𝑏
𝐼𝑇𝑏
𝐼𝑇𝑏
2
=
𝑠 𝑡 𝑑𝑡 +
𝑙−1 𝑇𝑏
𝜉2 𝑡 𝑑𝑡
2𝑠 𝑡 𝜉 𝑡 𝑑𝑡 +
𝑙−1 𝑇𝑏
𝑙−1 𝑇𝑏
When the energy bit y(lTb) 0 then binary “+1” was sent and when y(lTb) 0 it is less than “0”
was sent
Bit energy estimator
⬚
⦁ 𝑑𝑡
Recovered symbol
𝑇𝑏
Threshold
detector
Tb
Fig6: Non coherent Demodulation based on bit energy estimation
1.3
FLOWCHART
1.3.1 Transmitter Part:
Start
Chaos
generator
Bit Controlled Switch
Framing
Interleaving
Permutation Matrix
Channel
End
Fig 7: Transmission Part
1.3.1.1
DESCRIPTION OF TRANSMISSION PART
COOK uses a switch to aid in encryption of digital message signals. If symbol “+1” is needed to
be transmitted, the switch will close and the chaotic signal generated from the chaotic system
will be sent and if symbol “0” is needed to be transmitted, the switch opens and a constant that
was specified which in most cases is zero is transmitted as shown above
𝑆 𝑡 ={
𝑐 𝑤ℎ𝑒𝑛 + 1 𝑖𝑠 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
0 𝑤ℎ𝑒𝑛 − 1 𝑖𝑠 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
1.3.2 Receiver Part:
Start
Reframing
Inverse Permutation
De-Interleave
Multiply the Signal with Itself
Energy Detector
Comparison between transmitted bit
and received bit
Calculation Bit Error
Fig8: Receiver Part
End
1.3.2.1
DESCRIPTION OF RECEIVER PART
Figure above shows the block diagram of the receiver part method of chaotic on off keying here
r(t) is cipher text received from encryption here signal is recovered from calculating the bit error
rate bellow shows mathematical explanation of bit energy estimation
Since White Gaussian Noise (WGN) was added to our encrypted message signal, therefore, the
cipher-text r(t) then becomes:
𝑟 𝑡 =𝑠 𝑡 +ξ t
Where:
ξ t = noise signal
s t = Encrypted message signal(message signal sent)
r t = cipher text (encrypted message signal)
𝐼𝑇𝑏
𝑙𝑇𝑏
𝑟 2 𝑡 𝑑𝑡 =
𝑦 𝐼𝑇𝑏 =
𝑙−1 𝑇𝑏
𝑙−1 𝑇𝑏
𝑠2 𝑡 𝑑𝑡 + 2
𝐼𝑇𝑏
𝐼𝑇𝑏
𝑠 𝑡 𝜉 𝑡 𝑑𝑡 +
𝑙−1 𝑇𝑏
2
𝜉 𝑡 𝑑𝑡
𝑙−1 𝑇𝑏
Where: 𝑦 𝐼𝑇𝑏 Bit-Energy Estimator
The output is then passed to the threshold detector with the threshold set-to a mid-value of
𝑙𝑇𝑏
E=[∫ 𝑙−1 𝑇𝑏 𝑏 2 𝑡 𝑑𝑡] and zero
𝑙𝑇𝑏
Here, E=[∫ 𝑙−1 𝑇𝑏 𝑏 2 𝑡 𝑑𝑡]: Expectation Operator The decoded symbol is “+1” if the estimated
bit energy is larger than the threshold; otherwise, a “0” is recovered. Note that in the presence of
noise, the threshold should be shifted in order to optimize the performance