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# Adaptive secure data transmission method for OSI level 1

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Discussion

The polynomial response is sensitive to additive Gaussian noise (AWGN), which was also
studied. If noise is eliminated in simulations, the polynomial models of the ADM-channel
are as presented in Table 4.2.

Table 4.2. Polynomial models for the ADM-channel amplitude response

y = -7E-18x6 + 4E-14x5 - 1E-10x4 + 1E-07x3 - 0,0001x2 +
0,0331x + 76,175
R2 = 0,7687

y = -1E-14x5 + 6E-11x4 - 1E-07x3 + 7E-05x2 - 0,0206x + 80,933
R2 = 0,7654

y = -2E-11x4 + 7E-08x3 - 0,0001x2 + 0,0546x + 72,384
R2 = 0,7454

y = -1E-08x3 + 4E-05x2 - 0,0386x + 87,086
R2 = 0,6385

y = -7E-06x2 + 0,0096x + 75,221
R2 = 0,5165

y = -0,0086x + 83,745
R2 = 0,4054

Amplitude (relative amplitude vs frequency) and phase (phase in radians vs frequency)
models are presented with polynomials in Figures 4.12 and 4.13.

Fig. 4.12 ADM-channel amplitude response [V]

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Fig. 4.14 Correlation of the ADM-channel amplitude model

Figure 4.14 shows the correlation (R) of linear and different polynomial (degree 2-6) models
for the ADM-channel amplitude response. Third or fourth order models have better than
85% fitting. The 5-6 order models have the same level fitting as the fourth order model. Linear
model is not a proper attenuation model for this ADM-channel (100-2600 Hz, 16 kbps
sampling rate, 3-bit MLA). The amplitude response of the ADM-Channel is not linear. It has
an attenuation distortion found in measurements of chapter 3 and regulated in recommendations
[Eur86]. The attenuation distortion is qualitatively illustrated in simulations, Figures
4.12-4.13. Polynomial channel models are included in the figures. The phase is not linear as
illustrated by the polynomial model in Figure 4.13 and Table 4.3.

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Table 4.3. Polynomial models for the ADM-channel response of phase

y = -0,0009x + 1,6529
R2 = 0,9584

y = -1E-07x2 - 0,0006x + 1,4962
R2 = 0,9658

y = -2E-10x3 + 6E-07x2 - 0,0014x + 1,6802
R2 = 0,9716

y = -1E-13x4 + 5E-10x3 - 6E-07x2 - 0,0006x + 1,5623
R2 = 0,973

y = -2E-16x5 + 1E-12x4 - 3E-09x3 + 3E-06x2 - 0,0021x + 1,7356
R2 = 0,9746

y = -6E-19x6 + 5E-15x5 - 1E-11x4 + 2E-08x3 - 1E-05x2 + 0,0029x + 1,29
R2 = 0,9803

Table 4.3 shows that a linear model best describes the phase response of the ADM-Channel.
The correlation coefficient of it is very high >95%. Thus the ADM-channel is almost phase
linear.

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4.3.1. Distortion of Signals in Granular Channel

As stated earlier the ADM system causes granular distortion. Simulating with the
ADM-channel voice-coding model, presented in Figure 4.5 and paper [Lal04b], the
effect of using different sinusoidal frequencies (carrier frequency) is evaluated next.

Distortion Components

In Figure 4.15 one can find the simulated distortion components of the ADM-channel
caused by a 2000 Hz sinusoidal input signal. The components are 20 dB below the input
signal. These simulated results fulfill the requirements of the adaptive delta modulation
method described in reference [Eur87].

Fig. 4.15 Simulated distortion components of a 2000 Hz input sinusoidal signal

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Distortion of a Granular Noise Channel

A digital telecommunication network, in this case an ADM (adaptive delta modulation) system,
causes granular distortion. The effects increase with the frequency as simulated results
in Figure 4.16 present. The result is in accordance with the measured values. The measured
value fits with the simulation results in the A/Smin range 12.5…50.

Fig. 4.16 Distortion of the ADM-channel [Lal97b] and [Lal04b]

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4.3.2. Simulation Results of Analog Data Transmission

In this section data transmission with some traditional and new waveforms are studied with
n-point DFT–algorithm (n=13, 26…N) software detection using simulations. The results are
discussed and compared with measurement results of standard modems.

Analog data transmission over a granular channel - simulated results

The effect of frequency is seen in the results of the simulation of the 8-PSK data transmission
over the granular ADM-channel, Table 4.4 [Lal97b].

Table 4.4. Simulated phase jitter of ADM-channel
Frequency Deviation Maximal
phase
BER of
8-PSK

Hz of
phase
jitter
jitter

615 4.29 18.4 <10-4
1231 7.41 31.8 <10-4
1846 12.39 55.5 <10-2
2462 15.10 73.8 >10-2

The adaptive delta modulation effects are seen here in phase jitter (in degrees) and in resulting
bit error rate (BER). This result suggests an improvement of data throughput in the
ADM-channel by the selection of a lower carrier frequency and a lower symbol rate.

Table 4.5 presents simulation results and a comparison between the developed waveforms
(detection with a 26 sample DFT software algorithm) and the measured standard V.23 and
V.26 modem waveforms. In this case the corresponding bit rates are 2400 bit/s and modems
FSK&8-PSK with DFT26 detection and V.26 standard. The bit error is three times larger
with the V.26 standard waveform compared to the developed soft detection with a DFT26algorithm.
Details are presented in the papers [Lal97a] and [Lal97b]. The papers present the
adaptive waveform generation and selection principles.

Table 4.5. Comparison of standard modems and DFT26-algorithm
Modem Modulation Carrier frequency, Hz

BER bauds, bit/s
V.23
1E-4
FSK
1200, 1200
1300,
2100

V.26 4DPSK 1800
5.7E-3 1200, 2400
DFT26
1.6...1.8E-3
FSK & 8PSK
4FSK & 4PSK
600, 2400
615, 1231
1846, 2462

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New Data Transmission Waveforms and Different Channels

A combination of 2FSK and 8PSK or 4FSK and 4PSK is more reliable and acceptable than
standard 4DPSK for the simulated granular channel based on lower and more suitable carrier
frequencies. The use of low carrier frequencies and symbol rates has advantages compared to
standard modems with these channels. Results and analysis of the detection method, a DFT
(discrete Fourier transform) approach, are discussed in several original papers [Lal97b],
[Lal99], [Lal00], [Lal01], [Lal02], and [Lal04b].

Signal Impairments in a Granular Channel

A granular noise channel used in these simulations causes two kinds of impairments a.
granular noise, b. slope overload seen earlier in Figure 4.6 and now in the Figure 4.17. Bit
rates of 3000 bit/s may use with new complex waveforms (a combination of 4FSK and
8PSK). Figure 4.17 presents a simulated complex 2FSK-8PSK waveform before and after
the granular noise channel. Table 4.4 suggests the use of lower frequencies for granular
channel.

Fig. 4.17 2FSK-8PSK waveform in a granular channel [Lal97b]

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Effects of a Multi-path Channels

In the simulated results, presented in papers [Lal02] and [Lal04b], the data waveform has
impairments starting at S/N<15 dB…20dB. The qualitative result shows the effect in amplitude
and phase error, which can make the detection impossible in Figure 4.18. The normalized
values of A and P are one. The subject is quite broad and needs a lot more investigations.
The results in the paper show, that a robust worksheet modeling and simulation
method can give rapid answers to most practical questions.

Fig. 4.18 Channel impairments effects in received A and P [Lal02]

Soft Detection of Waveforms

Soft detection is the detection method used in simulations. It was performed with a N-point
DFT based calculation process. First the method is used in the simple cases of FSK and PSK
waveforms. Soon it was found that with N=26 and sampling frequency fS = 16000 detection
of some multi-carrier modulation methods (MFSK) can be carried out. Later it was obvious
that by using different sample numbers N and sampling frequencies fS more complex multicarrier
waveforms can be detected and with an inverse DFT multi-carrier waveforms were
generated in the simulations. The band-limited multi-carrier approach is used in a prototype
modem design described in chapter 5.

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Soft Detection of Noisy FSK-Signals

The first results with the FSK and PSK data transmission simulation over the 16 kbps ADMchannel
were the evaluation of the number of samples needed in the detection of one symbol.
Figure 4.19 presents qualitative results of soft detection of noise FSK-waveforms in a simulation
using a 13-point DFT (N=13 samples per symbol) in detection. N=13 was enough for
FSK but not for PSK where N=26 was needed.

Fig. 4.19 Soft detection of noisy FSK-signals [Lal97b]

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Robust examples of soft FSK detection simulation results with FSK waveform over granular
AWGN noise channel are presented in Tables 4.6 and 4.7. The S/N is 65 and 7 dB in these
cases giving an error in bit detection in the latter. Soft detection is based on the simple rule
“s elect the largest FSK signal”. Tables present the first 15 bits of the 205 bits in this example.

Table 4.6. Soft detection simulation results with FSK
S/N = 65 dB

RESUL
IN T FSK SIGNAL 1300
bits bits DFT13(0) DFT13(1) BIT nro
1 1 0,413343 0,879732 1
1 1 0,529696 1,380792 2
0 0 1,075283 0,679321 3
0 0 1,088647 0,569278 4
0 0 0,729953 0,668613 5
1 1 0,64243 1,301552 6
0 0 0,379822 0,285694 7
1 1 0,430707 0,86252 8
1 1 0,587002 1,354614 9
1 1 0,095181 1,487733 10
0 0 0,751494 0,444714 11
0 0 0,596189 0,347739 12
0 0 0,442083 0,251259 13
0 0 0,29109 0,156189 14
1 1 0,361007 0,651705 15
1 S/N 65,60253 dB
7 BER 0 205 205

Table 4.7. Soft detection simulation results with FSK
S/N = 7.5 dB

IN RESULT FSK SIGNAL
bits bits DFT13(0) DFT13(1)
1 1 0,413343 0,879732
1 1 0,529696 1,380792
1 1 0,430431 0,884521
1 1 0,361007 0,651705
1 1 0,353727 0,925599
0 1 0,203228 0,252977
0 0 0,294538 0,147042
0 1 0,215511 0,272362
0 1 0,203228 0,252977
0 0 0,29109 0,156189
1 1 0,361007 0,651705
1 1 0,28761 0,701455
1 1 0,45814 1,137804
0 0 0,791592 0,421765
0 1 0,203228 0,252977
S/N 7,455425 dB
BER 0,019512 201 205

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