# Adaptive secure data transmission method for OSI level 1

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. 4.13 ADM-channel phase response [rad]

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/S}_{min }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 f_{S }= 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 f_{S }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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