# Adaptive secure data transmission method for OSI level 1

Chapter IV

4. Data Transmission in Channels and Networks

– A Simulation Study

4.1. Worksheet Simulator

The use of a personal computer with programs already in use at the office was one goal in

modeling and simulations in this study. Compilers of simulation languages are expensive and

a simulation package is adapted to one type of problem only. The Excel worksheet program

as a standard language was selected for rapid modeling and during this study the author programmed

an Excel-simulator for simulations made in this study, presented in paper [Lal04b].

The reasons for this choice were mathematical, economical and practical. The simulator is

based on the mathematics programmed in Excel cells forming a block model, Figure 4.1. The

model blocks include mathematical entities. The simulations are executions of the programmed

mathematical formulae in networked Excel cells [Lal97b] and [Lal04b]. The Excel

worksheet program itself has all the mathematics and graphics needed. It is widely used and

thus available for most PC-users. It is an effective way of programming and it has excellent

graphics to present results. Most of the particular blocks and waveforms needed for this study

were not available in the libraries of the reference [Com90]. Thus a new computer simulation

method for evaluation of the characteristics of the ADM-channel and data transmission was

needed and its first version MIL.xls was developed in November-December 1992, based on a

standard worksheet program (Excel), Figure 4.1. The latest development of the robust worksheet

simulation, 26 data channels (AWGN, granular, and multi-path) with an adaptive

1…160-point DFT calculation, is presented in reference [Lal04b].

Fig. 4.1 Blocks of robust worksheet simulator

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The ADM-channel model included an ADM-modulator, an AWGN-channel, and an ADMdemodulator.

Adaptation simulations were made with this ADM-channel model using 2-bit,

3-bit or 4-bit memory in Modulation Level Analyzer (MLA). EUROCOM specifies the adaptation

with 3-bit memory, which was used in simulations unless otherwise stated. The

granular noise channel modeled is called here the ADM-channel model, Figure 4.1.

The data transmission simulation model used a random bit source, a waveform generator, the

ADM-channel model, and a data modem receiver simulator using the Discrete Fourier Transform,

which is called here the DFT-receiver. Most of the simulations were made with this

simulator system, which is called here the Excel-simulator.

The present worksheet simulation package for modeling data transmission over different

channels (incl. the adaptive delta modulated voice channel of the present 16 kbps network)

includes generation of waveforms, a model of discrete Fourier transform receiver for waveform

detection, random bit and symbol generation, calculation and estimation of simulated

BER, setting of Gaussian noise level, setting of multi-paths, setting of interference signals,

signal-to-noise ratio calculations, phase distortion calculations, and group delay calculations.

Limitation of Worksheet Program

The limitations with a worksheet simulation are the memory size available in PC, PC

throughput with Excel and Excel worksheet limitations. An Excel worksheet used in 1992

had 16384 rows and 256 columns. A minimum robust 1000-bit simulation used in this work

needed about 6 MB memory to manipulate 13000 samples stored in Excel cells. This was the

practical limit for the personal computers used earlier. These problems were minimized in

ten years and 10000-bits simulation is not a practical limit. To get a high quality waveform

in an Excel-simulator a sample rate about 10 times the highest signal frequency was used.

The same limitation was also observed in other simulators [Tes92].

Use of Discrete Fourier Transform

Two approaches were considered: Discrete Fourier Transform (DFT) and Fast Fourier Transform

(FFT), definition in Appendx 1. DFT was selected instead of FFT for the calculation of

the response of the ADM-channel and for the decision of the bits from the output waveforms

of different data modems. The main reasons for this are:

- The use of DFT makes the approach adaptive. The number of samples (N) was freely

selected.

- DFT is easy to program.

- DFT gives both amplitude and phase of a given signal.

- The number of multiplications of DFT is limited in calculations using N=13 or 26.

- The number of samples in FFT must be in powers of two. Thus the sample numbers used

in this study were not optimal for FFT.

- DFT works in the simulator with any limited number of samples.

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Computational Limitations of DFT and FFT

To calculate one magnitude point of frequency response the first version of MIL.xls simulator

(1993) made more than 20000 calculations. It took about 30 seconds while N=160 samples

were used in a direct computation. In reference [Pro92] the computational complexity for the

direct computation of the DFT is compared to the FFT algorithm. The number of multiplications

needed in DFT (N

2

) is much larger than in FFT (N/2)log_{2}(N), see Table 4.1. However

the rapid development of processor power and RAM memories have made the time delay

in simulations with DFT negligible. The FFT-values for N=13, N=26 and N=160 are “not po w-

ers of two” and thus not possible with FFT (N/A).

Table 4.1. Complexity of DFT versus FFT

Number of points N Multiplications

DFT FFT

N/2)log_{2}(N)

13 169 N/A

26 676 N/A

128 16384 448

160 25600 N/A

256 65536 1024

4.2 Modeling of Data Transmission

Simplified models are used in the simulation of data transmission over the ADM-channel (analog

voice grade channel, ADM coding), Figures 4.1-4.4. A detailed presentation of the data

transmission is found in reference [Ska01] and Appendix 2. In the simplified model random of

Figure 4.2 digital data bits were generated (Bits IN) and analyzed (Bits out) in the PCs. The

symbol waveforms or analog signals were generated and detected in the data modem (Data

Mod, Data Dem). The data waveform was led to the multiplexer (Mux), which includes the

equipment for the adaptive delta modulation coding of analog signals (A/D ADM, D/A ADM).

Crypto equipment is needed in wireless communications but was not modeled for the simulations.

The air interface is a radio link or a base station (Mod, Dem), which are modeled with an

AWGN or a multi-path channel model. Noise was added to the signal in the receiver (Dem).

In Figure 4.3 the channel is a radio channel or a wired channel. DM and PCM are source encoding

and decoding methods used for a base-band digital signal. Discrete channel encoders and

decoders for base-band line signaling are not modeled in simulations. The analog radio or wired

channel is robustly modeled with an AWGN, multi-path, and granular channel model.

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Fig. 4.2 Simplified model of analog data transmission

Fig. 4.3 Simplified simulation models of data transmission [Lal97a]

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Problems and Research Methods

The measurements demonstrated the quality of standard analog data transmission with 1200

bit/s or 2400 bit/s rate modems only using granular noise channels. The quality levels were

acceptable or poor. This motivates to study other than standard data modulation methods for

improvements of the data rate and transmission quality over granular (digital network),

AWGN (theoretical) and multi-path (radio) channels. The investigation was made with a robust

modeling and simulations method. The programming was made with a worksheet as discussed

in papers [Lal97b], [Lal99], and [Lal04b]. The results were verified with measurements

and reference simulators.

The information transmission chain is: digital data source or analog source waveform - granular

noise in source coding – AWGN noise and multi-path channel - receiver was modeled.

The simulation results show the probability of the correctly received message in different

cases or BER (bit error rate). The information transmission blocks are analyzed and described

in detail in papers [Lal97b], [Lal99], [Lal04a], and [Lal04b]. The three different channel

models causing different problems in data transmission (quality impairment) are discussed in

several references are available [Sha48, Cha66, Rum86]:

- AWGN.

- Granular noise.

- Multi-path interferences.

Discussion of the Results

The simulation results, conclusions and proposals in the papers [Lal99], [Lal00], [Lal01],

[Lal02], and [Lal04a-b] include:

- Simulation analysis of different granular noise channels (phase and amplitude distortion

and a polynomial channel model)

- Comparison of standard data transmission methods with the developed adaptive multicarrier

data transmission methods.

- Qualitative results using AWGN, granular noise and multi-path channels for data transmission.

- Recommendation for selecting adaptive data transmission parameters and design principles

for an adaptive modem.

- Results of simulations with a model for biomedical data network using adaptive versus

standard data transmission at different bit rates.

A brief summary is presented next.

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4.3. Adaptive Delta Modulation and Granular Channel

Figure 4.4.presents the adaptive delta modulator and demodulator of the Eurocom recommendation

[Eur86] and the simulation model of the adaptive delta modulator, paper [Lal04b].

The ADM-channel (granular noise channel) discussed in this study is established between

points C and C’. The demodulation process is simply the integrator and it includes the same

modulation level analyzer as the modulator. The MLA (modulation level analyzer) and the

first integrator in Figure 4.4 define the step size, which is propotional to the granular noise

level, described in more detail in reference [Eur86].

Fig. 4.4 ADM modulation demodulation process and blocks [Eur86]

Figure 4.4 shows the analogue/digital conversion of speech signals with a pulse modulator in

the transmitter and digital/analog conversion in the receiver end of the digital transmission

channel between (C-C´). The receiver has a leaky integrator (between F-G) and a VF (voice

frequency) filter (between G-B).

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Fig. 4.5 Simulation model of ADM modulator [Lal04b]

In the simulation model of Figure 4.5 the modulation level analyzer is developed into different

two, three or four bit versions and used for the ADM algorithm simulation process in

paper [Lal97b]. In Figure 4.5 a three bit algorithm (A+B+C)/3 = 1 or –1 is used in the simulated

result of the adaptive step size versus a continuous sinusoidal signal. The modulation

simulation result, the adaptive discrete audio signal x(nT), is presented in Figure 4.6 with the

original input signal 800 Hz.

Fig. 4.6 ADM modulation of 800 Hz test signal [Lal97b]

The integration is controlled by the adaptive step size s(t), formula (4.1).

1

s^{(}

t^{) }^{= }S^{(}t^{) }y^{(}iT ^{) (4.1)}

V

n

∑

_{C }i_{=}0

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Fig. 4.7 Simulated adaptive step size [Lal97b]

Figure 4.7 presents the step adaptation at different frequencies in the adaptive delta modulation

system. To avoid slope overload in a delta modulation system the step size S (line in the

figure) must be greater than a minimum value.

Adaptive Digital Channel

The performance of the delta-modulated voice channel is presented in the simulated results

of Figures 4.8-4.10. The simulated magnitude and phase response functions for different

amplitude to minimum step size ratios of the ADM-channel are seen.

Fig. 4.8 Simulated magnitude response of ADM-channel [Lal97b]

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Fig. 4.9 Simulated phase response of ADM-channel [Lal97b]

Fig. 4.10 Covariance between input and output samples

In Figure 4.10 the voice band signal has redundancy between delayed samples, which is seen

in the calculated covariance results between the 1...4 - sample delayed 16 kbps signals.

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Polynomial Channel Model

The Polynomial Signal Processing (PSP) of the simulation result gives the channel model.

The channel model polynomial in dB values is in formula (4.2) where the voltage y is normalized

and the frequency x is given in kHz. The results are presented in Figure 4.11. The

quality of the polynomial curve fitting was evaluated with the coefficient of determination r

also called correlation coefficient. The best fitting r = 0.9474 for the amplitude response is

achieved with the polynomial of degree 6 in Figure 4.11.

Fig. 4.11 ADM-channel amplitude response [Lal04b]

The polynomial amplitude response model [dB] of degree 6:

y = -0.0266x^{6}+0.2811x^{5}-1.2868x^{4}+2.6801x^{3}-2 .6318x^{2}+1.1013x+0.757; (4.2)

r = 0.9474

The polynomial phase response model of degree 3:

y = -4E-9x^{3}+2E-5x^{2}-0.0682x+97.429; (4.3)

r =0.9864

A very good fitting for the phase response (r=0.9864) is achieved with the polynomial of

degree 3 if the frequency range x is limited to 2600 Hz. The polynomial is presented in formula

(4.3) where the phase y is in degrees and the frequency x is given in Hz.

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