# Adaptive secure data transmission method for OSI level 1

Soft Detection of Noisy PSK-Signals

Phase detection is degraded due to phase jitter generated in the delta modulation process. Phase

jitter of the ADM-channel is calculated with a 26-point DFT algorithm as a phase receiver. The

software algorithm is programmed in Excel format in a worksheet simulator for the modeling of

software detection of PSK and other waveforms. The 26-point discrete Fourier transform

(N=26) is presented in formula (4.4). The simple calculation process is made assuming:

- The symbol waveform is sampled with sampling frequency ^{f}_{s }= 16000.

- The number of samples used in a symbol waveform is N=26.^{- }The carrier frequencies ^{f}_{c }are calculated and generated as = m ⋅ ∆_{( }f _{) }^{.}^{- }The selectivity in detection of waveforms is calculated as ^{∆}_{( }f _{) }^{= }f_{S }_{/ }N ^{.}

- The reference signal is an 8-PSK-waveform in the simulated evaluation of soft detection of

PSK-signals.

- The resulting lowest four carrier (m=1…4) frequency candidates, matching with the ADMchannel,

are ^{f}_{c }= 615, 1231, 1846 and 2462 Hz.

- The resulting frequency selectivity in detection of waveforms is ∆^{(f) }= 615 Hz.

f

C

26-Point DFT Algorithm

S

X

[^{m}^{∆}( ^{f })] ^{=}

26

∑

n^{=}_{1}

x_{[}n^{∆}_{(}t_{)]}e

^{−}_{2 }j^{π}m^{∆}_{( }f _{)}n^{∆}_{(}t_{)}

(4.4)

The complex signal spectrum ^{S}_{x }is the result of the DFT calculation in formula (4.4). The individual

carriers ^{f }^{= }^{m }^{⋅ ∆}^{( }^{f }^{) }are separately evaluated and calculated for phase detection of the

signal (for example an 8-PSK-signal as in Table 4.4-4.5. Every carrier ^{f }has its own ^{S}_{x}^{, }which

has a real part ^{x=Re(S}_{x}^{) }and an imaginary part ^{y=Im(S}_{x}^{)}. The phase detection can be modified

(some training is needed) from the phase estimate tan ( )

1

− ^{y}^{P }^{= }depending on the phase con-

x

stellation used. In general a phase estimate P for a frequency ^{f }^{= }^{m }^{⋅ ∆}^{( }^{f }^{) }^{is}

P ^{=}

tan ^{1}

−

Im{S

Re{S

X

X

[m^{∆}( f )]}

[m^{∆}( f )]} ^{(4.5)}

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AWGN Channel and Noise Model

Setting the noise level as demonstrated in reference [Bro93] the S/N-ratio was calculated for an

average signal ^{s(t) }power and noise ^{n(t), }formula (4.6). In the case of Gaussian white noise, relationship

between ó andthenoisepower spectrum ^{N}_{0 }is presented formula (4.7) [Bro93].

Var[s(t)]

= 10log_{σ }_{Var[n(t)]}

S/N

2

(4.6)

N

=

2

o

2

σ ^{(4.7)}

Additive random noise source was designed in order to evaluate the error performance of the

AWGN noise channels. Noise signal ^{N }(positive or negative impulses) was added to every

sample of AWGN channel waveform, see waveform examples earlier in Figures 4.6 or 4.17.

The complex transmission chain was simulated with AWGN noise sources at the input and/or at

the output of the granular channel, presented earlier in Figure 4.1. Figure 4.20 presents absolute

values of ^{N }for reference purposes with the normalized signal power of bits. The resulting

simulated S/N ratio was also calculated and referred to the set parameter values of S/N. Generation

of noise was based on the known simulated normal distribution by formula (4.8).

12

N ( RND(i) ^{− }6)_{σ }^{+ }_{µ }^{(4.8)}

i 1

= _{∑}

=

Where

N = Noise amplitude

RND(i) = Random number 0...1, i=1, 2, 3,...,12

ó = Deviation of the noise distribution

ì = Mean of the noise distribution

Positive and negative noise impulses were added to the signal (absolute values in fig. 4.4) so

that its mean ^{ì }was zero and its deviation ^{ó}set the noise power for S/N ratio. In the simulations

S/N was also calculated using the sample values of signal and noise peaks. The setting of S/N

was compared to the actually simulated S/N values in the simulations presented in this thesis.

Fig. 4.20 Sampled noise modeling during symbol (bit) time

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4.4. Simulations of Biomedical Data Networks

Image Transmission

An evaluation of the digital image management is in reference [Rat05] as

1. The storage of radiological images in digital format is a non-trivial problem due to the very

large volume of data that these images contain.

2. Projectional X-ray Images require very high resolution to be clinically acceptable. Such images

must be acquired and stored in image matrices of more than 2000 by 2000 pixels, with a

dynamic range of 8 to 12 bits per pixel. This represents between 4 to 8 Mbytes per image.

3. Digital imaging modalities such as computed tomography or magnetic resonance imaging

generate images with smaller matrices (typically 256x256 or 512x512 with a dynamic range

of 12 to 16 Bits per pixel).

4. The difficulty comes from the very large number of images generated for each patient examination.

One examination can generate between twenty and more than one hundred images.

This corresponds to storage requirements between 10 and 50 MBytes per study.

The conclusions of telemedicine simulations and the Comnet 3 LAN network traffic modeling are

presented in paper [Lal04a]. The main results are briefly given here.

Nature of band-limited data traffic– Simulated Results

The nature of data traffic was seen in Figure 4.21. The main difference between data and voice

communication is traffic bursts in data transmission. Delays depend heavily on the data transmission

lines used in simulations as the results of mean delays indicate:

<0.5 s delay with 9600 bps and

<100 s delay with 600 bps.

Many heavy unpredictable variations in traffic and delay times are seen in the low bit rate cases.

In the Figure 4.21 we had a fixed 1000 byte mean message size. Delay times with the 600 bps

lines are not acceptable but 9600 bps might be acceptable in some real world applications.

Fig. 4.21 Message delays [Lal04a]

63

Transaction Rate

We investigated increasing transaction rates in a network using the 22.5 kbps adaptive waveform,

as discussed earlier, in the backbone channels, results in Figure 4.22. We gradually increased

the network traffic from message sources having a fixed normal distributed message

size (100 kilobyte mean, 10 kilobyte standard deviation) and arrival time as variable 10

sec…160 sec. These arrival times gave us a practical transaction range of a biomedical institution

with 65 000 to 260 000 transactions per year. Delays have an average (ave) and a standard

deviation (std) value. We found that there is a transaction value limit below 250 000 per year at

which this backbone network causes increasing delay time. In the evaluation of the simulated

result the message size (100 kilobyte used) is a critical measure. If the messages include for example

large images (1 Megabyte) then the number of transaction limit may drop to 25 000 per

year. However, it is possible to work with a low data rate band-limited backbone but with larger

delays. One conclusion is that the X-Ray images need wide band channels in order to minimize

the delay times.

Fig. 4.22 Message delays [Lal04a]

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4.5. Summary

The subject is quite extensive. We have investigated and discussed one model of data networks

with limited simulated examples, network design principles using different channels (AWGN,

granular and multi-path) and the selection of some modulation methods (waveform). This chapter

serves as an introduction to the adaptive multi-carrier secure data communication system of

the next chapter. The DFT based approach is based on the presented simulated results and the

selection of waveforms using band-limited frequency hopping on the lowest OSI level in order

to get security and optimal throughput for different channels.

The adaptive delta modulation (ADM) is used in several systems (mobile military and commercial

digital recording systems) as a voice coding method. It was used in modeling digital granular

channels. Both PCM and ADM are waveform-coding methods and their performance is

similar in quality (S/N). Analog waveforms should stay at a high quality level (S/N) during the

transmission over digital networks if the analog data transmission (waveform) is used end-toend.

The high S/N-ratio and low error rate are also generally important in biomedical information

transmission.

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Chapter V

5. A DFT-Based Approach to Adaptive Data

Communications

The expression “adaptive” means showing or having the capacity of or a tendency towards ada p-

tation, while adaptation is the act or process of adapting or adjustment to environmental conditions

[Web94]. Adaptive communications consist of a wide area of adaptive methods used in present

communication technology and are described earlier. The following sections include a proposal

and description of an adaptive multi-carrier data transmission system for telemedicine, alert

systems and other authority use. It is a novel solution particularly with the security properties offered

for OSI Model level 1 (physical), which have not been presented in the band-limited data

transmission standardization. The modeling of the data transmission system and the simulation

process is presented in papers [Lal04a] and [Lal04b]. It is capable of simulating all kinds of

waveforms with given signal to noise (S/N) settings.

5.1. Basic theory

There are many elements, which have effects on the signal power, bandwidth, and time spent by a

voice sample, an information byte or data block during the transmission over different channels,

Figure 5.1. The data block or the information package of the figure is always a combination of

signal power (S) needed, time (T) spent and bandwidth (B) used. The selectivity of time, frequency,

amplitude and phase are the limiting factors and can be described as in chapter one with

the minimum Euclidean distance ^{d}, formula (5.1).

d ^{=}

N

∑

i_{=}1

2

( p ^{− }q (5.1)

1 i ^{)}

Fig. 5.1 Package of data in the channel [Lal97b]

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The average signal power ^{S }and additive white noise power ^{N}_{0 }are reference factors in the

communication theory as presented in reference [Sha48]. Time element is effectively used in

the present communication technologies like time division multiplexing (TDM). In the present

systems the symbol time is fixed. The wide frequency band is used in the most modern

telecommunication systems such as ultra wide band (UWB) systems.

In military telecommunication the signal power and time are often minimized because a data

package presented in Figure 5.1 is a target of electronic warfare. The whole package is usually

minimized. Many design parameters of the system have some effects on this package.

Adaptive Data Transmission

Adaptive data transmission is introduced in the original papers [Lal97b], [Lal99], [Lal01],

and [Lal02]. The three last papers can be found in the IEEE Communication Society Digital

Library.

- Signal classification by discrete Fourier transform [Lal99] presents a signal classification

method using Discrete Fourier Transform (DFT).

- Adaptive software modem technology [Lal01] presents a description of a new software

modem technology.

- Basic theory of adaptive data transmission [Lal02]. The paper presents the basic theory of

adaptive data transmission.

A brief description of adaptive data transmission, implemented as an adaptive modem, is

here:

- The adaptive modem uses symbol time as a parameter. Thus the symbol rate is also a variable.

- The single adaptive modem operates on a very limited band (a channel). The full available

bandwidth contains several channels. Thus the linearity of the total multi-carrier band is not

necessary.

- The modulation scheme of each carrier is based on the channel properties, which can be

automatically measured in a training process

- The best available complex digital modulation for the carriers is selected and thus the bit

rate of the system is made optimal.

- The classical bit constellations of standard analog data modems of ITU-T have generally 1-

5 bits in the digital modulation schemes. This is not limited in the adaptive modem theory because

the transmission channel may give better performance in different cases.

The adaptive modem is described in more detail in the original paper [Lal00].

Selectivity in Soft Detection with Discrete Fourier Transform

The main mathematical background in the generation and detection of waveforms is the discrete

Fourier Transform (DFT), formula (5.2). All the parameters in the formula are adaptively

selectable. Thus the full advantage of the adaptive modem is in the capability to change the

carrier frequencies, amplitudes, phases, and symbol lengths. The complex form of the discrete

Fourier transform includes the amplitude and phase information of the symbol.

The DFT is defined in several references, for example in [Mar62] and [Gol70], as an operation

on an ^{N}-point vector [x(0),x(1),…,x(N-1)] _{as}

∑

−

N _{1}

n_{=}_{0}

nk

^{X }_{(}^{k}_{) }_{= }^{x}_{(}^{n}_{)}^{W }, for k = 0, 1, 2, …, N-1 (.5.2)

N

67

where _{W}

N

− j^{2}π^{/ }N

= .

e

The complex form of the discrete Fourier transform includes the amplitude and phase information

of the symbol.

S

X

[_{m}^{∆}( _{f })] ^{=}

26

∑

n=^{1}

x^{[}n^{∆}^{(}t^{)]}e

−^{2 }jπm∆^{( }f ^{)}n∆^{(}t^{)}

(5.3)

S

X

[_{m}_{∆}( _{f })] _{=}

13

∑

n=^{1}

x^{[}n^{∆}^{(}t^{)]}e

−^{2 }jπm∆^{( }f ^{)}n∆^{(}t^{)}

(5.4)

The formula (5.3) calculates the discrete Fourier transform of a signal _{x(t) }with N=26 samples.

The formula (5.4) calculates with N=13 and could be used only for FSK-detection. Time is

sampled _{f}_{S }times per second, which gives the sample time in the formula. The frequency selectivity

is the ratio _{f}_{S}_{/N}. The individual mean filter frequency is _{m }times the basic frequency selectivity^{m}_{f}_{S}_{/N}^{, }while _{m = 1…M }and _{M = }number of carriers^{. }Thus the frequency selectivity

depends on this relation. This is illustrated in Figure 5.2. In general time is sampled _{f}_{S }times per

second, which gives the sample time in the discrete Fourier transform formula of a symbol of

the signal _{x(t) }with _{N }samples^{. }The total sampled signal _{x(t) }consists of a piecewise continuous

set of symbols that will be discussed later. The frequency selectivity comes from the ratio_{f}_{S}_{/N}^{. }The individual mean frequency of filter is _{m }times the frequency selectivity. Thus the

frequency selectivity depends on this relation, which is illustrated in Figure 5.2.

68

Fig. 5.2 DFT-filter [Lal99]

Limits for Bit Rates - Shannon’s Channel Capacity Formula

For the development of the adaptive modem the Shannon’s capacity limit ^{C }is the figure of

merit. Formula (5.5), presented by Shannon, shows for ^{S/N }(average signal power over average

white noise) the channel capacity is approximately ^{C }for limited band ^{B}^{. }The signal-to-noise

ratio and bandwidth define Shannon’s channel capacity limit for the AWGN -channel in 1940

[Sha48] as

S

C = B log

2

(1 + ) _{(5.5)}

N

The formula (5.5) includes important design parameters:^{C }= Channel capacity bps^{B }= Bandwidth Hz^{S/N }= Signal-to-noise ratio.

Shannon states that to approximate this limiting rate ^{C }of transmission the transmitted signals

must approximate, in statistical properties, a white noise. This approximation in a band-limited

channel is done using multi-carrier systems (OFDM) with an adaptive modem designed and

described later in this thesis. From the Shannon’s limit one can generate the design principle

used in the modem design and present wideband network development: To improve information

transmission, in bits per second per Hz, it becomes necessary to increase the S/N or the

bandwidth of the channel. In search for error free transmission, this theory yields to the use of

complex modulation methods. OFDM has been found one of the most promising. Shannon’s

voice band capacity of different channels versus S/N is presented in Figure 5.3.

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Fig. 5.3 Shannon’s capacity of different channels versus S/N [Lal99]

5.2. Adaptive Modem

The basic principle of the adaptive modem is the free selection of the data transmission parameters

optimized to the channel conditions. This was implemented in the adaptive modem prototype,

presented in papers [Lal00] and [Lal01].

In simulations a wide range of modulation method and bit rates were studied with the following

results:

1. Bit rates 4000 –240 000 bps.

2. Bit constellation with 16-256 states.

3. Symbol rates 1000-3000 symbol/s.

In the modulation process of an adaptive modem several frequencies; symbol phases and amplitudes

(QAM-states) are used. Its performance is calculated for example in a four-carrier ^{k}^{=4 }as:

1. Using ^{f}_{S }= 45000, ^{N}=26 the symbol rate is ^{R}_{S }= 1730.7.^{2. }Using ^{M }=5…8 bits per symbol the maximum bit rate is ^{R}_{b }= 8653...13846 bps with one

channel.^{3. }^{R}_{b }= 34.6...55.4 kbps with four channels (carriers), where _{R}_{b }_{= }_{kMR}_{s }^{.}

Figure 5.4 presents a simulated complex piecewise continuous waveform. There is a block of

six symbols made with a multi-carrier soft modulation. Generation of these piecewise continuous

symbol waveforms will be discussed in more detail later.

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