# Adaptive secure data transmission method for OSI level 1

In field tests a wide range of modulation method and bit rates were studied in wireless and

wired environments, Figures 5.9-5.10. The following settings (parameters) over a VHF radio

channel were used in the field tests of the adaptive modem prototype:

1. Symbol length 16, 20, 24, 48 and 64 samples.

2. Symbol time 444 -1422 microseconds.

3. Symbol rate 703-2250 Bd.

4. Modulation 4QAM, 8QAM, 16QAM and 32QAM.^{5. }Number of carriers 1, 2, 4, 5, 6 and 8.

Fig. 5.9 Spectra of adaptive waveform measured in the VHF field test, [Lal02] and

[Lal04b]

Fig. 5.10 Waveform captured in the VHF field test

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Case 1 Wireless Channel

Adaptive waveforms were generated with the earlier given settings. The results of the data

transmission tests with these settings in the band-limited wireless case with VHF military radios

were:

1. Bandwidth 600 - 4800 Hz.

2. Bit rates 1.4 … 22.5 kbps.

Figure 5.11 shows some results of the VHF-range field tests. The bit rate was developed with

multiple carriers and thus using bandwidth. The bandwidth was limited to the voice grade. The

received waveform in Figure 5.10 is 4-QAM with no impairments observed. By changing the

parameters described earlier one could find an optimum throughput for the radio channel in

question.

The best result of the VHF radio channel test (no error found in test messages) was about 6.8

bit/Hz sing a two carrier 16-QAM-modulation. The spectrum of the 22500 bps 16-QAM waveform

is presented in Figure 5.11. Other examples of adaptive data communication development

and DFT-detection are described in a paper presented in 2002 a Milcom conference [Lal02].

Fig. 5.11 Spectrum of 22.5 kbps signal – a result of the VHF field [Lal01]

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Test results:

The best bit rate for the channel used in the test was

_{bps}

R

b

^{22500}

2250

5

2

_{=}

⋅

⋅

_{= }using 32-

QAM

The spectral efficiency was then about 6.8 bit/Hz.

In general the evaluation of bit rate

^{R}

_{b }of the adaptive modulation method is made in a multicarrier

(

^{k }carriers) case with formula (5.20) as

s

b

^{kMR}

R

^{= }

^{(5.20)}

Where

- Number of carriers

^{k }= 1, 2, 4, 5, 6 and 8.

- Bit constellation

^{M }= 2-5 bits.

^{- }Symbol rate

^{R}

_{S }= 703-2250 Bd.

Table 5.3. Adaptive communication test results

Band

Carriers

Symbol rate

Bit rate

Modulation A-P

QAM level

550-1100 Hz

2

600

600

2FSK

550-2200 Hz

4

600

1200

4FSK

550-4400 Hz

8

600

1800

8FSK

550-4400 Hz

8

1200

3600

8FSK

550-4400 Hz

8

2400

7200

8FSK

550-4400 Hz

8

2400

12000

8FSK, A=1 P=1

550-4400 Hz

8

2400

19200

A=1

550-4400 Hz

8

2400

19200

P=1

550-4400 Hz

8

2400

38400

A=1 P=1

4QAM

550-4400 Hz

8

2400

76800

A=2 P=2

16QAM

550-4400 Hz

8

2400

153600

A=4 P=4

256QAM

Case 2 Wired Channel

The bit rates of the adaptive modem were 600-153,600 bps in the wired telecommunication

network test, Table 5.3. During these tests the method of adaptive selection of waveforms was

demonstrated as presented in the Table 5.3. The modulation method (algorithm) was selected

during the test by changing the modulation parameters (soft detection). The table presents test

results of data transmission over band-limited channels (^{A }= amplitude bits, ^{P }= phase bits).

Multi-carrier QAM-modulation methods are advantageous. MFSK offers much slower bit rates.

The wired channel bit rates of the adaptive modem were much higher than 5625-22500 bps the

result of the wireless telecommunication network test, paper [Lal00]. Several other examples

with DFT-detection algorithms are described in paper [Lal01] and [Lal02].

Conclusions of adaptive data transmission theory are summarized here:

- The adaptive data modulation method uses DFT in detection of waveforms.

- There are a lot of signal ^{f, A, P, T }and software detection parameters ^{N, m, fs }available in

the optimization process of the data communications in radio or wired networks.

- The optimal use of the bandwidth is designed in this study by the proper selection of carriers

(f).^{- }Waveform is made to resist noise and interference with optimal selection of symbol time ^{T,}

carrier frequency ^{f}^{, }and bit constellations ^{A, P.}

- DFT-parameters, sampling frequency ^{fs}^{, }number of samples ^{N }and number of frequencies

^{m}^{, }are selected in reception for the best performance needed for BER or data rate or other

metric.

- The throughput can be optimized in regard to BER versus S/N by selecting the most suitable

bit constellation used in the digital modulation method.

The proposal for using adaptive waveforms in different channels in telemedicine (alert systems

etc) or in the software-defined radios (SDR) is presented. In the future more studies on optimal

waveforms for multi-path propagation should be made.

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5.6. Discussion of Fourier Theory, Limitations and Applications

In this section some basic theories and applications of adaptive data communications are discussed.

The basic theories are first of all Shannon’s channel capacity formula and the Discrete Fourier

Transform (DFT), which is used in the selection of adaptive data communication waveforms and

soft detection. Waveforms are generated in an IDFT process and detected with a Discrete Fourier

Transform (DFT) algorithm. Sampling is made with A/D or D/A devices. The discrete event simulation

theory is used as a research tool, study and development of secure adaptive data communications

and a prototype modem [Mit82]. Ciphering in the modulation is a proposed process for planning

secure adaptive data communications. The focus in this chapter is on the realization of secure

data transmissions with complex waveforms in accordance with the Shannon’s channel capa city

theory.

Fourier Theory

Jean Baptiste Joseph Fourier did his important mathematical work on the theory of heat in 1807

publishing ”On the Propagation of Heat in Solid Bodies”. The Fourier series are based on Fourier's

expansions of functions (trigonometrical series) of this old work [Bos17].

A waveform is a continuous signal in time domain. The Fourier Transform provides the means of

transforming a signal defined in the time domain into one in the frequency domain. A digital symbol

can be transformed into a finite waveform (signal) in a digital modulation process for transmission

in different analog communication channels. The Discrete Fourier Transform (DFT) is an approximation

of the continuous Fourier transformation. The Fast Fourier Transform (FFT) is a DFT

algorithm developed by Tukey and Cooley in 1965 [Coo65]. It reduces the number of computations

of a N-point transform (N samples) on the order of N2 to N log N in digital operations.

Limitations of DFT

In data communications Discrete Fourier Transform (DFT), microcomputers and Digital Signal

Processing (DSP) with high processing speed are used quite early [Har82]. DFT is commonly used

for calculation of a power spectrum. DFT thus includes an algorithm for detection of MFSK signals.

The DFT algorithm can be used to approximate the transformation of a continuous time function

with the following limitations:

- The signal must be band-limited.

- Aliasing. The sampling rate must be sufficiently high to avoid to any spectral overlap.

- Leakage. The observation of the signal is limited to a finite interval. The effect is a spreading or

leakage of the spectral components and an undesirable modification of the total spectrum (distortion).^{- }Picket-Fence Effect. The inability of the DFT to observe the spectrum as a continuous function

but only at discrete points. The spectrum is limited to integer multiples of the fundamental frequency^{F }(reciprocal of the sample length ^{N}). The major peak of a signal component might not be

detected.

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In Digital Signal Processing (DSP) different means are employed to avoid the problems:

- Use sampling rate high enough to avoid any spectral overlap or an anti-aliasing filter.

- Multiply the signal by a suitable window function that minimizes the spreading.

- A procedure for reducing the picket-fence effect is to vary the number of points in a time

period by adding zeros at the end of the original record. The original record is intact.

Waveform Generation and Detection with DFT

A DFT calculation gives complex values ^{z=x+jy }of a finite signal for a finite time period and a

given frequency. Amplitude and phase response (spectrum) is a Fourier series calculated by

DFT. DFT performs symbol (bit constellation) detection of a digital modulation method. The

inverse DFT is used as a signal generator, Figure 5.12. It digitally modulates the symbols

stream

^{[}^{s },^{s },^{s },...,^{s s }^{]}

{^{S}_{N}} ^{=}

0 1 2 ^{k }^{,..., }^{N }_{−}1 ^{(5.21)}

into a piece-vice continuous waveform ^{x(t) }in a symbol by symbol ^{(k) }waveform generation as

x^{(}t^{)}

+∞ ^{N}_{S }^{−}^{1}

^{= }∑ ∑

i_{=}^{0 }k_{=}^{0}

{[_{s}

2

I

(_{k}) + _{s}

2

Q

T_{S}

(_{k})]_{p}(_{t }− _{k N}

− _{iT })}

S

(5.22)

Fig. 5.12 Digital wave generation and detection

DFT is used in the waveform generation and detection of very high data rate OFDM systems

[Kif01]. In a band-limited software modem design and in a data transmission simulator DFT is

the starting point of the algorithm design [Lal04a, Lal04b], Figure 5.12.

A symbol waveform is a finite interval signal and thus with a proper selection of parameters one

can use the Discrete Fourier Transform (DFT) for real time detection of adaptive multi-carrier

waveforms. Fast Fourier Transform (FFT) was not quite suitable for the adaptive software modem,

because the use of the number of samples N is limited to powers of two or in some cases

to four. FFT is not fully adaptive as a DFT solution, when an adaptive selection of carrier frequencies,

frequency selectivity, symbol rate or bit constellation states is wanted. All these are

selected with a few parameters ^{N }and _{∆}^{(t) }in ^{DFT, }formula (5.23). The sample interval _{∆}^{(t) }is

defined by the sampling rate ^{f}_{s}^{.}

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S [m^{∆}( f )] ^{=}

X

N

∑

n_{=}1

x[n^{∆}(t)]e

−^{2 }^{j}^{π}

m_{∆}( f )n_{∆}(t)

(5.23)

The balance between the number of samples ^{N }and the sample frequency ^{f}_{S }is set in the detection.

The other parameters used in the adaptive data communications theory are the bit rate ^{R}_{B},

symbol rate ^{R}_{S}^{, }symbol time ^{T}_{S}^{, }the number of bits in one symbol, bit constellation, digital

modulation scheme, and the number of frequencies used in the channel. All these parameters are

selectable variables. The channel characteristics are used in optimizing the waveform and for

adjusting the modulation parameters. Then the software algorithm is optimized according to the

selected test measure (BER versus S/N, bit rate versus bandwidth).

Adaptive Selection of Modulation Method

Fig. 5.13 Adaptive selection of modulation method,

S/N versus constellation

A comparison of modulation methods is made in reference [Car86] pp. 552-554. Adaptive selection

of the modulation method is illustrated in Figures 5.13 - 5.15. Figure 5.13 presents a

comparison of modulation methods based on the minimum signal-to-noise ratio needed for

working on the BER-level = 1.0E-03. In cellular networks a modulation working on a low S/N

ratio level can be economically a sound solution, because a large cell size is available. However,

in the future low or high bit rates needed randomly in various services argue for an adaptive

approach in the use of digital modulation methods and thus the selection of an optimized waveform.

At the same time the adaptation of bit rates to distance can increase the tariff possibilities

offered by the operators. Adaptation can follow technology in a way that high bit rates are in

smaller cells and the lowest bit rates are offered in larger cells and for distant customers. Appendices

1-3 explain some proposals made for adaptive communications.

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5.7. Adaptive Multi-Carrier Data Communications

The adaptive multi-carrier data communications like OFDM have been intensively studied

[Ist99], Appendces 2-3. A band-limited prototype modem (an upgrade device for wireless radios)

is one example of field-tested adaptive systems. Its main property is the adaptive selection

of the following data transmission parameters [Lal01]:

• Channel bandwidth.

• Carrier frequencies.^{• }Bit constellation (amplitude/phase) states.^{• }Symbol and bit rate.

Table 5.4 presents examples of simulated band-limited adaptive multi-carrier waveforms, symbol

rates, QAM modulation states, number of channels, equivalent MFC-code and the corresponding

bit rates achieved. Symbol generation is made with an inverse DFT algorithm. Symbol

detection is based on the complex DFT, formula (5.23). The complex DFT of the symbol calculated

over the symbol time fully describes the particular bit pattern in the constellation diagram

i.e. amplitude and phase at the DFT frequency used. Thus it gives us the symbol identification

parameter estimates (amplitude, phase and frequency) with known frequency selectivity described

later.

Table 5.4. Adaptive multi-carrier modulation methods and bit rates [Lal01]

Adaptive Data Communication Applications

Adaptive data communication applications are discussed in this section. They can be designed

according to the principles studied in earlier sections and chapters using adaptive selection of

modulation method and waveforms. This section presents a method for adaptive selection of

waveforms, adaptive filters and filter banks and a secure communication system. In the detection

of waveforms adaptive filters or filter banks are needed. In securing data transmission an

adaptive multi-carrier modulation system can be used.

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Bit Stream

One describes a bit stream, which has to be transmitted on-line or via the air. In the transmission

of the bit stream adaptive digital modulation methods symbol by symbol are used. One describes

a symbol with a waveform that contains several bits. The adaptive modulation method

means that one can adapt the generated symbol waveform to the analogue channel used. The

modulation of the particular carrier is made by changing the software algorithm, which converts

each symbol to a specific amplitude-phase constellation point and uses a proper symbol time.

Depending on the channel bandwidth ^{B }(wired or radio) there is one or several transmission

carriers (channels) in use for the optimal Shannon’s capacity. Depending on the channel characteristics

or signal to noise ratio one can select the best amplitude phase constellation. One uses

the discrete Fourier transform (DFT) in the detection and the demodulation of the symbol waveform.

5.8 Adaptive Selection of Modulation Method

A long-range transmission of bits is not possible in the form of a two DC state signal i.e. a binary

signal, which is the way a PC operates. The sinusoidal waveforms of a symbol sequence

can travel long ranges in the air or on-line. There are effective digital modulation methods,

which combine several bits into one symbol and make a corresponding symbol waveform, Figure

5.14. One describes the adaptive software modulation method instead of standard digital

methods. The reason for the use of adaptive waveforms is due to practical telecommunication

networks, where one has a variety of different channels. They offer different bandwidths, SNR

and continuously varying characteristics in mobile cases. Design of an adaptive modulation

method begins in the selection of dynamic range and selectivity of the system using carrier frequency^{f, }amplitude ^{A}, phase ^{P }and time period ^{T. }The limits for the selectivity and dynamic

range of each parameter are set according to the channel characteristics.

Fig. 5.14 Symbol waveform stream [Lal04b]

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The adaptive modulation method and waveforms are a generalization of known digital modulation

methods and waveforms. A development team has carried out experiments with a prototype

adaptive modem during the field tests in order to demonstrate the effectiveness of different

modulation methods, Figure 5.15.

Fig. 5.15 Adaptive selection of modulation method,

bit rate versus baud rate

The MFSK method is not very effective as one can see in Figure 5.15. Increasing the symbol

rate (baud rate) does not help the situation. To get high bit rates one has to use more complex

modulation methods and multi-carrier systems. OFDM is a data transmission solution, which

gives high bit rates and is the basis for the most recent communication system development

projects [Kif01]. The adaptive selection of the modulation method gives advantageous bit rates

and also the proper bit error performance for the individual cases. This is an optimization problem

discussed in paper [Lal04b].

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