Document Text (Pages 91-100) Back to Document

Adaptive secure data transmission method for OSI level 1

by Lallo, Pauli, PhD


Page 91

Adaptive Filter

A human ear can detect fine frequency differences. The same with software detection using
DFT was presented earlier in Figure 5.2. It explains the situation with DFT i.e. by increasing the
number of samples one gets more narrow filters and the possibility to use narrow frequency
bands and channeling. One can adapt multi frequency signal waveforms to the bandwidth in
use. The number of samples N and the sampling frequency fs define the frequency selectivity
and the useful channel bandwidth. Figure 5.16 presents simulation results using two, the 13point
adaptive filters in the detection of FSK-signal transmitted over ADM-channel.

Fig. 5.16 DFT as filter [Lal97b]

Adaptive Filter Bank

The detection of multi-carrier waveforms is made with adaptive DFT filter banks. A simulation
model and example of a 26-point DFT filter bank is in Figure 5.17. The first six filters and their
output amplitudes at different frequencies are shown in the figure. The center frequency of the
first filter is 615 Hz and the next is 1230 Hz etc. The bandwidth of the filters is also 615 Hz.
The noise floor (S/N) at 615 Hz is 15 dB. The noise floor with DFT detection depends on the
number of samples used in detection and thus the relation between sample frequency and the
signal frequency. Thus the realization of the DFT-based software filters is not easy at higher
frequencies. The present technology level might be at the 2 GHz [Mil03].

The important components are A/D or D/A devices and the processors, which are used for the
Joint Tactical Radio System (JTRS). One can easily change all the parameters of the waveform
and thus also the bandwidth of a band-pass filter and carrier frequencies etc. The change of a
parameter may also have an effect on the resulting throughput bit rate. The noise level and the
bit rate must be balanced with the selected digital modulation method for an error free result.

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Fig. 5.17 Adaptive DFT filter bank [Lal02]

Secure Communication

An example of secure communications is a multi-carrier system with m=8 carriers tested with
the adaptive modem prototype, later in Figure 5.18. The figure includes a synchronism signal
sent first in the waveform stream. A proposal for securing data communication is proposed by
applying a band-limited frequency hopping (FH) waveform. As an example a FH waveform
using m=8 carriers is analyzed. One designs a secure waveform with FH carriers representing a
symbol sequence S ={Sk}, formula (5.24).

[s , s , s ,...,s s ]

=

0 1 2 k ,..., N 1

{S N }


(5.24)

Where

sk = the k
th symbol

k = 0,1,2,...,N-1
N = the number of symbols.

A secured band-limited signal is the sum waveform of eight carriers (a multiplex signal). The
physical securing of S is made using a random FH signal as one in the multiplex signal of eight
carriers. The ciphered data is digitally modulated in one FH signal among the multiplex signal
of the eight carriers. The other seven carriers are digitally modulated with random data. Some
problems might be in the selection of carriers. The problem with large m is the Picket-Fence
Effect as described earlier. Thus the carriers for the sum waveform should be selected carefully
in order avoid major peaks in the signal. Also the selection of a digital modulation method depends
on the particular channel quality.

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5.8. Adaptive Secure Data Transmission Method for OSI
Level 1

Security

By passing adaptive waveforms over the Internet or over a telephone network to another LAN
server we can build our own VPN tunnel channel with OSI level one securing. The securing is
made in the adaptive modem with band-limited frequency hopping in the voice frequency band.
This can be done with the adaptive modem software algorithm in the data modulation process
with a multi-carrier system. The basic theory is presented in paper [Lal02b]. It is a question of a
signal microscope in the signal space, when a N-point DFT with a large enough N is used for
symbol detection as described in chapter 3. In a hardware world such a filter is impossible to
make. A DFT-based soft detection method uses such algorithms adaptively.

A Proposal Application for Secure DFT-based Alert System Using
Broadcasting

Remembering the worst earthquake catastrophe in Asia on 26.12.2004, with a missing swell
alert system, it is obvious that a reliably working global alert system is needed. A general warning
system for any kind of catastrophes based on public radio broadcasting with added multitones
is proposed here. Short multi-tone voice messages describing the alert message in question
can be detected with a DFT-based software algorithm application described earlier in this
chapter. Normal radio receivers should have a small additional device for receiving these messages.
The government offices (police stations, rescue authorities etc) should have the responsibility
to listen to the broadcasting 24 hours a day and at the same time possible alerts and carry
out necessary actions. For example, a three-tone detection and DFT filter needed with the receiver
is easy to realize with an adaptive DFT detection algorithm (ref. fig.5.14) formula
S(m1,m2,m3) for a three-tone signal as

S (m , m

+

N


1

n=1
2

, m ) =

3

x[n(t)]e

N


n=1

x[n(t)]e

2 jπm3( f )n(t )
2 jπm1( f )n(t)

+

N


n=1

x[n(t )]e

2 jπm2( f )n(t)

(5.25)

Where m1, m2, and m3 define the three multi-tone carriers. In a reliable detection method the
thresholds are set for all detected individual tones S1, S2, and S3. The alert is accepted with the
simultaneous detection of all tones.

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Secured Waveform

It is well known that wireless Internet access or LANs are open to any recording, taping, interfering
etc. There is no standardization for security in the physical OSI reference level. Thus
there is a need for data encryption as a minimum requirement in Internet traffic with TCP/IPprotocol
systems. For example in biomedical and telemedicine data traffic one needs a standard
for the physical level data security [Var03].

Fig. 5.18 Secured multi-carrier (m=8) waveform [Lal04b]

A simple version of the proposal for securing data transmissions on the physical or modulation
level is illustrated in Figures 5.14, 5.17 and 5.18. Figure 5.14 gives an example of a secured
waveform. Figure 5.18 shows the signal on the frequency band seen by the receiver and Figure
5.17 presents the filter bank function for its detection.

Suppose one has a symbol sequence Sk for data transmission, formula (5.24). One defined symbol
stream vector S = {Sk}, which is the transmitted message. In a digital modulation process
this stream is converted into a piecewise continuous waveform stream vector W={Wk}, formula
(5.26).

[w ,w ,w ,...,w w ]

{WN} =

0 1 2 k

,...,

N 1 (5.26)

Where wk = the k
th waveform.

The whole multiplex signal matrix M={Mm,k} is made in a random process. For a message of N
symbols and M carriers one gets a signal as

m1,1 m1,2 m1,N
⎢ ⎥
m2,1 m2,2 m2,N
{
M = ⎥

k,N} (5.27)

⋅ ⋅ ⋅ ⋅
⎢ ⎥
mM ,1 mM ,2 mM ,N

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Using an orthogonal frequency base of M frequencies one can modulate each carrier using an
adaptive digital modulation method i.e. by selecting adaptively the proper QAM-level for each
carrier according to the channel quality.

A secured waveform for a particular message transmission is generated by hopping the frequency
in a random sequence, which is at least as long as the message N. Taking the advantage
of frequency hopping (FH) in a base-band modulation process one has now the secured waveform
on a physical level.

Cryptographic methods are not studied here, however, for additional securing of the message
one can use secret bit constellations (A, P) presented by formulae (5.17-5.18), which are other
than those defined in standards.

In decoding the signal from the multiplex of M signals one needs to know the hopping code {C}
for the particular message signal as

c1,1 c1,2 c1,N
⎢ ⎥
c2,1 c2,2 c2,N
{
C = ⎥

k,N} (5.28)

⋅ ⋅ ⋅ ⋅
⎢ ⎥
cM ,1 cM ,2 cM ,N

N message elements ck,N one in each column are 1, k=1…N, while all other elements are 0. In
the similar way hopping codes for other messages can be constructed in a hopping system.

One gets the decoded signal S in general as resulting signal carriers in a matrix operation as

T

S = CF (5.29)

Hopping sequence is secret i.e. the carriers are selected with a secure random process known
only by the two end users of the secure adaptive end-to-end communication. Vector F={FM}
defines in general the M frequencies used.

[f , f , f ,..., f f ]

{ M } =

0 1 2 k ,..., M 1

F (5.30)

Robust Complexity Evaluation

In Figure 5.18 the number of carriers is M = 8 (the second broader peak is caused by a synchronizing
deterministic sequence of symbols). FH is now a random sequence of eight carriers and
the hopping rate is the symbol rate. The multiplex waveform includes eight random waveforms.
If the message size is N = 10 symbols, there are 10 columns in the code {C10,8} and matrix
element 1 means a symbol in each column of {C10,8} as

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96


























=
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
}
{ 8
,
10
C
(5.31)
The code matrix is thus a 10x8 matrix and may be called a block code for eight messages. Eight
carriers can send eight messages each containing ten symbols in this example case. Each message
has an individual code matrix, where in every column only one element on a random row
one. All other elements of that code are zero.
Supposing the carrier set (M=8) is the same for all symbols k=1…10 and it is a priori
known and the eight carriers are presented in the carrier frequency vector as
[ ]
5640
,
4935
,
4230
,
3525
,
2820
,
2115
,
1410
,
705
}
{ 8
, =
k
F (5.32)
Then in the special case of fig. 5.15 the carriers in the message of ten symbols are calculated as
T
CF
S = (5.29)
The result is
[ ]
1230
,
3075
,
1230
,
3075
,
1845
,
4305
,
2460
,
1845
,
4920
,
615
}
{ 8
,
10 =
S (5.33)
It is supposed that the digital modulation method is a priori known. Thus final decoding of the
information from the waveforms represented in {S10,8} is made as described earlier in formulae
(5.17-5.18).
The complexity of this cipher system (one of eight carriers) is 5.85E+48. A reference value of
the DES code with 54-bit sequence is 1.8E+16. Using a 512-carrier system in the same way as
the proposed cipher system one gets the reference level of complexity 2E+146.

Page 97

5.9. Sensitivity Analysis of Adaptive Data Communications

A simulation method can only give qualitative results of the error performance of the investigated
systems. However, due to mathematical complexity several systems can only be investigated
with modeling and simulation. The sensitivity analysis thus gives robust information of
error performance of the presented adaptive data communication method, which uses DFTbased
soft detection and IDFT-waveform generation. The channel models are granular, AWGN
and multi-path.

5.9.1. Sensitivity of the Soft DFT Detection in AWGN-Channel

Simulation settings in Figure 5.19 are:
- AWGN noise is a parameter. It is generated in the transmission channel and a received signal
is disturbed by this noise.
- Signal amplitude A is a variable.
- f1=615 Hz, f2=1230 Hz, and f3=1846 Hz.
- N=26.

Fig. 5.19 Error performance of DFT soft detection in presence of AWGN

Figure 5.19 presents amplitude sensitivy of a multicarrier signal transitted over an AWGN
channel and detected using using soft DFT detection. Error performance of a 26-point DFT
detection is a simulated result. The amplitude sensitivity against AWGN noise sets the limits for
usable S/N and amplitude selectivity in the selection of the modulation method. The qualitative
result gives at S/N=10 dB and amplitude variation of 10%.

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5.9.2. Sensitivity of the Signal Detection in Granular Channel

Simulation settings in Figure 5.20 are:
- Granular noise is generated in the adaptive delta modulation process and is in the received

signal.
- AWGN noise is generated in the transmission channel in the same way as presented in Figure
5.19.
- Signal amplitude is a variable.
- F1=615 Hz, f2=1230 Hz, and f3=1846 Hz.
- N=26.

Figure 5.20 Error performance of DFT soft detection in presence of granular and Gaussian noise

Error performance of a 26-point DFT detection is a simulated result. The normalized amplitude
sensitivity is disturbed by the granular noise all the time. The adaptive delta modulation proces
sets the limits for the amplitude selctivity in the selection of modulation method. The qualitative
result in Figure 5.20 gives basic variations in the received amplitude, which is at least 10% at
S/N=120 dB. AWGN noise increases the variation of the recived signal at S/N= 10 dB to about
40%.

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5.9.3. Frequency Deviation Sensitivity of the Soft Signal Detection

Simulation settings in Figure 5.21are:
- Granular is not present.
- A three tone signal is used f=615, 1230 and 1846 Hz, A=0,5 V.
- N=26 samples and sampling rate is 16000 giving 615 Hz selectivity of DFT.

Fig. 5.21 Performance of DFT soft detection in function of frequency deviation

A three-tone signal of 615, 1230 and 1846 was used in the evaluation of frequency sensitivity of
DFT detection. Frequency deviation of 300 Hz in the basic 615 Hz signal gives about 40
degrees error in the received signal value in detection. However, the soft detection is working
well at the whole measured deviation area as seen in the values of other signal elemets (1230
Hz and 1846 Hz). The selectivity of the DFT filter is given by a sampling rate per number of
samples, and is 16000/26=615 Hz.

The figure shows that the whole pass-band 615 Hz is usable and the soft detection is not very
sensitive to frequency deviation of the carrier.

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5.9.4. Frequency Deviation Sensitivity of the Soft DFT Detection
in ADM-Channel

Simulation settings in Figure 5.22 are:
- Granular noise is generated in the ADM-channel and it is present in the detected signal.
- The same three tone signal parameters as before are used f=615, 1230 and 1846 Hz, A=0,5

V and random phase.
- N=26 samples at sampling rate 16000 Hz gives 615 Hz selectivity of DFT.
- Detection of three tones is made with a 3-finger receiver using DFT.

Fig. 5.22 Performance of DFT soft detection in ADM-channel in case of frequency
deviation

The evaluated granular channel is not very suitable for analog data transmission. The granular
channel introduces amplitude variations in the detected analog signal values (615.38 in figure).
Reference analog signal components values (1230.77 and 1846.15 Hz) are not granular signals
(thus only small variations in the amplitude). Reliable amplitude and phase detection of a multicarrier
data transmission system working in the ADM-channel is not possible. A MFSK system
is one solution.

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