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Adaptive secure data transmission method for OSI level 1

by Lallo, Pauli, PhD


Page 71

Fig. 5.4 Simulated complex waveform [Lal02]

In Figure 5.5 a step function is used as the input signal (IN) and the result is the simulated output
of the 16 kbps granular channel (OUT). This result shows the performance of the robust
worksheet method and the usefulness with different waveforms. This case is with for example
detection of PPM (pulse phase modulation) used in UWB. This is a subject for other studies.

Sampling rate limits the performance in the received “OUT” signal, which is the input signal for
the adaptive modem. Figure 5.5 illustrates the granular channel properties. The performance and
sensitivity of adaptive modem with different channel models are evaluated in a later section.

Fig. 5.5 Simulated narrow step functions

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5.3. Generation of Symbol Waveforms

The best available complex digital modulation is selected and thus the bit rate of the system is
made optimal. The present bit constellations of standard analog data of ITU-T have 1-5 bits in
the digital modulation schemes. This is not limited in the adaptive modem basic theory because
the channel may give better performance. In military telecommunication networks signal power
and time are often minimized. A data package presented in Figure 5.1 is a target of electronic
warfare. This target is usually minimized. Many design parameters of the system have some
effects on this package. The simulation process, presented in papers [Lal97b], [ Lal04a] and
[Lal04b], is capable of simulating all kinds of waveforms with given signal to noise (SNR) settings.
Instead bits symbols (a specific number of bits) are converted to waveforms as described
earlier in the simulation process.

A symbol is earlier called the data block and presented with its parameters in Figure 5.1. Several
random digital bits (bit stream or block of bits) are collected together in a symbol using bit
constellations as discussed earlier. A symbol waveform of one symbol (several bits) is a continuous
waveform during the symbol time T. However, a waveform stream of several symbols
is a piece-vice continuous waveform. Then a band-limited OFDM system is a combination of
several piece-vice continuous symbol waveforms, which can be described as a three dimensional
system (time, frequency and amplitude phase constellation) refer to Figure 5.1.

Signal Source and Bit Stream

A digital information source generates bit streams. The signal source can be a computer, a human
voice or any voice grade source or even a still picture or video source. However, if the
source generates analogy information (voice or video), it must be coded into the digital form
using different coding algorithms. The binary sequence BN = {BN} is usually made by a random
process. One has the N-bit random digital stream {Bk}= b0 , b1 ,b2 ,...bk ,...bN-1
available for the transmission over wired telephone lines, optical fibers or wireless radio channels,
formula (5.6).

[b ,b ,b ,...,b b ]

=

0 1 2 k

,...,

N 1

{B }


,k = 0,1,2,..,N-1 (5.6)

N

Where bk is the kth bit and N is number of bits in this representation.

Symbol Stream and Waveform Generation

{ L
S by using digital modulation methods
discussed in Chapter 2. Thus the original binary signal is developed to a symbol stream
{S L}presented in Formula (5.7)

This stream of bits BN is transformed into a signal }

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

{S L} =

0 1 2 k ,..., L1 (5.7)

In a digital modulation process these bits or symbols (group of bits), performing with the digital
modulation a digital to analog conversion (DAC), are converted and generated to analog voltages
for transmission over analog telephone lines. Traditional telephone lines are band-limited
thus the analog voltage (waveform) must be adapted to the line conditions (amplitude scale,
frequency band, etc). A voltage representing these binary digits or symbols is transmitted over
a communication channel as a waveform (a binary or symbol waveform). The present analog
voice band modems, discussed in Chapter 2, can combine at least five bits into a symbol waveform.

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In digital radio links the symbol waveforms can have more than ten bits in a symbol waveform
while the useful bandwidth is not limited to the voice grade channel, see Table 5.1. The useful
bandwidth is at present in the range of a few GHz. There are Giga-sample analog-to-digital
converters (ADC) commercially available. All-digital UWB devices for indoor use have been
proposed (Standard 802.15.3a for UWB-OFDM indoor system [Mil03]. Commercially available
Giga-sample analog digital converters are presented in Table 5.1.

Table 5.1. Commercially available Giga-sample ADCs [Mil03]
Vendor Bits Giga-samples
per second
Bandwidth
GHz
Power
W

Maxim 8 1.5 2.2 5
(Evaluation kit)
Atmel 10 2 3 4.6

Alma project 2/3 4 2-4 2
(France)
Rockwell 8
6
3
6
-
-
5.5
3.8

Let’s say one has M bits in one symbol S } [b ,b ,b ,...,b b ]
{


L,k = 0 1 2 k

,...,

M 1

. By a teaching

mechanism one can test the maximum bit constellation M = Mmax of symbols, which the digital
modulation method can use in a particular channel. The standard data modems of ITU-T use
1…6 bit per symbol. The digital modulation methods make a D/A transformation bit-by-bit or
symbol-by-symbol to waveforms, Appendces 1-3. Using M bits per symbol one gets the L-
symbol stream {S L}, formula (5.7).

Use of Design Parameters in Waveform Generation (Proposal)

The waveform describes the symbol stream - a message. All symbols are formed of several bits.
The following parameters were used in the software modem algorithm development in order to
get the most suitable functionality. The performance of the modulation was then tested in the
field (description of the test results in the coming sections).

Parameter
Symbol time
Amplitudes and phases
Modulation method
Number of carriers

Effects
Symbol rate - Sampling rate - Number of samples.
Bit constellation - A-P range and selectivity.
Bit rate - BER performance versus S/N.
Bandwidth - Frequency selectivity.

The adaptive parameter selection principle was proposed and used in field test: Parameter values
were selected during the modulation training process for use in the symbol signal waveform
as:
1. Amplitude.
2. Phase.
3. Symbol time.
4. Carrier frequency.

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In the Figure 5.6 one finds a design example of the simulated adaptive and complex four-carrier
waveform. One finds the design parameters: symbol length N=26 samples, 4 carrier frequencies,
and bit constellation (several amplitudes and phases). The symbol waveform is adaptive
when it is adapted optimally to the transmission channel.

Fig. 5.6 Simulated complex four-carrier waveform [Lal01]

Several different waveforms and channel models were studied with simulations of the robust
method [Lal04b]. Waveforms or their use are discussed in all original papers especially in
[Lal97b], [Lal99], [Lal00] and [Lal01]. Table 5.2 summarizes the simulations and the harmful
effects associated with different channels. The simple waveforms (FSK, PSK and DPSK) best
resisted the different effects listed in the table. The sensitivity of the adaptive data transmission
method against the harmful effects will be presented later in a sensitivity analysis section.

Table 5.2. Data waveform and channel models
Modulation Granular AWGN Multi-path

method DM, ADM
FSK Simulated,
tested
Simulated,
tested
Simulated,
tested
PSK
DPSK
Simulated,
tested
Simulated,
tested
Simulated,
tested

MFSK Granular noise Noise level Interference
level

MPSK Slope overload Noise level Interference
level

Multi-carrier
QAM
Granular noise
Slope overload
Noise level Interference
level

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Adaptive Selection of Modulation Method

It is an adaptive data modulation concept, where one defines adaptive data modulation as the
modulation, where modulation parameters are optimized to the transmission parameters of the
channel. Channels are:
- Analog channel (voice channel).
- Digital channel (data or digital coded voice channel).
- Multi-path fading channel (air interface).
The following channel parameters were in the adaptive modem algorithm selection process
considered for different channel types:
1. Bandwidth.
2. S/N and S/(N+I+J) ratio.
3. Frequency range.
4. Multi-path signals in radio channel.

Adaptation of the bit rate to the channel characteristics is defined as selection of the number of
carriers and with the change of modulation signal constellation (for example 4QAM to
16QAM). Examples of tested waveforms are presented in the session 5.3.2 field tests, where the
selection method was:
- Number of carriers k = 1, 2, 4, 5, 6 and 8.
- Bit constellation M = 2-5 bits.
- Symbol rate RS = 703-2250 Bd.
- Number of samples N > Symbol length.
- Sampling frequency fS > Symbol time > Symbol rate RS= fS /N.
- Number of amplitude and phase bits M > Modulation > Bit constellation.
- Number of carriers k > Channels.

Base-Band Signal

The voice grade channel of a telecommunication network has a limited bandwidth about 3.1
kHz (300 to 3400 Hz) for information transmission in a signal m(t), formula (5.8). The standard
voice grade data modems have been limited to use this limited band.

m(t) = A (t)cos[(ω (t) + φ (t)] (5.8)

m C C

The data bits are presented by a base-band signal m(t). Information can be modulated at least
into four basic development parameters: Time, frequency, amplitude and phase. The last two
parameters are used in the well-known two-dimensional constellation mapping of bits into symbols.
The basic formula (5.8) presents three generally used modulation parameters: carrier fre-
ω (t) 2 f (t)
quency fc in

C

= πC , A (t)
amplitude

m

, φ (t)
and phase

C

. The resulting data waveform
is a random (stochastic) piecewise continuous waveform, which represents the symbol
stream of random bits.

If A(t) = Am, fc(t) = φ
fc, and

C

(t) = φC i.e. all three are known constants, one has a deterministic
waveform. Deterministic sinusoidal signals were used in the field tests for measurement
of the telephone channel characteristic and in system synchronization processes (amplitude
level adjustment and first symbol identification and detection) and random waveforms for data
transmission by modems.

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In this study random waveforms were used for the simulations of data transmission over ADMchannel.
Constant amplitude Am and carrier frequency fc as a parameter selected from a band
between 0…4000 Hz were used for simulation of the ADM-channel characteristics.

Adaptive Multi-Carrier Signal

The band-limited adaptive signal is made using the sum (multiplex) signal S(t) of M carriers
each modulated with a selected modulation method as adaptive selection of the modulation
method, Formula (5.9).

S(t) =

M


m=1

A (t) cos[(ω (t) + φ (t)] (5.9)

m C,m C,m

Where M is number of carriers (sub-channels). Each carrier fC,m (t) , amplitude Am (t) , and

phase φ ( ) depend both on the selected adaptive modulation method, the symbol set (ASCII

C,m

t

etc) used and the present symbol in transmission at the moment t. In some references the adaptive
modulation method was selected in the wireless case according to the distance, attenuation
and S/N ratio requirement of the particular modulation method (for example16QAM, 8PSK,
2FSK). The complex sampled multiplex signal x(t) is discussed in Chapter 2 in Section 2.3
“OFDM System Model”, Formula (5.10) [Guo02].

x(t)

+∞ NS 1

= ∑ ∑

i=0 k=0

{[s

2
I

(k) + s

2
Q

TS
(k)]p(t k N

iT )}

S

(5.10)
Where N is the number of samples in a symbol waveform, TS = symbol time, discrete time is

iTS , i = 1..., number of carriers is NS , k = 0… NS –1, x(t) amplitude is the resultant sum of

I and Q-channels (SI and SQ), t is time and p(i,k,t,N,TS ) is the pulse function of symbols.

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77
5.4. Soft Detection of Symbol Waveforms
The formula (5.3) calculated the discrete Fourier transform of a signal x(t) with N=26
samples. The formula (5.4) calculated with N=13 and could be used only for FSKdetection.
Time is sampled fS times per second, which gives the sample time in the formula.
The frequency selectivity is the ratio fS/N. The individual mean filter frequency is
m times the frequency selectivity, m = 1…M and M = number of carriers. Thus the frequency
selectivity depends on this relation. This was illustrated in Figure 5.2. The detection
of the constellation of a particular carrier )
(
, f
m
f n
C
= is made setting m and
fS/N. Thus one gets the individual signal amplitudes as a complex value from formula
(5.3) as

=




=

26
1
)
(
)
(
2
)]
(
[
)]
(
[
Re
n
t
n
f
m
j
X e
t
n
x
f
m
S π (5.11)

=




=

26
1
)
(
)
(
2
)]
(
[
)]
(
[
Im
n
t
n
f
m
j
X e
t
n
x
f
m
S π (5.12)
From (5.8) one gets I- and Q-signals for N = 26 as

=



=

26
1
)]
(
)
(
2
cos(
)]
(
[
)]
(
[
Re
n
X t
n
f
m
t
n
x
f
m
S π (5.13)

=



=

26
1
)]
(
)
(
2
sin[(
)]
(
[
)]
(
[
Im
n
X t
n
f
m
t
n
x
f
m
S π (5.14)
Simplifying real and imaginary parts one get I and Q signals as
)]
(
[
Re f
m
S
S X
I
= (5.15)
)]
(
[
Im f
m
S
S X
Q
= (5.16)
Amplitude A and phase P of each carrier )
(
, f
m
f n
C
= will be as
2
2
Q
I S
S
A +
= (5.17)
I
Q
S
S
P 1
tan
= (5.18)
In simulations and prototype development of an adaptive modem the amplitudes Am of multicarrier
signal are normalized for all carriers fc,m , m = 1….M as
M
A
A
m = (5.19)
Phase in formula (5.18) is more difficult to adjust, because it is periodic. It can be trained to a
proper value range for each particular symbol as will be shown a little later in an example for 8-
PSK detection.

Page 78

Modeling Software Detection

Data waveforms have a constant symbol rate RS. In software detection with the DFT
algorithm the sampling frequency fS and the number of samples N give the symbol rate

fS /N. The detection of the waveforms is based on the set of parameters. The resulting bit

rate is generated from the selected symbol rate, sample frequency, number of samples,
and number of carriers used as:
- Symbol rate RS = fS /N.
- Sample frequency fS.
- Number of samples in a symbol N.
- The bit rate Rb = kMRs .
- The number of carriers used k.
- The number of bits in the symbol M.

Software detection is made with the DFT algorithm of the simulation system presented in Figures
5.7-5.8 based on paper [Lal04b]. This simulation system was used for the development of
the adaptive detection of different waveforms and their performance. The result of the development
work is the full adaptive modem with the ability of the selection of frequency f, amplitude
A, phase P, and symbol time T.

Fig. 5.7 Data waveform simulations with worksheet

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Fig. 5.8 DFT-Detection of sampled waveforms [Lal04b]

Figure 5.7 presents a MFSK detection case and Figure 5.8 a more generalized case, where QAM
states of carriers are decoded (in literature called a finger or RAKE receiver).

Example

In the simulations the different digital modulation schemes have to be modeled. In this example
the detection within a 45 degrees range of 8-PSK is possible using different carrier frequencies.
BER values presented earlier in the chapter were simulated with 8-PSK. The algorithm used for
a bit decision of 8-PSK with DFT26-algorithm in a worksheet simulator was trained as:

=IF(AND(FY56>93;FY56<138);1;
IF(AND(FY56>139;FY56<188);2;
IF(AND(FY56>188;FY56<227);3;
IF(AND(FY56>229;FY56<259);4;
IF(AND(FY56>273;FY56<317);5;
IF(OR(AND(FY56>319;FY56<360);
AND(FY56>0;FY56<8));6;
IF(AND(FY56>8;FY56<49);7;8)))))))

The principle of using 2FSK-8PSK-signal in a granular voice channel was first presented in
[Lal97b].

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5.5. Implementation and Test Results of 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,
papers [Lal00] and [Lal01]. The use of adaptive waveforms in data transmission was also
discussed in a Milcom 2002 conference tutorial and paper [Lal02]. Modeling software detection
is a large subject for another study.

5.5.1. Simulated Waveforms

In simulations a wide range of modulation methods and bit rates were studied as an approach to
the design of an adaptive modem prototype. For example high band-limited data rates as:
1. Bit rates 4000 –240 000 bps.
2. Bit constellation with 16-256 states.
3. Symbol rates 1000-3000 symbol/s.

In Figures 5.4 and 5.6 a simulated complex waveform of the adaptive modem were presented.
In the Figure 5.4 a six-symbol block with four carrier frequencies and several phases and amplitudes
is seen. Its performance is evaluated with formula (5.20) for example as:
1. Using fS = 45000, N=26 the symbol rate is RS = 1730.7.
2. Using M =5…8 bits the maximum bit rate is Rb = 8653...13846 bps with one channel and

Rb = 34.6...55.4 kbps with four channels (carriers).

R = kMR (5.20)

b s

Where
- Number of carriers is k.
- Bit constellation has M bits.
- Symbol rate is RS [Bd].

5.5.2 Field Tests

Field Test Arrangements

During a data transmission field-test the team made wave generation and detection experiments
using the adaptive software modem, Figures 5.9-5.11. The team examined data transmission
waveforms over an analog voice channel with AN/PRC-77 type VHF radio set upgraded with
the adaptive modem. The upgrade device connected to the radio “POWER” connector (a wide
band audio modification) gave a 22.5 kbps (6.8 bit/Hz) band-limited wireless bit rate performance.
The spectrum of the tested base-band waveform is presented in Figure 5.11. This was a
good voice band result compared to cellular radios in 2000, which had 9.6 kbps. The present
higher data rates were due to the wide band use in frequency domain (multi-slot in time domain),
B in formula (5.5). The adaptive waveform generation was based on the software algorithm,
which can be downloaded from Internet or built-in into the digital communication system
control files.

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