Adaptive secure data transmission method for OSI level 1
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
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
- 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.
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
) is much larger than in FFT (N/2)log2(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
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.
Fig. 4.2 Simplified model of analog data transmission
Fig. 4.3 Simplified simulation models of data transmission [Lal97a]
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]:
- 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.
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).
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).
t) = S(t) y(iT ) (4.1)
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]
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.
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 = -0.0266x6+0.2811x5-1.2868x4+2.6801x3-2 .6318x2+1.1013x+0.757; (4.2)
r = 0.9474
The polynomial phase response model of degree 3:
y = -4E-9x3+2E-5x2-0.0682x+97.429; (4.3)
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.