Generalized Receiver Employment in Ultra-Wideband Systems:
Performance Analysis
VYACHESLAV TUZLUKOV
Department of Technical Maintenance of Aviation and Radio Electronic Equipment
Belarusian State Aviation Academy
77, Uborevicha Str., 220096 Minsk
BELARUS
Abstract: - In the present paper, a performance analysis of an ultra-wideband (UWB) system based on the ge-
neralized approach to signal processing in noise is discussed. The UWB system utilizes a new pulse design that
made the performance analysis possible, since the new not only has a short duration to reduce collision, but is
also spectrally compliant to the standards on UWB systems. We present the performance analysis of the UWB
system constructed based on the generalized receiver processing different pulse shapes and with various num-
bers of users. New simulation results on multiuser performance of the impulse radio are also presented.
Key-Words: - Generalized receiver, impulse radio, multiuser systems, pulse-design algorithm, ultra-wideband
(UWB).
Received: May 7, 2021. Revised: April 3, 2022. Accepted: May 4, 2022. Published: June 18, 2022.
1 Introduction
Ultra-wideband (UWB) technology [1] has recently
become a darling of the telecommunications indust-
ry. Although under exploration since the 1980s,
UWB technology was mainly considered for radar
applications. However, recent development in high-
speed switching technology has made UWB much
more attractive for low-cost consumer communica-
tion applications [2]. One well-known approach,
known as the UWB impulse radio, communicates by
transmitting pulses of very short duration over ultra-
wide bandwidth [3]. Since UWB radio signals requ-
ire extremely broad bandwidth for transmission and
must share a frequency spectrum with other existing
systems [4], the well-known adopted standards ha-
ve, thus far, restricted UWB systems to frequencies
3.1 GHz, respectively [1].
The Gaussian monocycle pulse, commonly used
in UWB impulse radio [3], [5]-[7], must be modifi-
ed and filtered to meet the standard requirements.
Pulse shapers can be designed to meet the standard
constraint. However, careless designing can extend
the pulse duration and, thereby, lower the data rate.
Parks-McClellan filtering of the Gaussian pulse by
[8] has been successfully utilized. Its pulse spectr-
um closely matches the mask, but some scaling is
needed to keep spectral ripples below the mask. Al-
ternatively, in [9], there was presented a new algor-
ithm to meet this pulse-design challenge utilizing
the prolate spheriodal wave function of Slepian and
Pollak [10], [11]. Here, the performance analysis of
the UWB systems based on the generalized receiver
is presented that utilize the new pulse design.
Generally, our approach can be extended to differ-
ent pulse selections.
The remainder of this paper is organized as foll-
ows. In Section 2, the UWB pulse-design algorithm
is discussed. In Section 3, the main functioning prin-
ciples of the generalized receiver constructed based
on the generalized approach to signal processing in
noise are discussed. In Section 4, the performance of
the UWB multiuser systems based on the generaliz-
ed receiver is evaluated for two modulation schem-
es, utilizing one of the pulses numerically generated
by our pulse-design algorithm. Design issues conce-
rning the bit error rate (BER), with respect to the
modulation scheme and the multiuser parameters,
are discussed. In Section 5, simulation results of the
multiuser UWB systems based on the generalized
receiver are provided, along with multipath effects.
In Section 6 some conclusions are discussed.
2 UWB Pulse-Design Algorithm
In [9], a new pulse-design algorithm is presented by
utilizing prolate spheriodal wave functions [10],
[11]. The standard spectral mask requires new pulse
to have short durations while limited within 3.1-10.6
GHz. Our proposed design has several advantages
for UWB pulse design over previous methods [5],
[11]. Firstly, the pulse spectrum is concentrated in
the desired frequency band, while the pulse duration
can be controlled for high data rates. Secondly, our
algorithm yields multiple orthogonal pulses that can
be used for multiple user access. Thirdly, it provides
pulse-design flexibility to fit frequency masks with
single or multiple pass bands.
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The pulse design begins with a desired frequency
mask
)( fH
or its corresponding impulse response
)(th
. Our goal is to design a pulse signal
)(tsm
that
is time limited to the pulse duration
m
T
, while exhi-
biting minimal distortion as it passes through the
mask filter with impulse response
)(th
. The short
pulse duration is necessary as its inverse defines the
maximum data rate through the UWB system based
on the generalized receiver. Minimum distortion re-
quires that when the pulse
)(tsm
is sent through the
filter
)(th
, the output should be
)(tsm
with only an
attenuation factor
. The pulse
)(tsm
is time limited
to
m
T
. The output of the mask filter
)(th
is the convo-
lution of the pulse
)(tsm
with the filter impulse resp-
onse
)(th
as shown below
−
−=
m
m
T
T
mm dthsts
5.0
05
)()()(
. (1)
The closed-form solution to (1) is known as the
prolate spheriodal wave function [9], [10]. For each
eigenfunction
)(tsm
, its eigenvalue
defines the per-
centage of its energy contained within the frequency
mask
)( fH
. The greater the eigenvalue, the better
the power spectrum fits. Thus, only eigenvectors co-
rresponding to the larger eigenvalues should be tak-
en as pulse design for UWB. On the other hand, as
eigenfunctions of the Hermitian function are real
and the eigenfunctions corresponding to distinct eig-
en-values are orthogonal [12], the orthogonal eigen-
functions may be useful as the signalling pulses of
multiple co-channel users in UWB systems based on
the generalized approach to signal processing in noi-
se.
Using this design algorithm for a bandpass frequ-
ency mask that coincides with standard regulations,
we can design pulses [9] that have most of their po-
wer concentrated in the 3.1-10.6 GHz frequency
band. To show the flexibility of our proposed algor-
ithm, numerical examples are provided for a double
pass band frequency mask. This frequency mask is
represented in the frequency domain as follows:
=
elsewhere
GHzfGHz
GHzfGHz
fH
, 0
96 , 1
4 1 , 1
)(
(2)
whose impulse response is also easily obtained.
Eigenvalue decomposition generates multiple ei-
genvectors whose spectra fit the desired frequency
mask. We chose
2=
m
T
nsec to achieve a good fit
with the desired frequency mask and plotted one of
the suitable eigenvector pulses in Fig. 1. The corres-
ponding power spectrum, Fig. 2, shows that the po-
wer spectral density is contained under the mask.
This flexibility to design pulses that meet multiple
pass bands distinguishes our algorithm from existing
frequency-shift methods.
Fig. 1. Pulse shape obtained from the pulse-design algo-
rithm using a double-passband frequency mask.
Fig. 2. Power spectral density of the pulse shape obtained
from the pulse-design algorithm using a double-
passband frequency mask.
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3 Generalized Receiver: Main
Functioning Principles
The generalized receiver is constructed in accordan-
ce with the generalized approach to signal process-
ing in noise [13]-[15]. The generalized approach to
signal processing in noise introduces an additional
noise source that does not carry any information ab-
out the parameters of desired transmitted signal with
the purpose to improve the signal processing system
performance. This additional noise can be consider-
ed as the reference noise without any information
about the parameters of the signal to be detected.
The jointly sufficient statistics of the mean and
variance of the likelihood function is obtained under
the generalized approach to signal processing in noi-
se employment, while the classical and modern sig-
nal processing theories can deliver only the suffici-
ent statistics of the mean or variance of the likeliho-
od function. Thus, the generalized approach to sig-
nal processing in noise implementation allows us to
obtain more information about the parameters of the
desired transmitted signal incoming at the generaliz-
ed receiver input. Owing to this fact, the detectors
constructed based on the generalized approach to si-
gnal processing in noise technology are able to imp-
rove the signal detection performance of signal pro-
cessing systems in comparison with employment of
other conventional detectors.
The generalized receiver (GR) consists of three
channels (see Fig. 3): the GR correlation detector
channel (GR CD) – the preliminary filter (PF), the
multipliers 1 and 2, the model signal generator
(MSG); the GR energy detector channel (GR ED) –
the PF, the additional filter (AF), the multipliers 3
and 4, the summator 1; and the GR compensation
channel (GR CC) – the summators 2 and 3, the acc-
umulator 1. The threshold apparatus (THRA) device
defines the GR threshold.
As we can see from Fig.3, there are two bandpass
filters, i.e., the linear systems, at the GR input, nam-
ely, the PF and AF. We assume for simplicity that
these two filters or linear systems have the same am-
plitude-frequency characteristics or impulse respon-
ses. The AF central frequency is detuned relative to
the PF central frequency.
There is a need to note the PF bandwidth is mat-
ched with the transmitted signal bandwidth. If the
detuning value between the PF and AF central freq-
uencies is more than 4 or 5 times the transmitted si-
gnal bandwidth to be detected, i.e.,
s
f54
, where
s
f
is the transmitted signal bandwidth, we can beli-
eve that the processes at the PF and AF outputs are
uncorrelated because the coefficient of correlation
between them is negligible (not more than 0.05).
This fact was confirmed experimentally in [16] and
[17] independently. Thus, the transmitted signal plus
noise can be appeared at the GR PF output and the
noise only is appeared at the GR AF output. The sto-
chastic processes at the GR AF and GR PF outputs
present the input stochastic samples from two inde-
pendent frequency-time regions. If the discrete-time
noise
][kwi
at the GR PF and GR AF inputs is Gaus-
sian, the discrete-time noise
][k
i
at the GR PF out-
put is Gaussian too, and the reference discrete-time
noise
][k
i
at the GR AF output is Gaussian owing
to the fact that the GR PF and GR AF are the linear
systems and we believe that these linear systems do
not change the statistical parameters of the input
process. Thus, the GR AF can be considered as a ge-
nerator of the reference noise with a priori informa-
tion a “no” transmitted signal (the reference noise
sample) [14, Chapter 5]. The noise at the GR PF
and GR AF outputs can be presented as
−=
−=
−=
−=
miAFi
miPFi
mkwmgk
mkwmgk
, ][][][
; ][][][
(3)
where
][mgPF
and
][mgAF
are the impulse responses
of the GR PF and GR AF, respectively, and
−kwi[
]m
is the noise at the generalized receiver input. In
a general, under practical implementation of any de-
tector in wireless communication system with sens-
or array, the bandwidth of the spectrum to be sensed
is defined. Thus, the GR AF bandwidth and central
frequency can be assigned, too (this bandwidth can-
not be used by the transmitted signal because it is
out of its spectrum). The case when there are inter-
fering signals within the GR AF bandwidth, the ac-
tion of this interference on the GR detection perfor-
mance, and the case of non-ideal condition when the
noise at the GR PF and GR AF outputs is not the sa-
me by statistical parameters are discussed in [18]
and [19].
Under the hypothesis
1
H
(“a yes” transmitted sig-
nal), the GR CD generates the signal component
][][ ksks i
m
i
caused by interaction between the model
signal
][ksm
i
, forming at the MSG output, and the in-
coming signal
][ksi
, and the noise component
][ksm
i
][k
i
caused by interaction between the model sig-
nal
][ksm
i
and the noise
][k
i
at the PF output. GR
ED generates the transmitted signal energy
][
2ksi
and
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the random component
][][ kks ii
caused by interac-
tion between the transmitted signal
][ksi
and the noi-
se
][k
i
at the PF output. The main purpose of the
GR CC is to cancel completely in the statistical sen-
se the GR CD noise component
][][ kks i
m
i
and the
GR ED random component
][][ kks ii
based on the
same nature of the noise
][k
i
. The relation between
the transmitted signal to be detected
][ksi
and the
model signal
][ksm
i
is defined as:
, ][ ][ ksks i
m
i
=
(4)
where
is the coefficient of proportionality.
The main functioning condition under the GR
employment in any signal processing system includ-
ing the communication one with radar sensors is the
equality between the parameters of the model signal
][ksm
i
and the incoming signal
][ksi
, for example, by
amplitude. Under this condition it is possible to can-
cel completely in the statistical sense the noise com-
ponent
][][ kks i
m
i
of the GR CD and the random co-
mponent
][][ kks ii
of the GR ED. Satisfying the GR
main functioning condition given by (4),
=][ksm
i
][ksi
,
1=
, we are able to detect the transmitted si-
gnal with the high probability of detection at the low
SNR and define the transmitted signal parameters
with the required high accuracy.
Practical realization of the condition (4) at
→
1
requires increasing in the complexity of GR structu-
re and, consequently, leads us to increasing in com-
putation cost. For example, there is a need to emp-
loy the amplitude tracking system or to use the off-
line data samples processing. Under the hypothesis
0
H
(“a no” transmitted signal), satisfying the main
GR functioning condition (4) at
1→
we obtain on-
ly the background noise
][][ 22 kk ii
−
at the GR out-
put.
Under practical implementation, the real structu-
re of GR depends on specificity of signal processing
systems and their applications, for example, the rad-
ar sensor systems, adaptive wireless communication
systems, cognitive radio systems, satellite communi-
cation systems, mobile communication systems and
so on. In the present paper, the GR circuitry (Fig.3)
is demonstrated with the purpose to explain the ma-
in functioning principles. Because of this, the GR
flowchart presented in the paper should be consider-
ed under this viewpoint. Satisfying the GR main fu-
nctioning condition (4) at
1→
, the ideal case, for
the wireless communication systems with radar sen-
sor applications we are able to detect the transmitted
signal with very high probability of detection and
define accurately its parameters.
In the present paper, we discuss the GR implem-
entation in the broadband space-time spreading MC
DS-CDMA wireless communication system. Since
the presented GR test statistics is defined by the sig-
nal energy and noise power, the equality between
the parameters of the model signal
][ksm
i
and trans-
mitted signal to be detected
][ksi
, in particular by
amplitude, is required that leads us to high circuitry
complexity in practice.
For example, there is a need to employ the ampli-
tude tracking system or off-line data sample proces-
sing. Detailed discussion about the main GR functi-
oning principles if there is no a priori information
and there is an uncertainty about the parameters of
transmitted signal, i.e., the transmitted signal para-
meters are random, can be found in [13], [14, Chap-
ter 6, pp.611–621 and Chapter 7, pp. 631–695].
Fig. 3. Generalized receiver.
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The complete matching between the model signal
][ksm
i
and the incoming signal
][ksi
, for example by
amplitude, is a very hard problem in practice becau-
se the incoming signal
][ksi
depends on both the fad-
ing and the transmitted signal parameters and it is
impractical to estimate the fading gain at the low
SNR. This matching is possible in the ideal case on-
ly. The GD detection performance will be deteriora-
ted under mismatching in parameters between the
model signal
][ksm
i
and the transmitted signal
][ksi
and the impact of this problem is discussed in [20]-
[23], where a complete analysis about the violation
of the main GR functioning requirements is presen-
ted. The GR decision statistics requires an estimati-
on of the noise variance
2
using the reference noi-
se
][k
i
at the AF output.
Under the hypothesis
1
H
, the signal at the GR PF
output, see Fig. 2, can be defined as
][][][ kkskx iii
+=
, (5)
where
][k
i
is the noise at the PF output and
][][][ kskhks ii =
, (6)
where
][khi
are the channel coefficients. Under the
hypothesis
0
H
and for all i and k, the process
=][kxi
][k
i
at the PF output is subjected to the complex
Gaussian distribution law and can be considered as
the i.i.d. process.
In the ideal case, we can think that the signal at
the GR AF output is the reference noise
][k
i
with
the same statistical parameters as the noise
][k
i
. In
practice, there is a difference between the statistical
parameters of the noise
][k
i
and
][k
i
. How this di-
fference impacts on the GR detection performance is
discussed in detail in [14, Chapter 7, pp. 631 - 695]
and in [20]-[26].
The decision statistics at the GR output present-
ed in [16] and [17, Chapter 3] is extended for the ca-
se of antenna array when an adoption of multiple an-
tennas and antenna arrays is effective to mitigate the
negative attenuation and fading effects. The GR de-
cision statistics can be presented in the following
form:
−
= =
=
1
0 1
][][2)(
N
k
M
i
m
iiGR kskxT X
][][
0
1
1
0
1
0 1
2
1
2GR
N
k
N
k
M
ii
M
iiTHRkkx
−
=
−
= ==
+−
H
H
, (7)
where
)1(),...,0( −= NxxX
(8)
is the vector of the random process at the GR PF
output and
GR
THR
is the GR detection threshold.
Under the hypotheses
1
H
and
0
H
when the amplitu-
de of the transmitted signal is equal to the amplitude
of the model signal,
][][ ksks i
m
i=
,
1=
, the GR de-
cision statistics
)(X
GD
T
takes the following form in
the statistical sense, respectively:
−=
−+=
−
= =
−
= =
1
0
2
1
2
0
22
1
0 1
2
1
]}[][{)(:
]}[][][{)(:
N
ki
M
iiGD
ii
N
k
M
iiGD
kkT
kkksT
X
X
H
H
. (9)
In (9) the term
s
N
k
M
iiEks =
−
= =
1
0 1
2][
corresponds to
the average transmitted signal energy, and the term
−
= =
−
= = −1
0 1
2
1
0 1
2][][ N
k
M
ii
N
k
M
iikk
is the background
noise at the GR output. The GR output background
noise is the difference between the noise power at
the GR PF and GR AF outputs. Practical implemen-
tation of the GR decision statistics requires an esti-
mation of the noise variance
2
using the reference
noise
][k
i
at the AF output.
4 UWB System-Performance
Evaluation
The performance of UWB multiuser communication
systems based on the generalized approach to signal
processing in noise is defined by several factors, in-
cluding modulation scheme, pulse shape, number of
users, and the number of time slots per frame. In this
Section, we analyze the BER performance for both
the pulse position modulation and binary phase-shift
keying schemes that utilize the new pulse design.
4.1 Basic Assumptions
Let us first define the assumptions made in our ana-
lysis:
1. The BER is calculated for a receiver over a
single channel carrying signals from multi-
ple wireless users, each randomly transmit-
ting one bit per frame.
2. The system has perfect power control, such
that multiuser interference arrives from
each wireless unit at the base station receiv-
er with equal power.
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3. Synchronization with the desired user is ac-
hieved. To simplify calculations, timing jit-
ter and imperfect tracking are not consider-
ed.
4. Time of signal arrival for each interferer is
modeled as independent uniformly distribu-
ted (i.i.d.) random variables over one frame
period.
5. User data are binary with the equal proba-
bility.
6. User pulse collision is considered without
utilizing distinct time-hopping codes for
each symbol. In other words, each user has
only one hop per symbol,
1=
h
N
.
4.2 BER Analysis in Multiuser Environment
Given
u
N
co-channel users, the received signal from
the additive white Gaussian noise (AWGN) channel
consists of
=
+−= u
N
kkkk twtsAtr
1
)()()(
, (3)
where
k
A
is the amplitude of the signal received
from the k-th transmitter;
k
s
is the transmitted signal
from the k-th transmitter; the random variable
k
is
the time delay between the transmitter k and the re-
ceiver, and
)(tw
is the AWGN. The received signal
can be viewed as the desired user’s signal plus user
interference and noise
=
+−+−= u
N
kkkk twtsAtsAtr
2
111 )()()()(
. (4)
Without loss of generality, the system performance
is characterized by user 1’s BER. Thus, our subseq-
uent calculations are given for the receiver of user 1.
To begin, the output of the ideal generalized re-
ceiver in Fig. 4 is given by
+++
++
−−−=
cc
j
f
c
j
f
TTcjT
TcjT
cjf
m
fdttrTcjTtsjTy
1
)1(
1
)1(
)()(2)( 1
)1()1(
+++
++
+++
++
+−
ccf
cf
ccf
cf
TTcjT
TcjT
TTcjT
TcjT
j
j
j
j
dttdttr
1
)1(
1
)1(
1
)1(
1
)1(
)()( 22
, (5)
where
f
T
is the frame duration;
c
T
is the slot duration;
)1(
j
c
is the j-th bit of the desired transmitter’s time-
hopping sequence;
)(t
is the reference noise form-
ing at the GR AF output.
Fig. 4. Block diagram of multiuser generalized receiver
1 – impulse generalized receiver; 2 – generalized
receiver mask generator; 3 – time-hopping code
generator; 4 – impulse train integrator; 5 – syn-
chronization control.
For the pulse-position modulation (PPM) scheme
the correlation mask takes the form
)()()(
−−= ttts corcor
m
, (6)
while for the binary phase-shifted keying (BPSK)
scheme it is simply
)()( tts cor
m
=
. (7)
Note that
)(t
cor
is the transmitted pulse shape
)(
1tsm
,
is the PPM modulation index.
Substituting (4) into (5), we can write the genera-
lized receiver output in the following form
+++
++
−−−=
ccf
cf
TTcjT
TcjT
cjf
m
f
j
j
TcjTtsjTy
1
)1(
1
)1(
)(2 )( 1
)1()1(
+−+−
=
u
N
kkkk ttsAtsA
2
111 )()()(
dttttAtA u
N
kkkk ss
−++−+−
=
)()()()( 2
2
2
111
(8)
From (8), a more useful form of
)(
)1( f
jTy
is obtain-
ned
)()()()( )1(
2
)1()1()1( fw
N
kfkfsf jTyjTyjTyjTyu+−=
=
, (9)
where taking into consideration the main function-
ing condition (4) of the generalized receiver we ob-
tain
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)(
)1( fs jTy
dttsATcjTts
ccf
cf
TTcjT
TcjT
cjf
m
j
j
)()(2 1111
)1(
1
)1(
1
)1(
−−−−=
+++
++
;
(10)
+++
++ =
−=
ccf
cf
u
TTcjT
TcjT
N
kkkkfk
j
j
tsAjTy
1
)1(
1
)1(
2
2
)1( )()(
dttsAt u
N
kkkk
−
=
+
2
)()(2
; (11)
+++
++
−=
ccf
cf
TTcjT
TcjT
fw
j
j
dtttjTy
1
)1(
1
)1(
)]()([)( 22)1(
. (12)
Here in (9)-(12) the term
)(
)1( fs jTy
is the signal com-
ponent; the term
=
u
N
kfk jTy
2
)1( )(
is the interference
component; the term
)(
)1( fw jTy
is the background no-
ise of the generalized receiver.
If there is only one hop per symbol,
1=
h
N
then
there is no processing gain and the i-th information
bit
)1(
h
I
of the user 1 is obtained by sending
)(
)1( f
jTy
through the detector threshold. On the other hand, if
the symbol energy is spread over multiple frames, i.
e.,
1
h
N
it is necessary to sum the energy collect-
ed from the generalized receiver output over
h
N
fra-
mes, such we obtain
)(
1
)1(
)(
1
)1( )()(
fs
h
f
h
iTZ
N
jfs
iTZ
N
jfjTyjTy ==
=
)(
)(
1
)1(
)(
1
)1( )()(
f
ff
iTZ
iTZ
N
jfw
iTZ
N
jfk
noise
w
h
in
hjTyjTy ==
++
. (13)
Upon collecting the energy,
)1(
ˆi
I
is determined by
the decision rule defined in (14), where
)1(
ˆi
I
is the es-
timate of the i-th information symbol sent by the us-
er 1
)1(
i
I
=0)( 1,
0)( 0,
ˆ)1(
f
f
iiTZ
iTZ
I
. (14)
In this case, the probability of error can be defined
in the following way
)0|)()((5.0 )1( =−= ifsfnoiseerror IiTZiTZPP
)1|)()((5.0 )1( =−+ ifsfnoise IiTZiTZP
. (15)
To calculate the probability of error
error
P
there is
a need to define the probability density function of
the total noise forming at the receiver output, i.e.,
)( fnoise iTZ
that consists of the summation of
h
N
in-
dependent random variables. The probability density
function of
)( fnoise iTZ
takes the following form
nsconvolutio
)()()(
h
noisenoisenoise
N
noiseYnoiseYZ yfyfzf =
, (16)
where
noise
y
is the summation of multiuser interferen-
ce energy plus the background noise forming at the
generalized receiver output. The total noise energy
is characterized by the McDonald probability densi-
ty function or approximated Gaussian probability
density function [14, Chapter 3, pages 250-263;
Chapter 4, pages 324 -328] with the zero mean and
variance
4
4w
, where
4
w
is the variance of the Gau-
ssian noise. However, the multiuser interference
)( fin iTZ
is characterized by a distribution determi-
ned by
,,)(),(su
m
cor NNtst
c
T
.
To find the probability density function of the in-
terference component
)( fin iTZ
it is necessary to first
calculate the probability density function for every
possible number of collisions. Let p be the probabi-
lity that a pulse from the user k collides with a pulse
of the user 1 and let q be the probability that the user
k does not collide with the user 1. A collision occurs
when the time of arrival of an undesired user pulse
causes interference with the user 1’s pulse. As stated
in the assumption 4 (see Section 4.1), the probability
density function of signal arrival time of the user k
is uniform over one frame. Therefore for PPM, the
user k’s pulse occurs at the time
)( kf
jT
+
half of
the time, and at the time
)(
++ kf
jT
the other half
of the time. Since the modulation of the k-th user is
independent of the user 1, user k’s PPM can be en-
veloped into the random variable
k
without chan-
ging its distribution:
=
−
otherwise
TT
ffkf
k
k , 0
0 ,
)(
1
. (17)
Similarly, for BPSK modulation, the user k’s pulse
arrives at
)( kf
jT
+
and the modulation of user k
can be ignored, since we define a collision as an un-
desired pulse interference, either constructive or de-
structive, with the user 1’s pulse.
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By modelling the multiuser interference this way,
a collision occurs if
ckm TT +− 11
, where
m
T
is
the pulse duration and
c
T
is the slot duration. Note
that p can now be found by integrating the probabili-
ty density function
)( k
k
f
over the collision interval
as
sc
mc
f
mc
T
T
kf NT
TT
T
TT
dTp c
m
1
1
1
1
+
=
+
==
+
−
−
; (18)
sc
mc NT
TT
pq 1
11
+
−=−=
, (19)
where
s
N
is the number of slots per frame. Therefo-
re, the probability of having exactly m collisions
with the user 1 is defined in the following form
mN
m
uu
qp
m
N
mp −−
−
=1
1
)(
. (20)
Note that
−
=−−
−
=
)|(
1
)( 1
1
0
myfqp
m
N
yf noise
mN
m
N
m
u
noiseY u
u
noise
)( kN yf
(21)
is the summation of the multiplication of the proba-
bility of exactly m collisions with the conditional
probability density function
)|( myf noise
for all valu-
es m convolved with
)( kN yf
, where the probability
density function
)|( myf noise
is the convolution of
the probability density function
)1|( kY yf k
with itself
m times and
)( kN yf
is the Gaussian probability den-
sity function and
nsconvolutio
)1|()1|()|(
m
kYkYnoise yfyfmyf kk =
. (22)
To find
)1|( kY yf k
, the following random-variable
transformation of
to
k
y
is used:
+=
c
T
cor
m
kdtttsy
0
)()()(
. (23)
The above equation assumes that exactly one collisi-
on occurs and that
is the solution to this equation.
Since
is the uniformly distributed random variable,
we can obtain the following conditional probability:
)(
)(
)1|(
1
−
=f
d
dy
yf k
kYk
, (24)
where
−
+
=
otherwise
TT
TT
fcm
mc
, 0
,
1
)(
. (25)
If the closed form for the pulse
)(t
cor
is not avai-
lable, then the transformation of (23) is not possible
analytically. However, since
is the uniformly dist-
ributed random variable, the probability density fun-
ction
)1|( kY yf k
can be estimated by generating, acc-
ording to (23), a histogram of
)(
k
y
from random sa-
mples of
. Once the probability density function
)1|( kY yf k
is determined,
)|( myf noise
can be calcula-
ted using (22) before finding
)( noiseY yf noise
. Finally,
the probability density function of
)( fnoise jTZ
that
allows BER analysis, can be calculated using (16).
Since the generalized receiver masks for BPSK
and PPM differ, not only in shape, but also in dura-
tion, the probability of collision for BPSK is greater
than that of PPM. In the ideal case, when there is no
channel dispersion, the probability of collision for
PPM is
)2(3 s
N
and for BPSK is
s
N2
. However,
this can be misleading, since the frame time of PPM
is twice as large as that of BPSK. If
f
T
is fixed at the
same value for both PPM and BPSK, then twice as
many time slots are available for BPSK and the pro-
bability of collision is halved, thus becoming
s
N1
.
If the received pulse is time dispersed, then the pro-
bability of collision increases from that of the ideal
case. It can still be calculated using (17) by modify-
ing
m
T
to match the width of the extended pulse whi-
le leaving
c
T
unchanged. It is important to realize
that the probability of collision increases linearly
with the pulse width.
4.3 Analytical BER Results
The BER is calculated holding
m
T
constant so that the
transmission slot period
c
T
is fixed according to that
modulation scheme is used. Since
csf TNT =
,the fra-
me period is varied only by
s
N
. After selecting the
pulse shape and modulation scheme, the input para-
meters of the BER calculation are limited to
u
N
and
s
N
. The BER is calculated for
s
N
values of 100 and
500 to demonstrate how
s
N
must be carefully selec-
ted, such that system performance is adequate for
the expected number of users. Similarly,
u
N
is varied
from 1 to 40, showing performance variations for di-
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Volume 4, 2022
fferent traffic loads. In our calculations, the pulse
was spread over the single frame,
1=
h
N
. Thus, the
probability density function
)( noiseY yf noise
is used to
determine the probability of error
error
P
.
Our analytical results method followed the form
of our derivation utilizing
)(
1tsm
as the transmitted
pulse shape. Since we do not know a closed form of
)(
1tsm
, we estimated the probability density function
)1|( kY yf k
using a histogram of 500 bins on
)(
k
y
as
defined in (23), where the pulse shape
)(
1tsm
consist-
ed of 50 000 samples and had the fixed duration
m
T
of 1 nsec. For BPSK simulations,
)()( 1tsts mm =
,
whereas for PPM modulation,
−−= tststs mmm ()()( 11
)
, where the modulation index
m
T=
was used.
For a variety of different scenarios, the BER results
are given in Figs. 5-8.
The analytical results are intuitively reasonable.
As
u
N
increases, the BER degrades, since the proba-
bility of collision increases. As
u
N
increases from a
small number of users, the probability of collision
increases quickly. However, as
u
N
becomes large,
the rate of increase slows down. This characteristic
can be seen in the BER curves, as the distance bet-
ween the curves becomes smaller as the number of
users increases. In other words, increasing the num-
ber of users in the system has a greater impact on
the system with a smaller
u
N
.
Another observation is on the relationship betwe-
en the signal-to-noise ratio (SNR) and multiuser int-
erference. When the SNR is low, the BER curves are
packed closely together, indicating that the multius-
er interference has a little effect. As the SNR increa-
ses, the impact of the generalized receiver backgro-
und noise on system performance decreases and the
multiuser interference becomes more dominant on
system performance. As a result of the multiuser in-
terference, the BER reaches a floor determined by
the number of users and the number of slots per fra-
me in the system. Since the multiuser interference li-
mits the BER performance of UWB communication
systems,
s
N
should be carefully selected to provide
an acceptable BER performance for the maximum
number of users in the system.
It is clear from the results that the increasing slot
number
s
N
can also reduce the probability of collisi-
on, which in turn increases the range of SNR values
unaffected by the multiuser interference. This allows
the multiuser BER performance to remain close to
the single-user BER performance for higher SNR va-
lues. The number of users
u
N
has only a small effect
on which the SNR value the BER performance diver-
ges from in the single-user case. Since UWB comm-
unication systems must transmit the low-power sig-
nals to comply with the standard regulations, these
communication systems should be designed under
the low SNR. Therefore, selecting a large
s
N
determ-
ines the system performance with little effect from
u
N
.
5 Simulation Conditions and Results
5.1 Simulation Comparisons
To verify the validity of Figs. 5-8, we performed a
simulation in which we generated a random messa-
ge. We used this random message to modulate our
pulse shape
)(
1tsm
, and randomly generated
u
N
inter-
fering pulses of equal amplitude randomly starting
over the frame duration. We then added the desired
signal, the overlapping parts of the
1−
u
N
interfering
signals, and the AWGN of the proper variance for
the desired SNR together and sent the received sig-
nal through the generalized receiver. This process
was repeated for all combinations of modulation ty-
pe, number of users, number of slots per frame, and
SNR values. Figures 9 and 10 demonstrate the mea-
sured performance versus the analytical performan-
ce using the derivation above. The measured and
analytical performances are very similar, with dif-
ferences resulting from the use of a histogram in-
stead of the actual closed-form solution.
5.2 Multipath Simulation
We also present a simulation result for the UWB
communication system under multipath distortions.
In this specific example, we make the following
assumptions.
• Because of the large frame duration, we assu-
me that the multipath interference received co-
me from the desired user’s current bit. Interfe-
rence from the previous user bits will dissipate
well before the next frame starts.
• Our multipath channel is of the form
=
−+= L
iii tttth
1
)()()(
, (26)
where
i
is the random variable that is norm-
ally distributed with the zero mean and vari-
ance equal to 0.3;
i
t
is the random variable
uniformly distributed over the interval
],0[ kT
The value
kT
is proportional to the time-slot
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duration.
• Included in the multipath simulation is also a
multiuser simulation with
20=
u
N
,
10=
s
N
.
The BPSK modulation was employed.
Fig. 5. BER for the UWB communications system using
BPSK with
100=
s
N
: 1-
1=
u
N
; 2 -
10=
u
N
; 3 -
20=
u
N
; 4 -
30=
u
N
; 5 -
40=
u
N
.
Fig. 6. BER for the UWB communications system using
BPSK with
500=
s
N
: 1-
1=
u
N
; 2 -
10=
u
N
; 3 -
20=
u
N
; 4 -
30=
u
N
; 5 -
40=
u
N
.
It should be noted that our simulation cases are
not general enough for a highly rich scattering envi-
ronment, since the number of multipaths is low. For
each multipath ray, the probability of multipath inte-
rference is approximately
)(1 kT
. Thus, if
kT
is not
Fig. 7. BER for the UWB communications system using
PPM with
100=
s
N
: 1-
1=
u
N
; 2 -
10=
u
N
; 3 -
20=
u
N
; 4 -
30=
u
N
; 5 -
40=
u
N
.
Fig. 8. BER for the UWB communications system using
PPM with
500=
s
N
: 1-
1=
u
N
; 2 -
10=
u
N
; 3 -
20=
u
N
; 4 -
30=
u
N
; 5 -
40=
u
N
.
small or the number of rays is low, there is a very
small effect from the multipath interference. Basica-
lly, simulation for multipath is very similar to the
multiuser simulation. The difference is that we are
confining the arrival of the “users” (rays) to a small-
ler interval around our desired pulse, thereby increa-
sing our probability of collision. For the 3-ray mod-
el, there is no significant multipath interference at
kT
5
nsec, and even at
5=kT
nsec, since the mul-
tipath interference did not cause that large of a shift
in the BER curves. Increasing the number of rays in
Fig. 11 to five and keeping
5=kT
nsec, results in a
noticeable increase in the BER performance. Also,
as a random case, we chose 20 rays with
40=kT
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nsec, and some multipath degradation was noticed
in terms of the BER performance floor in Fig. 11.
Fig. 9. Comparison of the predicted and measured BPSK
performance: 1-
1=
u
N
; 2 -
1000,10 == su NN
;
3 -
100,40 == su NN
.
Fig. 10. Comparison of the predicted and measured PPM
performance: 1-
1=
u
N
; 2 -
1000,10 == su NN
;
3 -
100,40 == su NN
.
6 Conclusions
In this paper, we study the system performance of
new UWB pulse-shape design algorithm applicable
to the UWB communication systems constructed ba-
sed on the generalized approach to signal processing
Fig. 11. Effect of multipath for the BPSK system with
20=
u
N
and
100=
s
N
: 1-
1=
u
N
; 2 – no mul-
tipath; 3 – 20 ray
40=kT
nsec; 4 – 5 ray
=kT
5
nsec.
in noise. The theoretical performance of the UWB
communication systems constructed based on the
generalized approach to signal processing in noise in
relation to the selection of the modulation scheme,
the number of users, and the number of time slots
available per frame is presented. Simulation results
are provided as verifications of the analytical appro-
ach. In addition, the robustness of the UWB comm-
unication systems constructed based on the genera-
lized approach to signal processing in noise against
a limited number of multipaths is also demonstrated.
References
[1] J. Forester, E. Green, S. Somayazulu, and D.
Leeper, Ultra-wideband technology for short-or
medium-range wireless communications//Intel
Technology Journal. Q2. 2001, Vol. 5, No. 2.
pp. 1-11.
[2] M.Z. Win and R.A. Scholtz, Impulse radio:
How it works//IEEE Communications Letters.
1998, Vol. 2, No. 2, pp. 36-38.
[3] T. Mitchell, Broad is the way//IEE Review.
2001, Vol. 47, No. 1. pp. 35-39.
[4] B. Parr, B. Cho, K. Wallace, and Z. Ding, A
novel ultra-wideband pulse design algorithm//
IEEE Communications Letter. 2003, Vol. 7,
No. 5, pp. 219-221.
[5] P. Bora, K. Bhattcharyya, Ultra-wide band
(UWB) pulse design and channel modeling//
Journal of Telecommunications. 2018, Vol. 4,
No. 2, pp. 1-9
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2022.4.1
Vyacheslav Tuzlukov
E-ISSN: 2766-9823
11
Volume 4, 2022
[6] J. Yan and C. Nguyen, A new ultra-wideband,
ultra-short monocycle pulse generator with re-
duced ringing//IEEE Microwave Wireless Co-
mponent Letters. 2002, Vol. 12, No. 6, pp. 206-
208.
[7] M.H. Hayes, Statistical Digital Signal Proces-
sing and Modeling. New York: Wiley, 1996.
[8] B. Li, Z. Zhou, W. Zou, D, Li, C. Zhao, Optim-
al waveforms design for ultra-wideband impul-
se radio sensors//Sensors. 2010, Vol.10, No.12,
pp. 11038-11063.
[9] A. Valizade, P. Rezaei, A.A. Orouji, A design
of UWB reconfigurable pulse transmitter with
pulse shape modulation//Microwave and Opti-
cal Technology Letters. 2016, Vol. 58, No. 9,
pp. 2221-2227.
[10] D. Slepian and H.O. Pollak, Prolate spheriodal
wave functions, Fourier analysis, and uncertai-
nty-I//Bell System Technology Journal. 1961,
Vol. 40, No. 1, pp.43-46.
[11] D. Slepian, Prolate spheriodal wave functions,
Fourier analysis, and uncertainty-V: The disc-
rete case//Bell System Technology Journal.
1978, Vol. 57, No. 5, pp. 1371-1430.
[12] X. Luo, L. Yang, and G.B. Giannakis, Design-
ing optimal pulse-shapers for ultra-wideband
radios//Journal Communication Networks.
2003, Vol. 5, No. 4, pp. 344-353.
[13] V. Tuzlukov, A new approach to signal detecti-
on theory//Digital Signal Processing: Review
Journal. 1998, Vol.8, No. 3, pp.166–184.
[14] V. Tuzlukov, Signal Detection Theory. Spring-
er-Verlag, New York, USA, 2001, 746 pp.
[15] V. Tuzlukov, Signal Processing Noise. CRC
Press, Boca Raton, London, New York, Washi-
ngton, D.C., USA, 2002, 692 pp.
[16] M. Maximov, Joint correlation of fluctuative
noise at outputs of frequency filters//Radio En-
gineering. 1956, No. 9, pp. 28–38.
[17] Y. Chernyak, Joint correlation of noise voltage
at outputs of amplifiers with no overlapping re-
sponses//Radio Physics and Electronics. 1960,
No. 4, pp. 551–561.
[18] Shbat, M., Tuzlukov, V.P. Definition of adapti-
ve detection threshold under employment of
the generalized detector in radar sensor syst-
ems//IET Signal Processing. 2014, Vol. 8, Iss-
ue 6, pp. 622–632.
[19] Tuzlukov, V.P. DS-CDMA downlink systems
with fading channel employing the generaliz-
ed//Digital Signal Processing. 2011. Vol. 21,
No. 6, pp. 725–733.
[20] Communication Systems: New Research, Edit-
or: Vyacheslav Tuzlukov, NOVA Science Pub-
lishers, Inc., New York, USA, 2013, 423 pp.
[21] Shbat, M., Tuzlukov, V.P. Primary signal dete-
ction algorithms for spectrum sensing at low
SNR over fading channels in cognitive radio//
Digital Signal Processing (2019). https://doi.
org/10.1016/j.dsp. 2019.07.16. Digital Signal
Processing. 2019, Vol. 93, No. 5, pp. 187- 207.
[22] V. Tuzlukov, Signal processing by generalized
receiver in wireless communications systems
over fading channels,” Chapter 2 in Advances
in Signal Processing. IFSA Publishing Corp.
Barcelona, Spain. 2021. pp. 55-111.
[23] V. Tuzlukov, Interference Cancellation for
MIMO Systems Employing the Generalized
Receiver with High Spectral Efficiency//
WSEAS Transactions on Signal Processing.
2021, Vol. 17, Article #1, pp. 1-15.
[24] M. Shbat and V. Tuzlukov, SNR wall effect al-
leviation by generalized detector employment
in cognitive radio networks//Sensors, 2015, 15
(7), pp.16105-16135;doi:10.3390/s150716105.
[25] V. Tuzlukov, Signal processing by generalized
detector in DS-CDMA wireless communication
systems with frequency-selective channels//Ci-
rcuits, Systems, and Signal Processing. Publi-
shed on-line on February 2, 2011, doi:10.1007/
s00034-011-9273-1; 2011, Vol.30, No.6, pp.
1197–1230.
[26] M. Shbat, V. Tuzlukov, Generalized detector
as a spectrum sensor in cognitive radio net-
works//Radioengineering.2015, Vol. 24, No. 2,
pp. 558–571.
Dr. Vyacheslav Tuzlukov
received the MSc and PhD degrees in radio physics from
the Belarusian State University, Minsk, Belarus in 1976
and 1990, respectively, and DSc degree in radio physics
from the Kotelnikov Institute of Radioengineering and
Electronics of Russian Academy of Sciences in 1995.
Starting from 1995 and till 1998 Dr. Tuzlukov was a Vi-
siting Professor at the University of San-Diego, San-Die-
go, California, USA. In 1998 Dr. Tuzlukov relocated to
Adelaide, South Australia, where he served as a Visiting
Professor at the University of Adelaide till 2000. From
2000 to 2002 he was a Visiting Professor at the Universi-
ty of Aizu, Aizu-Wakamatsu City, Fukushima, Japan and
from 2003 to 2007 served as an Invited Professor at the
Ajou University, Suwon, South Korea, within the Depart-
ment of Electrical and Computer Engineering. Starting
from March 2008 to February 2009 he joined as a Full
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Volume 4, 2022
Professor at the Yeungnam University, Gyeonsang, South
Korea within the School of Electronic Engineering, Com-
munication Engineering, and Computer Science. Starting
from March 1, 2009 Dr. Tuzlukov served as Full Profes-
sor and Director of Signal Processing Lab at the Depart-
ment of Communication and Information Technologies,
School of Electronics Engineering, College of IT Engine-
ering, Kyungpook National University, Daegu, South Ko-
rea. Currently, Dr. Tuzlukov is the Head of Department
of Technical Exploitation of Aviation and Radio Engine-
ering Equipment, Belarusian State Academy of Aviation,
Minsk, Belarus. His research emphasis is on signal pro-
cessing in radar, wireless communications, wireless sen-
sor networks, remote sensing, sonar, satellite communi-
cations, mobile communications, and other signal proce-
ssing systems. He is the author over 280 journal and con-
ference papers, seventeenth books in signal processing
published by Springer-Verlag and CRC Press. Some of
them are Signal Detection Theory (2001), Signal Proces-
sing Noise (2002), Signal and Image Processing in Navi-
gational Systems (2005), Signal Processing in Radar Sys-
tems (2012), Editor of the book Communication Systems:
New Research (2013), Nova Science Publishers, Inc,
USA, and has also contributed Chapters “Underwater
Acoustical Signal Processing” and “Satellite Communi-
cations Systems: Applications” to Electrical Engineering
Handbook: 3rd Edition, 2005, CRC Press; “Generalized
Approach to Signal Processing in Wireless Communicati-
ons: The Main Aspects and Some Examples” to Wireless
Communications and Networks: Recent Advances,
InTech, 2012; “Radar Sensor Detectors for Vehicle Safe-
ty Systems” to Electrical and Hybrid Vehicles: Advanced
Systems, Automotive Technologies, and Environmental
and Social Implications, Nova Science Publishers, Inc.,
USA, 2014; “Wireless Communications: Generalized Ap-
proach to Signal Processing” and “Radio Resource Mana-
gement and Femtocell Employment in LTE Networks”,
to Communication Systems: New Research, Nova Science
Publishers, Inc., USA, 2013; “Radar Sensor Detectors for
Vehicle Safety Systems” to Autonomous Vehicles: Intelli-
gent Transport Systems and Automotive Technologies,
Publishing House, University of Pitesti, Romania, 2013;
“Radar Sensor Detectors for Vehicle Safety Systems,” to
Autonomous Vehicles: Intelligent Transport Systems and
Smart Technologies, Nova Science Publishers, Inc., New
York, USA, 2014; “Signal Processing by Generalized Re-
ceiver in DS-CDMA Wireless Communication Systems,”
to Contemporary Issues in Wireless Communications.
INTECH, CROATIA, 2014; “Detection of Spatially Dist-
ributed Signals by Generalized Receiver Using Radar Se-
nsor Array in Wireless Communications,” to Advances in
Communications and Media Research. NOVA Science
Publishers, Inc., New York, USA, 2015; “Signal Process-
ing by Generalized Receiver in Wireless Communication
Systems over Fading Channels” to Advances in Signal
Processing. IFSA Publishing Corp. Barcelona, Spain.
2021; “Generalized Receiver: Signal Processing in DS-
CDMA Wireless Communication Systems over Fading
Channels” to Book Title: Human Assisted Intelligent Co-
mputing: Modelling, Simulations and Its Applications.
IOP Publishing, Bristol, United Kingdom, 2022. He par-
ticipates as the General Chair, Keynote Speaker, Plenary
Lecturer, Chair of Sessions, Tutorial Instructor and orga-
nizes Special Sections at the major International Confere-
nces and Symposia on signal processing.
Dr. Tuzlukov was highly recommended by U.S. experts
of Defence Research and Engineering (DDR& E) of the
United States Department of Defence as a recognized ex-
pert in the field of humanitarian demining and minefield
sensing technologies and had been awarded by Special
Prize of the United States Department of Defence in 1999
Dr. Tuzlukov is distinguished as one of the leading achie-
vers from around the world by Marquis Who’s Who and
his name and biography have been included in the Who’s
Who in the World, 2006-2013; Who’s Who in World,
25th Silver Anniversary Edition, 2008, Marquis Publisher,
NJ, USA; Who’s Who in Science and Engineering,
2006-2012 and Who’s Who in Science and Engineering,
10th Anniversary Edition, 2008-2009, Marquis Publisher,
NJ, USA; 2009-2010 Princeton Premier Business Leaders
and Professionals Honours Edition, Princeton Premier
Publisher, NY, USA; 2009 Strathmore’s Who’s Who
Edition, Strathmore’s Who’s Who Publisher, NY, USA;
2009 Presidental Who’s Who Edition, Presidental Who’s
Who Publisher, NY, USA; Who’s Who among Executi-
ves and Professionals, 2010 Edition, Marquis Publisher,
NJ, USA; Who’s Who in Asia 2012, 2nd Edition, Marqu-
is Publisher, NJ, USA; Top 100 Executives of 2013 Mag-
azine, Super Network Publisher, New York, USA, 2013;
2013/2014 Edition of the Global Professional Network,
Business Network Publisher, New York, USA, 2013;
2013/2014 Edition of the Who’s Who Network Online,
Business Network Publisher, New York, USA, 2014; On-
line Professional Gateway, 2014 Edition, Business Netw-
ork Publisher, New York, USA, 2014; 2014 Worldwide
Who's Who", Marquis Publisher, NJ, USA; 2015 Strath-
more Professional Biographies, Strathmore’s Who’s Who
Publisher, NY, USA; Who’s Who in World, 2015, Marq-
uis Publisher, NJ, USA; 2015-2016 Membership in Excl-
usive Top 100 network of professionals in the world, NY,
USA, 2015; 2015 Who’s Who of Executives and Profes-
sionals Honours Edition, Marquis Publisher, NJ, USA;
Worldwide Who’s Who – Top 100 Business Networking,
San Diego, CA, USA, 2015.
Phone: +37517345328
Email: slava.tuzlukov@mail.ru
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS,
COMPUTATIONAL SCIENCE AND SYSTEMS ENGINEERING
DOI: 10.37394/232026.2022.4.1
Vyacheslav Tuzlukov
E-ISSN: 2766-9823
13
Volume 4, 2022
