=Paper=
{{Paper
|id=Vol-2005/paper-05
|storemode=property
|title=Interference Immunity of Signal Processing in the Presence of Interferences in Information System by Means of Optimal Loading Matching
|pdfUrl=https://ceur-ws.org/Vol-2005/paper-05.pdf
|volume=Vol-2005
|authors=Maxim V. Grachev,Yury N. Parshin
}}
==Interference Immunity of Signal Processing in the Presence of Interferences in Information System by Means of Optimal Loading Matching==
https://ceur-ws.org/Vol-2005/paper-05.pdf
Interference Immunity of Signal Processing
in the Presence of Interferences in Information
System by Means of Optimal Loading Matching
Maxim V. Grachev and Yury N. Parshin1
1
Ryazan State Radio Engineering University, Ryazan, Russia
parshin.y.n@rsreu.ru
Abstract. An information system with multi-channel receiving system
and mutual influence of channels is considered. Signal and interference
are spatially concentrated sources of radio emission. The mutual influence
of channels is researched by calculating the matrix of mutual impedances
for thin vibrators. The magnitude of the load impedances in individual
channels influences the resulting signal-to-interference ratio. Also, the
value of the load impedances depends on correlation properties of the sig-
nal and interference at the input of the spatial channels. It complicates
the problem of optimal matching. The problem of finding the optimal
load impedances as a function of the signal-interference ratio is solved.
The solution of the optimization problem is carried out by a numeri-
cal analysis using the MatLab or, in a particular case, by the analytical
method. The optimal load impedances are compared depending on the
degree of mutual influence of the channels of the information system, spa-
tial structure, and interference parameters. Comparing the optimum load
impedances, spatial structure and parameters of interferences is carried
out depending on a degree of mutual influence of the information system
channels. The output signal-interference ratio behavior at different val-
ues of the load impedances is researched. The gain of optimal matching
versus the load impedances is calculated in the absence of mutual influ-
ence and in the case of applying non-optimal mutual impedances when
there is the mutual influence.
Keywords: Interference mutual influence, mutual impedances, informa-
tion system, signal processing
1 Introduction
Evolution of the integral semiconductor technology, microwave solid state high
efficiency amplifiers, and super high frequency digital circuitry stimulate design
of radio systems with signal processing in spatial channels of antenna array (AA)
[1 – 3]. Often, characteristics of the AA are obtained without mutual influence
of the elements. It is obtained with multiplying the beam pattern of one element
by the factor AA. If there is a significant mutual influence of the elements, the
characteristics of a real antenna can differ from the calculated characteristics.
42
In paper [4], the effect of mutual coupling on the performance of adaptive an-
tennas has been a topic of considerable interest. The mutual influence can lead
to deterioration and improvement of antenna array characteristics. For adaptive
antennas based on minimizing the mean squared error between the array output
and a locally generated reference signal, the mutual coupling between antenna
elements hardly affects the nulling performance of adaptive antennas. In fact, in
a given size aperture, as the number of antenna elements is increased one obtains
better nulling performance irrespective of the increased mutual coupling between
antenna elements. Paper [5] deals with the near-field DOA-Matrix method for
source localization using a uniform linear array antenna. The mutual coupling
between array elements degrades the DOA estimation accuracy. Influence of the
mutual coupling in source localization using the near-field DOA-Matrix method
and the improved method is investigated. Paper [6] deals with direction-of-arrival
estimation for very closely spaced dipoles. The mutual coupling can produce am-
plitude and phase difference of embedded element patterns, which can be utilized
to greatly improving the direction-of-arrival estimation performance by incorpo-
rating the pattern diversity into the estimation algorithm. In paper [7], there
is analysis of the noise immunity of signal processing in the antenna array with
influence of the elements in the form of thin vibrators in presence of the spatially
concentrated and spatially extended jammers. It is established that mutual in-
fluence can lead to both increase and a decrease in noise immunity. In paper [8],
analysis of nonlinear properties of receiver channels for coherent and noncoherent
composition of intermodulation interferences at output of each RF stage is per-
formed. Spatial correlation matrices of the sum of active and intermodulation
interferences for active antenna array are evaluated with and without mutual
influence of the antenna elements. The results of recent studies prove the impor-
tance of mutual influence the basic characteristics of radio systems. The mutual
influence of the antenna elements affects not only the directivity characteristics
of the antenna array and the signal-to-noise ratio at its output, but, also, the
output impedances of each of the AA elements [9, 10]. The value of the output
impedances in the presence of mutual influence of the elements of the AA also
depends on the amplitude-phase relations of the signals and the noise. The choice
of load impedances is a difficult computational task. The object of this work is
to investigate the influence of the mutual impedances of the antenna array to
the noise immunity of signal processing in the presence of spatially concentrated
noise. Matching the impedance load of the antenna elements is important for
different signals, interference parameters, and the spatial structure of the AA.
2 Statement of problem
The antenna array includes N omnidirectional elements arranged in a certain
way in space. In space, there are signal source of variance DS and M interfer-
ence of variance Dm , m = 1, . . . , M . The spatial position of signal sources and
interference is defined by the vectors V S and V m , m = 1, . . . , M respectively.
The spatial correlation matrices of the signal and interference in the elements of
43
M
the antenna array are equal to RS = DS V S V H Dm V m V H
P
S , RJ = m , where
m=1
the sign H means Hermitian transpose.
The mutual influence of the antenna array elements affects to the charac-
teristics of the signal and interference at output. The value of mutual influence
is characterized by a matrix of mutual impedances Z [9,10]. The electric field
strength in the vicinity of AA is related to the voltage at the load impedances of
the AA elements by the relation U = Z L (Z + Z L )−1 J [7], where Z L is the di-
agonal matrix with a vector of load impedances V L on the main diagonal. As a
result, the correlation interference matrices and the form of the output sugnal at
the AA elements are: RU = Z 1 RJ Z H 1 , S 1 = Z 1 S , where Z 1 = Z L (Z + Z L )
−1
means the coefficient of signal transmission from the inputs of the AA elements
to their outputs.
In addititon to external interference, there are internal noise in the system
caused by losses from the diagram-making circuit and frontend of receivers of the
active antenna. The total noise power associated to AA elements load is equal
to ( ) !
2
R11 ZL
Pn = kT ∆f Re + NF − 1 ,
ZL ZL + Z11
where k = 1, 38 × 10−23 J/K is the Boltzmann constant, T is the temperature
(degrees Kelvin), ∆f is the bandwidth, R11 is the active component of the
antenna element impedance equal to the emitting resistance, Z L is the load
impedance, N F is the frontend noise nfactor.o Power of the signal in the load
|U |2
of the antenna element is: PS = Re ZL . As a result, the signal-to-noise
ratio q = PS /Pn depends on the load impedance. Next, it should be taken into
account the load impedance optimization. In the antenna array, we assume that
the noises in the impedance load are not correlated to each other and have a
diagonal correlation matrix RT with signal power vector:
P T = {Pn , n = 1, . . . , N }
on the main diagonal.
The correlation matrix of the interference, which emitted in the load impe-
H
p
is√equal to RIL = U L U L , where U L = U × Re {1/V L } =
dance
= Un Gn , n = 1, . . . , N is the normalized value of interference at the load
impedance, Gn , n = 1, . . . , N , is the active conductivity of the load. As a result,
the correlation matrix of noise and noise at the output of AA elements with
taking into account their mutual influence is equal to
p p T
H
R1 = Z 1 RJ Z 1 × Re {1/V L } Re {1/V L } + RT .
p
The signal at the load impedance is equal to S L = (Z 1 S ) × Re {1/V L }. The
signal-to-interference ratio is obtained as a result of optimal processing the sig-
−1
nal from the output of the elements AA. It is equal to [11] q = S H L R1 S L .
44
3 Interference immunity evaluation
There is calculating of the signal-to-noise ratio depending of the receiving system
spatial structure with different modes of the load matching. Suppose that the
elements of AA are equidistant and that the AA is spatially linear. The calcula-
tion is carried out for antenna elements in the form of thin vibrators, which are
located vertically. The value of the mutual impedance between two any vibrators
is equal to [9,11]
n h p i
Z1 = 30 2Ei(jk0 d) − 2Ei −jk0 ( d2 + L2 + L)
h p io
−2Ei −jk0 ( d2 + L2 − L) ,
where Ei(±jx) = Ci(x) ± jSi(x) is the integral exponential function. It is cal-
culated on the basis of the functions of the integral cosine and integral sine
with k = 2π λ as the wave number, d the distance between the vibrators, L the
length of vibrator. With a large spatial separation of the vibrators AA, the
mutual influence becomes insignificant and the matrix of mutual impedances is
Z = I × (73.1 + j42.5)Ω.
Optimization of the load impedance is a difficult calculational problem. Com-
monly, it solved by numerical methods. The optimal load impedances also depend
on the angular position of the signal and the interference sources.
Consider an example of an analytical solution of the problem of optimal
matching for an antenna array with two elements (N = 2). The field of each
antenna element is inphase. This ensures the symmetry of the problem. With
a large distance between the elements, the mutual coupling is negligible. The
output resistance of a thin vibrator is equal to (73.1 + j42.5)Ω. Optimal value
of each of the antenna elements loads impedance ZL = (73.1 + j42.5)Ω. An
equivalent circuit that shows the effect of the mutual impedance of the AA
elements is given in Fig. 1.
Fig. 1. Equivalent circuit of a 2-element inphase antenna array
45
In the example, the currents in the circuit of each antenna element are the
E
same and equal I = Zl +2Z12
. The power in the load of one of the elements is P1 =
E 2 RL
|Zl +2Z12 |2 . The maximum value of the power is achieved with compensation of
the reactive impedance in the denominator ImZL = −2ImZ12 − ImZ11 . Solution
of the optimization problem max(RL ) P1 (RL ) gives the values of the optimum
load resistance RLopt = ReZ11 + 2ReZ12 .
In the more general case of several antennas, optimization of the load impe-
dances is performed by numerical method (using the fminsearch function in the
MatLab). It should be noted that in order to obtain achievable values of the
load impedances, it is necessary to introduce constraints. The real part of the
impedances be nonnegative. To finding an optimum close to the global optimum,
the value obtained at the previous step of calculating the dependence is chosen
as the initial value of the impedances.
Optimization of the load impedance was carried out for various values of load
impedances
– without the mutual influence of antenna elements; for all elements impedance
is equal to ZL0 = 73.1 − j42.5Ω; the solid line graphic in Fig. 2;
– with the mutual influence of the antenna elements in the form of thin vibrators;
for all elements the impedances is equal to ZL0 = 73.1 − j42.5Ω; the dashed line
graphic in Fig. 2;
– with the mutual influence of the antenna elements in the form of thin vibra-
tors, the impedances were obtained as a result of optimization by the numerical
method in the MatLab; the dotted line graphic in Fig. 2.
a) N F = 0.4 dB b) N F = 10 dB
Fig. 2. Signal-to-interference ratio
Figure 2 shows the dependence of the signal-to-interference ratio on the in-
terelement distance AA. The number of elements N = 4, number of interference
M = 3, signal-to-noise ratio is equal to qs = DkT
S /73.1
∆f = 1, interference-to-noise
ratio qI = DkT
I /73.1
∆f = 100 for each of interference, frontend noise factor N F = 0.4
46
dB. Angular interference positions were −350 , 200 , 700 , direction of the arrival
of the signal is perpendicular to the plane of the AA elements placement.
Benefits 5 . . . 8 dB of the gain in relation to the signal interference were ob-
tained as a result of optimization of load impedances. The benefits from the
load impedances optimization are especially noticeable for small distances be-
tween AA elements d/λ = 0.1, . . . , 0.3. With an increase of the frondend noise
factor, the gain from optimizing the spatial structure decreases and it is sig-
nificant (Fig.2.) With a decrease in the frontend noise figure, the fminsearch
optimization procedure is unstable (there is not well-defined optimum). For the
technical implementation of the optimal matching principle, it is necessary to
know the dependence of the load impedances on the operating conditions of the
AA. Figure 3 shsows the dependence of the norm of the difference on the load
impedance vector and the value ZL0 the distance between the AA (N F = 0.4
dB). Increasing the noise figure N F > 10 dB enhances optimization process
stability. The value of load impedance approaches to ZL0 .
Fig. 3. The norm of the load impedance difference (N F = 0.4 dB)
4 Conclusions
The multi channel information system with active antenna array is investigated.
As a result of the research, it was established that the matching impedance of the
load has a great influence onto increasing the noise immunity of signal processing
in the antenna array with mutual influence of the elements. The calculations for
the antenna array in the form of thin vibrators (with small distances between)
show a gain from the optimization of the load impedance of 5 . . . 8 dB. This
47
should be taken into account when performing optimization of the spatial struc-
ture of the multi channel information system involving of heavily filled antenna
arrays.
5 Acknowledgment
The research was supporeted by the Ministry of education and science of the
Russian federation project no. 8.2810.2017 in the Ryazan State Radio Engineer-
ing University.
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