The Influence Of Propagation Environment On The Accuracy Of Emission Source Bearing

Abstract

This paper focuses on the radio direction finding (DF) in multipath environments. Based on the measurement results presented in the open literature, the authors analyse the influence of environment transmission properties on the spread of the signal reception angle. Parameters that define these properties are rms delay and angle spreads. For these parameters, the mutual relationship is determined. This relationship is the basis for the assessment of the required number of bearings that minimize the influence of the environment on the accuracy of DF procedure. In the presented analysis, the statistical properties of signal reception angle are approximated by the normal distribution. The number of bearings versus the rms delay spread is presented as the main objective of this paper. In addition, the methodology of the bearings' spatial averaging that provides a better estimation of the reception angle is shown.

Full text

Metrol. Meas. Syst., Vol. XXII (2015), No. 4, pp. 591–600.
THE INFLUENCE OF PROPAGATION ENVIRONMENT ON THE ACCURACY
OF EMISSION SOURCE BEARING
Cezary Ziółkowski, Jan Marcin Kelner
Military University of Technology, Faculty of Electronics, Gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland
(cezary.ziolkowski@wat.edu.pl, * jan.kelner@wat.edu.pl, +48 26 183 9619)
Abstract
This paper focuses on the radio direction nding (DF) in multipath environments. Based on the measurement
results presented in the open literature, the authors analyse the inuence of environment transmission properties
on the spread of the signal reception angle. Parameters that dene these properties are rms delay and angle
spreads. For these parameters, the mutual relationship is determined. This relationship is the basis for assessment
of the required number of bearings that minimize the inuence of the environment on the accuracy of DF
procedure. In the presented analysis, the statistical properties of the signal reception angle are approximated by
the normal distribution. The number of bearings versus the rms delay spread is presented as the main objective
of this paper. In addition, a methodology of the bearings’ spatial averaging that provides better estimation of the
reception angle is shown.
Keywords: DF, methodology of bearing measurement, bearing accuracy, measurements in multipath environment,
power azimuth spectrum.
© 2015 Polish Academy of Sciences. All rights reserved
1. Introduction
During execution of a radio direction nding (DF) procedure, the main causes of errors are:
–errors of the used DF method;
–practical implementation of the DF method;
– environmental interference – natural and industrial;
–movement of signal sources;
–phenomena associated with multipath propagation of radio waves in real environments.
In urban areas, the most important reason that limits use of the DF procedure is the multipath
propagation of radio waves. In these cases, the radio DFs are performed in non-line-of-sight
(NLOS) propagation conditions. This greatly enhances the impact of the multipath propagation
phenomenon on the angular power spread of the received signals, which is a major cause of
errors in procedures determining the direction of the electromagnetic wave source. Assessment
of these errors is the basis for determining the error ellipse of the source location [1, 2].
Therefore, the problem of minimizing the environmental impact has a signicant importance
on the accuracy of DF procedures. In practice, many techniques are used to minimize errors
of these procedures. To estimate the directions of the reception wave, the super-resolution
techniques such as MUSIC [3–5], CLEAN [6], ESPRIT [7], SAGE [8], SPACE [9] are
adopted. The complex procedures of digital signal processing (DSP) make it possible to obtain
a high-resolution measurement of the angle of arrival (AOA). In addition to DSP techniques,
the methods based on the antenna adaptive beamforming are used [4, 5, 10]. However,
these techniques do not provide for elimination of multipath components of the wave which
signicantly impede determination of the direction to the source. Under these conditions, the
Article history: received on Jun. 16, 2015; accepted on Aug. 28, 2015; available online on Dec. 07, 2015; DOI: 10.1515/mms-2015-0042.
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C. Ziółkowski, J.M. Kelner: THE INFLUENCE OF PROPAGATION ENVIRONMENT ON THE ACCURACY …
spatial averaging the bearings is necessary in order to eliminate scattered components. This fact
is described in [11].
This paper is devoted to assessment of the bearing error as a function of the propagation
environment type whose properties are characterized by parameters dened on the basis of the
radio channel impulse response (IR). The aim of this paper is evaluation of the required number
of bearings that will provide the desired accuracy of the bearing in the multipath propagation
conditions. In this case, for statistical representation of propagation conditions, the position
change of the direction-nder (DFR) is always required. For a wide range of propagation
environments, measurement results in the open literature are the basis for AOA analysis
presented in this paper.
The results obtained by the authors are the basis for development of a methodology to
determine successive locations, where bearings are used. It provides signicant reduction in the
inuence of multipath propagation for radio DF errors.
The paper is organized as follows. Section 2 presents the rms delay spread as a fundamental
criterion for the classication of propagation environment types. Use of the Gaussian probability
density function (PDF) as the approximating PDF of AOA is shown in Section 3. Analysis of the
number and methodology of space measurements is presented in Section 4. In conclusion, the
practical possibility of quantitative evaluation of the bearing error in a multipath environment
is emphasized as a result of the presented analysis.
2. Transmission properties of propagation environments
In terms of the radio signal transmission properties, the radio channel IR parameters are
the basis for the propagation environment classication. The rms delay spread, στ, is the
fundamental criterion for the classication of propagation environment types [12]. This
parameter is dened as the square root of the second-order moment of the power delay spectrum
(PDS), Pτ, according to the relation:
( )
( )
( )
( )
2
2
00
00
d d
.
d d
PP
PP
τ
τ ττ τττ
σ
ττ ττ
∞∞
∞∞



= −




∫∫
∫∫
(1)
This parameter can be interpreted as a multipath phenomenon intensity measure that is
determined based on the time domain.
An example of propagation environment classication due to their transmission properties
is standard COST 207 [13]. In this case, four propagation environment types: the rural area
(RA), the typical urban area (TU), the bad urban area (BU), and the hilly terrain (HT) are
distinguished. Each type has a different PDS represented by a discrete set of time delays and
the corresponding powers. For individual types of the propagation environments, the criteria
values of στ are presented in Table 1.
Table 1. Classication of the radio propagation environments [13].
Type of the environment RA TU BU HT
Average στ [μs] 0.1 1.0 2.5 5.0
The presented values are the measurement ranges that determine the classication of the
environment types.
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Metrol. Meas. Syst., Vol. XXII (2015), No. 4, pp. 591–600.
The power azimuth spectrum (PAS) describes the reception directions of the received signal
components. This characteristic represents the relationship between the power, P(θ), and AOA,
θ, of the received signals. In this case, the reference direction (θ = 0) is the direction determined
by the locations of the signal source (transmitter, TX) and the receiver (RX). The measuring
methodology of PAS is based on use of the antenna system that is capable of producing
a spatially tuneable, narrow radiation pattern in the reception point. On the basis of PAS there
is dened a parameter that represents a quantitative measure of the spatial dispersion of the
received signal power. It is the azimuth angle spread, σθ, that is dened by the relationship, the
form of which is similar to (1), namely:
( )
( )
( )
( )
2
180 180
2
180 180
180 180
180 180
d d
.
d d
PP
PP
θ
θ θθ θθθ
σ
θθ θθ
−−
−−



= −




∫∫
∫∫




(2)
This parameter can also be interpreted as an intensity measure of the multipath phenomenon.
However, in contrast to στ, this parameter is dened on the basis of the received signal spatial
characteristic.
The above-stated parameters, στ and σθ, are the basis for the intensity assessment of the
multipath phenomena as a function of the propagation environment nature. Hence, for each
environment, the error of the bearing is associated with σθ that has a specic value for each type
of environment.
The assessment of the propagation environment’s inuence on the bearing errors is
based on the measurement results of PAS and PDS that are presented in [14–17]. The
described measurement scenarios and the empirical results have been obtained for different
propagation environments. In [14, 15], the presented results were performed in RA near
Bristol. The measurement results that are shown in [16] and [17] were made in Stockholm
(Sweden), Aarhus, and Aalborg (Denmark). These environments are TUs. In all scenarios,
the measurements were performed at the frequency of 1.8 GHz using broadband test
signals. The signal sources used TXs with omnidirectional antennas that were installed
on the vehicles (mobile stations – MS). The measurement RXs had a linear antenna array
consisting of the half-wave dipole antennas. In the analysed publications, the presented
PAS and PDS are the averaged measurement results that were obtained on different routes.
For each measurement scenario, the average distances, D, between the route and RX
antenna location are presented in Table 2. In this table, στ and σθ are determined from the
measurements of PDS and PAS, respectively. The remaining parameters are described in
Section 3.
The obtained values of parameters are used for the linear approximation of the relationship
between στ and σθ. The base for this approximation is the least-squares method [18]. In this
case, numerical calculation gives the following solution:
[ ]
15.95 s 0.94.
θτ
σσ
 = ⋅ µ+


(3)
In [16], between these parameters, an analogous relationship is determined as a statistical
analysis result of all partial measurements. In this case, the regression line is described by:
[ ]
17.37 s 2.08.
θτ
σσ
 = ⋅ µ+


(4)
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C. Ziółkowski, J.M. Kelner: THE INFLUENCE OF PROPAGATION ENVIRONMENT ON THE ACCURACY …
The graphs of (3) and (4) are shown in Fig. 1.
Table 2. The temporal and spatial power dissipation of the received signals
for analysed measurement scenarios.
Measurement
scenario
Pedersen et al. [15]
Fig. 1
(Bristol)
Pedersen et al. [16]
Fig. 4
(Aarhus)
Pedersen et al. [16]
Fig. 4
(Stockholm)
Mogensen et al. [17]
Fig. 3
(Aalborg)
Environment RA TU TU TU
D [m] 5000 1500 1500 2100
στ [µs] 0.10 0.29 0.59 1.13
σθ [˚] 1.84 6.79 9.79 19.01
σG [˚] 1.06 4.19 7.95 5.93
w = σG / σθ [1] 0.58 0.62 0.81 0.31
Fig. 1. The angle spread versus the rms delay spread for different propagation environments.
By averaging (3) and (4), the linear equation is obtained:
[ ]
16.66 s 0.57.
θτ
σσ
 = ⋅ µ+


(5)
The above equations show a clear relationship between the received signal power dispersion
in time and space domains. The (5) is taken into account for further analysis.
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Metrol. Meas. Syst., Vol. XXII (2015), No. 4, pp. 591–600.
3. Approximation of measurement data
The empirical results and analysis of PAS measurements in different propagation
environments are shown in [16]. One of the presented problems is verication of the Gaussian
distribution hypothesis for AOA of the received signal. The obtained results of the statistical
analysis show that for a condence level larger than 0.83, this hypothesis is rejected. In
practice, this result provides the basis for the use of the Gaussian PDF as the approximating
PDF of AOA. A goodness-of-t of the Gaussian PDF to the empirical dataset is the minimum
of least-squares error (LSE), δ. This measure is dened as:
( ) ( )
[ ]
∑
=
−= K
k
kGkm ff
K1
2
1
θθδ
, (6)
where: fm(θk) (k = 1,..., K) denotes the normalized values from the empirical dataset, K refers to
the cardinality of the set of measurement data, and fG(θk) represents the values for the Gaussian
PDF. For different propagation environments, the graphical comparisons of the measurement
results and the Gaussian PDFs are shown in Fig. 2.
Fig. 2. The measurement results and approximating Gaussian PDFs for different scenarios:
a) [15] Bristol; b) [16] Aarhus; c) [16] Stockholm; d) [17] Aalborg.
Approximation of measurements consists in selection of a Gaussian PDF deviation, σG, that
will provide the minimum of LSE. For the analysed measurement scenario, the values of σG
and σθ obtained from measurements are included in Table 2.
These data show that the analysed parameters are proportional. The averaged proportionality
coefcient is
avg
0.58w≅
. On the basis of this coefcient and (5), the relationship between the
propagation environment properties and the parameter that denes the approximating PDF of
AOA is:
a) b)
c) d)
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[ ]
avg 9.66 s 0.33
Gw
θτ
σ σσ
 ≅ = ⋅ µ−

. (7)
This relationship enables to assess the intensity of the received signal angular dispersion
according to the transmission properties of the propagation environment.
4. Inuence of the environment on the number of spatial measurements
The bearing θ0 is the angle between the direction towards the emission source and
the reference direction, usually the north direction. In real conditions, the bearing,
θ
~
, is
burdened with errors that arise from the nite accuracy of DFR and impact of the propagation
environment:
∆+=∆+∆+=
~
~
000
θθθ
e, (8)
where: Δ0 is a random variable that represents the DFR accuracy, Δe is a random variable that
maps the errors related to the propagation environment, whereas
e
∆+∆=∆
0
~
is a random
variable that represents the resultant error.
The basic model that reproduces the statistical properties of DFR is the Gaussian PDF [1, 2].
The rms DFR accuracy, σ0 , is one of the technical parameters of DFRs. Depending on the class
of DFR, the σ0 value is in the range from 0.2˚ to 5˚. For description of AOA of signals to RX,
use of the Gaussian PDF is shown in Section 3. In practice, Δ0 and Δe are independent and
the normal distribution describes their statistical properties. Thus, ∆
~
is also a normal random
variable where the standard deviation is
G
σσσ
+=
0
~
. This means that on the basis of N spatial
measurements, the estimated bearing,
θ
~
, is [19]:
z
N
σ
θθ
~
~
0+= , (9)
where: z is a normalized random variable with the normal distribution.
For specied errors of the rst and second kind, the acceptance of a hypothesis that the
bearing is
0
θ
is related to the determination of
θ
~
variation interval. The boundaries of this
interval are the basis for determining the desirable number of spatial measurements. For the
error of the rst kind, the lower bound of the interval is Nz
σθ
α
~
210 −
+, where
α
is the
signicance level, and
21
α
−
z
is 2
α
order quantile of the normal distribution. If the discreteness
of the bearing is
θ
∆
, the upper bound for the error of the second kind is
θβ
σ
θ
∆−+ Nz
~
0,
where
β
is the probability of the second kind of error, and
β
z
is
β
−
1 order quantile of the
normal distribution. The lower and upper boundaries are equal, so:
θβα
σ
θ
σ
θ
∆−+=+ −z
N
z
N
~~
0210 . (10)
Because 221
αα
zz −=
−, from (10) we have:
θβα
σ
∆+−= ~
2
N
zz
. (11)
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Metrol. Meas. Syst., Vol. XXII (2015), No. 4, pp. 591–600.
Hence, the desirable number of space measurements that provide errors of the rst and
second kind equal to α and β, respectively, is:
( )
( )
( )
2 2
2
2
20 2
22
9.66 0.33zz zz
N
αβ τ αβ
θθ
σ σσ
  
+ + ⋅− +
  
= =
∆∆
  
  

. (12)
For α = 0.1, β = 0.1, Δθ = 1.0º, and different σ0, the desirable number of space measurements
versus στ is presented in Fig. 3.
Fig. 3. The desirable number of space measurements versus στ for α = 0.1,
β = 0.1, Δθ = 1.0º, and different σ0.
Analysis of the inuence of the environment on the bearing accuracy is based on the
measurement data that are obtained for statistically independent propagation conditions. This
means that each measurement should be made in a different DFR position. The distance, d,
between successive RX positions that determine the statistical independence of received signals,
is presented in [20] as the so-called Lee criterion. This distance depends on the wavelength of
the carrier, λ0, and is d = 40λ0. The average bearing that is obtained on the basis of successive
measurements determines the direction of DFR movement. A method of determining the
successive DFR positions is presented in Fig. 4.
Spatial structures that occur in the real measurement environment limit execution of a large
number of bearings for different DFR positions. Thus, to minimize the error, increasing the
number of bearings is conditioned by the spatial structure of the environment. In practice, this
improving accuracy of bearing can only be used in poorly urbanized areas, such as RA and TU
with small στ . For typical parameters of RA and TU, the dispersion of bearing estimator, σB,
versus the number of measurements is shown in Fig. 5. The parameter σB is dened as:
0
22
9.66 0.33
B
zz
NN
τ
αα
σσ σ
σ
+ ⋅−
= =

. (13)
In Fig. 5, the number of measurements is selected for the RA and TU environments and
for the probabilities of the rst kind of errors that are equal to α = 0.1 . For the RA (στ = 0.1
μs), the dispersion of bearing equal to 2.69º is reduced to 0.85º for N = 10, whereas for the
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C. Ziółkowski, J.M. Kelner: THE INFLUENCE OF PROPAGATION ENVIRONMENT ON THE ACCURACY …
TU (στ = 0.1 μs), the dispersion decreases from 16.99º to 5.37º. This shows that the bearing
accuracy signicantly increases with N. However, the spatial structures that occur in the TUs
limit the number of permissible DFR positions. In this case, the presented graphs are the basis
for assessment of the bearing estimator dispersion.
Fig. 4. A method of determining the successive DFR positions.
Fig. 5. The dispersion of bearing estimator versus the number of space measurements
for α = 0.1, σ0 = 1.0, and different στ.
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Metrol. Meas. Syst., Vol. XXII (2015), No. 4, pp. 591–600.
5. Conclusion
In this paper, the inuence of the propagation environment on the accuracy of the bearing
is presented. Evaluation of the environment transmission properties is based on σ
τ
, whereas
σθ describes the spatial properties of the received signals. The relationship between these
parameters is obtained based on the measurement results that are presented in the open
literature. This relationship shows that the bearing errors signicantly increase with increasing
urbanization degree of the propagation environment. The spread of the error can be reduced by
the bearing estimation based on measurement results obtained for statistically different DFR
positions. For the specied precision of bearing, the required number of DFR positions versus
σ
τ
is presented. Additionally, for typical σ
τ
values that dene the RA and TU environments, the
effect of N on the dispersion of the bearing estimator is shown. In conclusion, it should be noted
that the presented results can be applied in practice, as they give a possibility of quantitative
evaluation of the bearing error in a multipath environment.
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