# Direction Finding Part 2: Array Signal Processing, Errors, Location Calculation - PowerPoint PPT Presentation

PPT – Direction Finding Part 2: Array Signal Processing, Errors, Location Calculation PowerPoint presentation | free to view - id: f3472-YmZjM

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Direction Finding Part 2: Array Signal Processing, Errors, Location Calculation

Description:

### angle f is the azimuth and q=90o-elevation angle. ... of the data matrix corresponds to azimuth direction f and forms a comparison vector. ... – PowerPoint PPT presentation

Number of Views:5222
Avg rating:5.0/5.0
Slides: 53
Provided by: ven77
Category:
Tags:
Transcript and Presenter's Notes

Title: Direction Finding Part 2: Array Signal Processing, Errors, Location Calculation

1
Direction FindingPart 2 Array Signal
Processing, Errors, Location Calculation
Series Workshop 3 "Measurements and Techniques"
• Prof. Venceslav Kafedziski
• University "Ss Cyril and Methodius"
• Skopje, Republic of Macedonia

2
Outline
• Correlative interferometer.
• Antenna array processing techniques.
• Classical beamforming.
• High resolution methods Capon's beamformer.
• High resolution methods Subspace methods
(MUSIC).
• Display of bearings.
• Classification of bearings.
• Error sources.
• Location calculation method of triangulation and
single site location.

3
Array processing
• Classical DF methods usually use several antennas
or antenna arrays to measure phase differences.
• Modern DF methods make use of all the information
received on different elements of the antenna
array.
• Array signal processing finds applications in
exploration.
• Next generations of wireless systems will use
antenna arrays - smart antennas. The goal is to
enhance the desired signal, and null or reduce
interference.
• Direction finding in multipath conditions also
uses smart antennas.

4
Antenna array basics
• angle f is the azimuth and q90o-elevation angle.
• a(f,q)1 a1(f,q) a2(f,q) ... aM-1(f,q) is
called steering vector.
• a(f,q) describes the phases of the signal at each
antenna element relative to the phases of the
signal at the reference element (element 0).

k2p/l is the wave number
5
Correlative interferometer
• The correlative interferometer is based on a
comparison of the measured phase differences
between the antenna elements of the DF antenna
system with those obtained for the same antenna
system at all possible directions of incidence.
• The comparison is made by calculating the
correlation of the two data sets (or the scalar
product of two vectors obtained by multiplying
the coordinates element by element and summing
the result).
• Using different comparison data sets for
different wave directions, the bearing is
obtained from the data set for which the
correlation is at a maximum.

6
Correlative interferometer example
• 5-element antenna array used
• each column of the data matrix corresponds to
azimuth direction f and forms a comparison
vector.
• the upper data vector contains the measured phase
differences
• each column of the reference matrix is correlated
with the measurement vector
• The angle associated with the comparison vector
resulting in maximum K(f) is the bearing.

7
Antenna array processing
• The development of Digital Signal Processing has
enabled the use of new approaches for direction
finding.
• The requirement for a simple and
frequency-independent relationship between the
signals obtained on antenna elements and the
bearing no longer applies complex mathematical
relationships can be efficiently computed.
• High-resolution methods allow the separation of
several waves arriving from different directions
• Methods of direction finding are based on
Direction of Arrival (DOA) estimation. DOA can be
converted to direction relative to the true north.

8
Antenna array processing
• The outputs of the individual antenna elements
are taken to a network which contains test
signal inputs and multiplexers.
• The signals are then converted to an
intermediate frequency and digitized.
• The digital data are down-converted into the
baseband. The complex samples of the baseband
signal ui (i1,2, ... M) are filtered and applied
to the bearing calculation section.

9
Beamforming
• Conventional methods of DOA are based on the
concept of beamforming, i.e. steering antenna
array beams in all possible directions and
looking for peaks in the output power.
• If the antenna array signals ui are multiplied by
complex weighting factors wi and added, a sum
signal is obtained which depends on the direction
of wave incidence.
• With conventional beamforming algorithms the
phases of the weighting factors are chosen so
that the weighted element signals are added in
phase and thus yield a maximum sum signal for a
given wave direction.

10
Delay-and-sum method
• The output signal is given by a weighted sum of
the element inputs
• The total output power of the conventional
beamformer is
• Ruu is the autocorrelation matrix of the input
data vector uu1 u2 ... uM'.

11
Beamforming block diagram
• S
• Since both u and w are complex vector-columns, y
is a complex scalar.
• The maximum of yy is searched for.
• The direction corresponding to maximum yy is
the bearing.

12
Beamforming regular arrays
• If the antenna array has a regular geometry, the
weighting factors can be calculated analytically.
• For a Uniform Linear Array (ULA) with antenna
spacing D the weights equal to
• (assuming that qp/2) can steer the antenna beam
to any desired direction f0.

13
Beamforming - analysis
• Consider a signal s(k) impinging on the array at
an angle f0. The power at the beamformer output
can be expressed as
• The output power is maximized when wa(f0). The
receiver antenna has the highest gain in the
direction f0, when wa(f0). This is because
wa(f0) aligns the phases of the signal
components arriving from f0 at the antenna
elements, causing them to add constructively.

14
Beamforming - analysis
• In the classical beamforming approach for DOA
estimation, the beam is scanned over the angular
region of interest in discrete steps by forming
weights wa(f) for different f and the output
power is measured
• If we have an estimate of the input
autocorrelation matrix and know the steering
vectors a(f) for all f's of interest (through
calibration or analytical computation), it is
possible to estimate the output power as a
function of the DOA f, called spatial spectrum.
The DOA can be estimated by locating peaks in the
spatial spectrum.

15
Beamforming spatial resolution
• The spatial resolution depends on the mainlobe
width.
• Figure gives an example for ULA and weights equal
to 1.
• Delay-and-sum method has a low resolution.
• The resolution can be increased by increasing M,
but this increases complexity and storage.

16
Super resolution DF methods
• If in the frequency channel of interest unwanted
wave, conventional beamforming may lead to
bearing errors.
• If the power of the interference wave component
is smaller than that of the wanted wave
component, the direction finder can be designed
to minimize the bearing errors by choosing a
sufficiently wide antenna aperture.
• If the interference wave component is greater or
equal to the wanted wave component, the
interference waves have to be also determined in
order to be able to eliminate them. This means
that the secondary maxima in the spatial spectrum
have to be evaluated too.

17
Super resolution DF methods
• The limits in determining secondary maxima are
reached if
• the ratio between primary maximum and
secondary maxima becomes too small, or
• the angle difference between wanted wave
and interference wave is smaller than the width
of the main lobe
• By optimizing the weighting factors, the level of
the secondary maxima can be reduced but at the
same time the width of the primary maximum is
increased. The aim of the super-resolution (SR)
DF method is to resolve this problem.

18
Capon's method
• Capon's minimum variance method attempts to
overcome the poor resolution problems associated
with classical beamforming.
• The technique uses some of the degrees of freedom
to form a beam in the desired look direction,
while simultaneously using the remaining degrees
of freedom to form nulls in the direction of
interfering signals.
• Minimizes the contribution of the undesired
interferences by minimizing the output power
while maintaining the gain along the look
direction to be constant (unity)
• minwEy(k)2minwwHRuuw subject to
wHa(f0)1

19
Capon's method
• Capon's method is also called a minimum variance
method, since it minimizes the variance (average
power) of the output signal while passing the
signal arriving in the look direction without
distortion.
• The output power of the array, as a function of
DOA is given by Capon's spatial spectrum
• By computing and plotting the spectrum over the
whole range of f, the DOA's can be estimated by
locating the peaks in the spectrum.

20
Capon's method
• Capon's method has better resolution than the
delay-and-sum method.
• The resolution strongly depends on the
signal-to-noise ratio.
• Capon's method fails if signals that are
correlated with the Signal-of-Interest are
present. The correlated components may be
combined destructively in the process of
minimizing the output power.
• Capon's method requires the computation of a
matrix inverse, which can be computationally
expensive for large antenna arrays.

21
Subspace methods
• The subspace methods are aimed at eliminating the
effect of noise. This can be done by splitting up
the M-dimensional space spanned by the antenna
element outputs into a signal subspace and a
noise subspace.
• These methods exploit the structure of a more
accurate data model for the case of arrays of
arbitrary form.
• MUSIC algorithm is a high resolution MUltiple
SIgnal Classification technique based on
exploiting the eigenstructure of the input
covariance matrix. Provides information about the
number of incident signals, DOA of each signal,
strengths and cross correlations between incident
signals, noise power, etc.

22
MUSIC
• If there are D signals incident on the array, the
received input data vector at an M-element array
can be expressed as a linear combination of the D
incident waveforms and noise
• where A is the matrix of steering vectors
• Aa(f1) a(f2) ... a(fD)
• ss1, ... , sD' is the signal vector, and
nn1, ... ,nM is a noise vector with components
of variance sn2.

23
MUSIC
• The received vectors and the steering vectors can
be visualized as vectors in an M-dimensional
vector space.
• The input covariance matrix is
• where Rss is the signal correlation matrix.
• The eigenvectors of the covariance matrix Ruu
belong to either of the two orthogonal subspaces,
the principal eigen subspace (signal subspace)
and the non-principal eigen subspace (noise
subspace).
• The dimension of the signal subspace is D, while
the dimension of the noise subspace is M-D.

24
MUSIC
• The M-D smallest eigenvalues of Ruu are equal to
sn2, and the eigenvectors qi, iD1, ... ,M,
corresponding to these eigenvalues span the noise
subspace.
• The D steering vectors that make up A lie in the
signal subspace and are hence orthogonal to the
noise subspace.
• By searching through all possible array steering
vectors to find those which are orthogonal to the
space spanned by the noise eigenvectors qi,
iD1, ... ,M, the DOAs f1,f2, ... ,fD, can be
determined.

25
MUSIC
• To form the noise subspace, we form a matrix Vn
containing the noise eigenvectors qi, iD1, ...
,M.
• Then aH(f)VnVnHa(f)0 for f corresponding to the
DOA of a multipath component.
• The DOAs of the multiple incident signals can be
estimated by locating the peaks of a MUSIC
spatial spectrum
• The resolution of MUSIC is very high even in low
SNR.
• The algorithm fails if impinging signals are
highly correlated.

26
Examples of Capon and MUSIC
Comparison with classical beamforming (a) Capon
beamformer with SNR100. (b) Capon beamformer
with SNR10. (c) MUSIC algorithm with SNR10.
(a)
(b)
(c)
27
Display of bearings
• The display of the DF results is of great
importance as an interface to the operator.
• Distinction is to be made whether the display is
the DF result of a single channel or of a
multichannel direction finder.
• In a single-channel display, the following
parameters are usually indicated numeric DF
value, azimuth in polar coordinates, elevation as
bar graph or polar diagram (combined with azimuth
display), DF quality, level, histogram of DF
values, DF values versus time (waterfall).

28
Multichannel direction finders
• Multichannel direction finders are implemented
with the aid of digital filter banks (FFT and
polyphase filters).
• These direction finders allow quasi-simultaneous
direction finding in a frequency range from some
100 kHz up to a few MHz. Scan mode is
additionally provided to cover larger frequency
ranges.
• Usually the following display modes are provided
DF values versus frequency, DF values versus
frequency and time (e.g. by using different
colours for the DF values), level versus
frequency (power spectrum), level versus time and
frequency (using different colours for level
values), histograms.

29
DF below 30 MHz
• Propagation between transmitter and receiver may
involve different modes, including a ground wave,
and single or multiple reflections on E or F
layers of ionosphere.
• Since the horizontal stratification of the
ionosphere and the ion-density are not stable,
the reflections are irregular.
• DF operating below 30 MHz are susceptible to
errors induced by reflections of transmissions
from the ionosphere.
• The error in the bearing due to a given angle of
inclination relative to the reflective surface
increases with the angle of elevation of the ray
received by the direction finder. Critical are
situations with multiple reflections.

30
Classification of HF bearings
• Reccomendation ITU-R SM.1269 classifies HF
bearings into four classes A, B, C and D.
• Classes A, B, C are defined as having probability
less than 5 that bearing errors exceed 2, 5, and
10 degrees respectively, and class D is for
larger errors.
• The errors in bearings are due to equipment,
site of the DF, propagation, and operator. The
total error variance n is equal to the sum of the
error variances due to equipment, site of the DF,
propagation, and operator.
• Classes in terms of error variance Class A for
nlt1, Class B for 1ltnlt6.5, Class C for 6.5ltnlt25,
class D for ngt25.

31
Classification of HF bearings
• Series of N measurements can be conducted, from
which the mean and the variance can be computed.
If am is the mean, the variance is computed
according to
• To decrease variance, n groups of measurements
are performed on the same transmitter. Each group
will have a different mean value. The variance of
the mean is going to decrease

32
DF above 30 MHz
• A basic system consists of two or more
remote-controlled direction-finding stations and
a manned monitoring station.
• System can have two or more mobile stations
equipped with a direction finder and monitoring
• The bearings are classified for accuracy into
four classes A, B, C and D.
• Classes A, B, C are defined as having probability
less than 5 that bearing errors exceed 1, 2, and
5 degrees respectively, and class D is defined as
resulting in errors larger than Class C.

33
DOA versus LOB
• It is important to differentiate the direction of
arrival DOA from geographic line of bearing
(LOB).
• The DOA does not relate to a geographical
direction. The DOA is a measurement that results
in a relative angle between an emitter and a
specific DF antenna orientation.
• The LOB is a measurement that contains a
combination of the errors introduced in the DOA
measurement and those contributed by the
with the true north deviation. It is with these
factors that a line can be plotted on a map.

34
Error sources
• The DF accuracy is affected by a number of
influences
• Wave propagation (usually disturbed by obstacles)
• Signals radiated by the emitters are modulated,
limited in time and their carrier frequency is
often unknown
noise, co-channel interferers
• Tolerances and noise in the DF system

35
Multiwave-related errors
• The simple case of a plane wave occurs seldom in
practice. In a real environment, other waves have
usually to be taken into account which result
• from other emitters in the same frequency channel
(incoherent interference) or
• from secondary waves (caused by reflection,
refraction, diffraction coherent in-channel
interference)
• Usually, a large number of waves is involved.

36
Multiwave-related errors
• The direct wave component with the amplitude 1
arrives from an angle of 90.
• There is a secondary reflected wave.
• If the majority of waves arrives from the
direction of the emitter, the DF error can be
reduced by increasing the antenna aperture.

37
Synchronization errors
direction finders are calibrated for synchronism
with the aid of a test generator prior to the DF
operation. The transmission parameters in each
section are measured in magnitude and phase, and
the level and phase differences are stored. In
the DF process the measured values are corrected
by the stored difference values before the
bearing is calculated.
• Special attention is to be given to the frequency
response of the filters. Digital filters have the
advantage that they can be implemented with
absolutely identical transfer characteristics.

38
Synchronization errors
• Consider a 2-element interferometer. Different
gain and phase in the receive sections cause DF
errors that are smaller if the relative antenna
aperture D/l increases.

39
Modulation errors
• Usually the carrier signal of the emitter is
modulated with a complex modulation function
(complex envelope).
• The modulation can affect the DF result in
several aspects
• Different envelope delay distortion in the DF
channels
• With sequential antenna scanning modulation
function is not sufficiently stationary for the
duration of the measurement or cannot be
compensated for by other measures prior to DF
evaluation
• Possible decorrelation between the antenna
elements if the spacing between the elements is
greater than the coherence length Lk c0/B (B is
the signal bandwidth).

40
Noise errors
• Interference caused by noise has a limiting
effect on the sensitivity of a DF system.
Sensitivity is the field strength at which the
bearing fluctuation remains below a certain
standard deviation.
• Consider internal noise produced in the system
(antenna amplifier, DF converter, A/D converter)
• For a 2-element interferometer the uncorrelated
noise in the two receive sections causes
statistically independent phase variations
according to the signal-to-noise ratio

41
Noise errors
• Mapping of the phase variation to virtual
variations of the DF antenna positions yields for
the bearing error
• Error is smaller for larger relative antenna
aperture D/l.

42
Noise errors
• The variations caused by noise can be reduced by
averaging. The variance improvement through
averaging over K values is
• Figure shows the two effects together antenna
aperture and averaging. Parameter is SNRdB for
bearing fluctuation of 1.

43
Location calculation
• The location calculation is directly dependent on
the quality of bearings of the various direction
finding stations. Bearings should be analyzed at
both DF stations and monitoring stations.
• At DF stations classifying the bearings in case
of the presence of interference, eliminating
aberrant shootings, calculating the mean value
and the variance of shootings.
• At the monitoring station determining the
bearings to be used for the location calculation,
calculating the position of the probable
transmission point, calculating the uncertainty
ellipse.

44
Location calculation steps
• Location calculation steps are given in the
following figure.
• The computer program "TRIANGULATION", that
generally follows these steps, is available
through ITU.

45
Determining reliable bearings
• If there exist fast links between Monitoring
Centre and DF stations, the Calculation Centre is
provided, for each direction finder, with a
number of elementary bearings. In that case,
simple processing only is used at DF stations.
• For slow links, making reliable bearings should
be performed at the DF station. Making a reliable
result is achieved by averaging the elementary
bearings regarding the signal of interest for the
Monitoring Centre.

46
Eliminate non-convergent bearings
• On each shooting, the area covered by the own
angular error of each of the shootings is
constructed.
• When areas partly overlap, shootings can be
associated.
• The association including the largest number of
shootings is kept as the best one.
• Shootings that are not parts of the best

47
Location calculation
• The optimum point is searched applying the least
squares method.
• If P is any point and d1, d2, d3, ... the
angular variations to be applied to each bearing
to intersect P and n1, n2, n3, ... the
variances of various bearings, define
• The optimum point is the point minimizing Sp.
• The uncertainty ellipse is the area centered
around the optimum point. This calculation is
performed from typical deviations from the
various bearings.

48
SSL for HF emissions
• The single site location (SSL) system allows
determining the geographical position of a
transmitter with a single radio direction-finder.
Processing system on data supplied by the radio
direction-finding (azimuth, elevation) associated
with ionospheric predictions, allows estimating
the transmitter distance with regard to the radio
direction-finder, ranging up to 2500 km.
• SSL radio direction finders simultaneously
deliver the azimuth and elevation angle of the
signal received by the antenna array. Propagation
is by ground wave and ionospheric wave through
multiple paths corresponding to different
elevation angles.

49
SSL
• The basis of SSL is the so-called Classical
Method of Range Estimation. Assumes that the
actual HF propagation may be modeled by assuming
that reflection takes place from a simple
horizontal mirror at the appropriate height.

50
SSL
• There are two contra-polarized waves (circular or
elliptical) - an ordinary (O) and an
extraordinary (X) wave.
• Location range calculation process calculating
elevation histograms, filtering elevation
diagrams, determining elevation packets,
determining four basic distances for LH and RH
polarization of O and X waves, and determining
the final distance.
• Limitations of SSL multi-hop propagation leads
to calculated distances which are shorter than
the real distances, and reflection may take place
from layers of different heights.

51
Conclusions
• Modern Direction Finders use digital signal
processing.
• Modern array signal processing methods for DF are
used in conditions when many signals are present
and achieve excellent resolution in the presence
of noise.
• To estimate bearing accuracy and calculated
location accuracy it is important to estimate
bearing errors.
• Therefore, it is important to understand the
error sources and the classification of bearing
errors.
• There is an increased need for monitoring
personnel to understand principles of digital
signal processing, which significantly improves
and facilitates spectrum monitoring.

52
Literature
• Smart Antennas for Wireless Communications IS-95
and Third Generation CDMA Applications, J.C.
Liberti and T. S. Rappaport, Prentice Hall, 1999.
• Adaptive Filter Theory, S. Haykin, Prentice Hall,
1991.
• Multidimensional Digital Signal Processing, D. E.
Dudgeon and R. M. Merserau, Prentice Hall, 1984.
• International Telecommunication Union Spectrum
Monitoring Handbook, ITU, 2002.
• Introduction into Theory of Direction Finding,
Rohde Schwarz.