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Direction FindingPart 2 Array Signal

Processing, Errors, Location Calculation

INA Academy Workshop Spectrum Management

Series Workshop 3 "Measurements and Techniques"

- Prof. Venceslav Kafedziski
- University "Ss Cyril and Methodius"
- Skopje, Republic of Macedonia

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.

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

mobile communications, radar, sonar, seismic

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.

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

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.

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.

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.

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.

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.

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'.

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.

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.

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.

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.

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.

Super resolution DF methods

- If in the frequency channel of interest unwanted

waves are received in addition to the wanted

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.

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.

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

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.

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.

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.

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.

MUSIC

- The received vectors and the steering vectors can

be visualized as vectors in an M-dimensional

vector space. - The input covariance matrix is
- RuuEuuHARssAHsn2I
- 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.

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.

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.

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)

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).

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.

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.

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.

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

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

equipment, connected via VHF radio data links. - 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.

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

determination of the magnetic heading as adjusted

with the true north deviation. It is with these

factors that a line can be plotted on a map.

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 - Received field is additionally superimposed by

noise, co-channel interferers - Tolerances and noise in the DF system

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.

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.

Synchronization errors

- The receive sections of most multireceiver

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.

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.

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).

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

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.

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.

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.

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.

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.

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

association are discarded.

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.

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.

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.

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.

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.

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.