HF spectrum occupancy and antennas - University of Leicester1].pdf · Key words Antenna Analysis – Antenna Synthesis ... When a distribution of point sources is giv- ... for a continuous

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ANNALS OF GEOPHYSICS, VOL. 52, N. 3/4, June/August 2009

Key words Antenna Analysis – Antenna Synthesis –Fourier Relation – Spectrum Management

1. Antennas

1.1. Introduction

The «Small Translation Theorem» devel-oped by Prof. Francisco Grilo in his classes atthe University of Porto gave rise to a new pro-cedure of dealing with antennas field that givesa new insight into the field and opens easy pro-cedures for practical applications. The Ph.D.Thesis of several professors (Casimiro, 1990;Azevedo, 2001; Xianfeng, 2004) covered thedifferent aspects of this new procedure as wellas other publications.

Since the propagation of signals through theionosphere can be significantly affected by its

presence, antenna arrays play an important rolein the mitigation of ionospheric effects. Inmany communication systems it is desirable forthe antenna to have a narrow beam with verylow side lobe levels. Other situations, such asGPS satellites, require shaped beam patterns.The interference could be mitigated by impos-ing appropriated nulls on the radiation patternand controlling the sidelobe levels.

This paper summarizes the basic conceptsand presents one application example coveringthe application of the new procedure to the an-tenna field, developed during the COST 296 ac-tion. The references cover the remaining devel-opments.

The understanding of these situations givethe possibility of new mitigation procedures notonly in the COST 296 area, but also in ther ar-eas, so opening an inter COST collaboration aswas already being made with COST 284 andnow with COST IC 0603.

Besides the one-dimensional antenna distri-butions, the Fourier Relation is also suited forthe two-dimensional case, and for the general3D distributions of sources. Even if all the situ-ations are fully covered by the developed Fouri-

HF spectrum occupancy and antennas

António Casimiro (1), Joaquim Azevedo (2), Lefteris Economou (3), Haris Haralambous (4), Ersin Tulunay (5) (6), Yurdanur Tulunay (5), Yildirim Bahadirlar (6),

A. Serdar Türk (6) and E. Michael Warrington (7)(1) CEFAT, DEEI, FCT, University of Algarve, Portugal

(2) Engineering and Mathematics Department, University of Madeira, Portugal(3) Intercollege, Cyprus

(4) Frederick University, Cyprus(5) Middle East Technical University, Ankara, Turkey

(6) TÜBITAK, MAM, Kocaeli, Turkey(7) Department of Engineering, University of Leicester, Leicester, UK

AbstractThis paper deals with the research made during the COST 296 action in the WG2, WP 2.3 in the antennas andHF spectrum management fields, focusing the Mitigation of Ionospheric Effects on Radio Systems as the sub-ject of this COST action.

Mailing address: Prof. Doutor António Casimiro, CE-FAT, DEEI, FCT, University of Algarve, Campus de Gam-belas, 8000-117 Faro, Portugal; e.mail: [email protected]

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A. Casimiro, J. Azevedo, L. Economou, H. Haralambous, E. Tulunay, Y. Tulunay, Y. Bahadirlar, A.S. Türk and E.M. Warrington

er Relation, it is useful to work in the particularaspects of one, two and three dimension anten-na distribution cases.

Going for the two-dimensional case, a planararray has two dimensions of control. Consider-ing that the relationship between the array factorand the array excitations for the far field regionis a Fourier transform in the appropriate vari-ables (Casimiro and Azevedo, 2005), much ofthe work achieved has been to obtain appropri-ated synthesis techniques based on this relation.

In a previous study the array elements werein a rectangular grid (Azevedo, 2007). Consid-ering the signal processing theory, for this caseit is possible to apply the sampling theorem tothe array factor.

Therefore, this kind of geometry permitsthe use of the Fast Fourier Transform algorithmto make the involved calculations. On the oth-er hand, since a ring array offers advantagesusing fewer elements than a filled planar arrayand a geometry that facilitates 360 degreesscanning, (Hansen, 1998), the Fourier relationcan be applied to planar arrays with the ele-

ments in a circular grid. To deal with circularapertures the Hankel transform could be con-sidered (Elliot, 1981).

1.2. Basic Concepts

When a distribution of point sources is giv-en, a spatial translation of any source only mod-ifies the produced field in the phase, accordingto the eq. 1.1 (Casimiro, 1990):

(1.1)

where βo = 2π/λ,λ is the wavelength “.” meansthe dot product. It can be said that all the sourcedistribution is under the Small Translation The-orem application. When it occurs, the array pat-tern is always a window in the Inverse FourierTransform of the source distribution if we use aconvenient representation of the variables in-volved.

( ) ( , )

( ) ( , )

c F

ac ae F

d

d d .dj

1 1

1 100

θ φ

θ φ+ b

Fig. 1. The Fourier Relation: the 3D general situation.

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This was called the Fourier Relation (Griloand Casimiro, 1991).

The general case of three-dimensionalsource distribution is represented in fig. 1 andthe Fourier Relation is given by

(1.2)

where c(x,y,z) is the source distribution,F(βx,βy,βz) is the array factor, F means theFourier transform, the bar under the variable in-dicates the temporal Fourier transform andβx=βcos(θx), βy=βcos(θy) and βz=βcos(θz).

The one-dimensional case and two-dimen-sional case are particular cases of this tridimen-sional one, as it is obvious. This approach hasbeen successfully used for the research in theantennas and propagation fields, namely duringthis action time as can be seen from the refer-ences. Next it will be illustrated by applying itat a circular antenna array.

1.3. Circular arrays of Antennas

A direct application of the Fourier Relationexpressed by eq. 1.2 is to planar arrays. In orderto control the radiation pattern, Azevedo (2007)presented a technique that controls directly thepeaks of a rectangular array factor. In the pres-ent work, the Fourier Relation is applied to cir-cular arrays.

For two-dimensional systems that exhibitscircular symmetry is more appropriate to dealwith the Hankel transform. This transform, alsocalled Fourier-Bessel transform, is defined by(Cohen, 1992).

(1.3)

with Jv(α) the Bessel function of first kind and

( ) ( ) ( )

( ) ( ) ( )

F s f r J sr rdr

f r F s J sr sds

0

0

v v

v v

=

=

3

3

#

#

( , , ) ( , , )

(2 ) ( , , )

( , , ) ( , , )

(2 )1

( , , )

F c x y z e dxdydz

F c x y z

c x y z F e d d d

F F

( )

3 1

( )

3

x y zj x y z

x y zj x y z

x y z

x y z

x y z

x y z

β β β

π

β β β β β β

πβ β β

=

=

=

=

3

3

3

3

3

3

3

3

3

3

3

3

b b b

b b b

+ +

---

-

- + +

---

7

7

A

A

###

###

order v. The two-dimensional Fourier transformcan be related with the Hankel transform(Wylie and Barret, 1995). If F(u,v) is the Fouri-er transform of f(x,y), and exists radial symme-try, it means f(x,y)=f(r) is independent of the φvariable, with r2=x2+y2, x=rcos(φ), y=rsin(φ),and if F(u,v)=F(q), then

(1.4)

These equations constitute the Hankel trans-form for Bessel functions of order v=0.

In the following, the Fourier Relation is an-alyzed for planar arrays with circular symme-try. Considering the polar coordinate system,

(1.5)

for a continuous source distribution, c(ρ, ϕ), thearray factor defined is:

(1.6)If the source distribution only depends on

the distance to the origin and considering that(Cohen, 1992)

(1.7)

then

(1.8)

This is the well-known result for a continu-ous disc source distribution, being similar to theone given by eq. 1.4. As noted by several au-thors (Elliot, 1981), since the source distribu-tion does not depend on ϕ, the array factor is al-so independent of ψ.

( ) ( )

2 ( ) ( )

F c e d d

c J d

( )

0

2

0

00

cosjξ ρ ϕ ρ ρ

π ρ ρξ ρ ρ

=

=

3

3

tp } {r

-: D##

#

( )21

J x e d0( )

0

2cosjx

π α= ar

#

( , ) ( , )

( , )

F c e d d

c e d d

( ). ( ) ( ). ( )2

( )2

cos cos sin sin

cos

j

j

00

00

ξ ψ ρ ϕ ρ ρ ϕ

ρ ϕ ρ ρ ϕ

=

=

3

3

p } t { p } t {r

tp } {r

+

-

7 A##

##

( )

( )

( )

( )

cos

cos

cos

sin

x

y

x y2 2 2 2 2 2

x

y

x y

ρ ϕ

ρ ϕ

ρ

β ξ ψ

β ξ ψ

ξ β β

=

=

= +

=

=

= +

( ) 2 ( ) ( )

( )21

( ) ( )

F q f r J qr rdr

f r F q J qr qdq

00

00

π

π

=

=

3

3

#

#

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For a discrete planar array with M concen-tric rings, as represented in fig. 2, using thechanging of variables defined in eq. 1.5

(1.9)

with ϕn=2πn/Nm and Nm is the number of ele-ments in ring m.

As performed for rectangular grids, the pre-vious result could also be obtained sampling thecontinuous definition with Diracs impulses inthe positions of the array elements divided bythe ring radius. Considering the decompositionin Fourier series,

(1.10)

for an array distribution that only varies with ρ,eq. 1.9 becomes

( ) ( , ) ( )

( ) ( )

F c j J e

c j J e e

0

1

0

12

2

0

1

0

1

m n

n

N

m

Mk

k mjk

Nn

k

mk

k mjk

k

jN

kn

n

N

m

M

m

m

m

m

ξ ρ ϕ ρ ξ

ρ ρ ξ

=

=

3

3

3

3

}r

}r

=

-

=

--

=-

=-

-

=

-

=

-

c m// /

/ //

( )e j J e( ) ( )cosj kk m

jk

k

m n nρ ξ=3

3t p } { } {- -

=-

/

( , ) ( , )

( , )

F c e

c e

0

1

0

1( ). ( ) ( ). ( )

0

1

0

1( )

cos cos sin sin

cos

m n

n

N

m

Mj

m n

n

N

m

Mj

m

m n m n

m

m n

ξ ψ ρ ϕ

ρ ϕ

=

=

p } t { p } t {

t p } {

=

-

=

-+

=

-

=

--

7 A//

//

(1.11)

Since the summation in n is equal to Nm ifk=Nmp, p=0, ±1, ±2, …, and zero otherwise, thearray factor is given by

(1.12)

Although the series in p is infinite, usuallythe first few terms are enough to produce a goodapproximation for the array factor. If only theBessel function of zero order is considered foreq. 1.12, the result is similar to sampling (1.8),corresponding to the array factor of a continu-ous distribution. The contribution of higher or-der terms diminishes with increasing Nm. On theother hand, in practical situations the number ofelements in each circle must be enough to pro-duce a good compromise between the beamwidth and the sidelobe levels. In fact, for a rec-tangular grid the distance between elements isusually around λ/2 to λ to avoid grating lobes in-side the visible window. In the same way for cir-cular arrays, increasing the distance between el-ements introduces sidelobes with high values in-side the visible window for radiation. Figure 3

( , ) ( ) ( )F N c J e 2

0

1

m m N p mjN p

pm

M

m

mξ ψ ρ ρ ξ=3

3}

r+

=-=

-c m//

Fig. 2. Concentric rings planar array.

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shows the contribution of each Bessel functionterm represented in eq. 1.12 as a function of ξfor a distance between elements around a wave-length. Three ring radiuses were considered.Since the distance between elements can be ap-proximated by the portion of the arc around thering, for a specified distance between elementsaround λ/2 the number of elements is given byNm=4πρm/λ. Since the visible window region isequal or less than β=2π/λ, for this situation thearray factor is given practically by the first termsof the summation.

The source distribution of the discrete arraycan be calculated using (eq. 1.2). Consideringthe changing of variables defined in (eq. 1.5),the following is obtained

(1.13)

In contrast to the continuous case, as it can beverified from (eq. 1.12), the array factor of a dis-crete planar has both dependence of x and y. On-ly when the approximation to the Bessel functionof order zero is accepted there is independenceof y and the source distribution is given by

(1.14)

In this case, the source distribution can be ob-tained using the Hankel transform of zero order.

( )(2 )

1( )

21

( ) ( )

c F e d d

F J d

2( )

0

2

0

00

cosm

j

m

m nρπ

ξ ψ ξ ξ

π ξ ρ ξ ξ ξ

=

=

3

3

t p } {r

-: D##

#

( , )(2 )

1( , )

(2 )1

( , )

c F e d d

F e d d

2( ). ( ) ( ). ( )

0

2

0

2( )

0

2

0

cos cos sin sin

cos

m nj

j

m n m n

m n

ρ ϕπ

ξ ψ ξ ξ ψ

πξ ψ ξ ξ ψ

=

=

3

3

p } t { p } t {r

t p } {r

+

-

7 A##

##

Fig. 3. First terms of the array factor infinite series: a) r=0.5l; b) r=l; c) r=1.5l.

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1.4. Results

For antenna arrays, an array with 81 ele-ments and distance between elements of 0.5λ isconsidered. The method presented in (Azevedo,2007) gives the result of fig. 4, for sidelobe lev-

els 30 dB below the main lobe.For a planar array with circular symmetry

M = 6 concentric rings were considered and thesame number of elements and positions as theprevious example. One element is in the origin.The rings have 6, 12, 18, 24 and 20 elements,

Fig. 4. Array factor for an array in a rectangular grid with sidelobe level of -30 dB.

Fig. 5. Array factor for a concentric rings array.

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Fig. 6. Source distribution: a) rectangular array; b) circular array.

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respectively. The distance between rings is 0.5λand the distance between elements of the innerrings is around 0.52λ. For the last ring the dis-tance between elements is 0.78λ. For compari-son with the previous example, an array factorwith a similar beam width was considered.Since the desired array factor does not dependson φ the source distribution was calculated us-ing (eq. 1.14), considering that F(ξ)=1 forξ<1.3 λ and F(ξ)=0 otherwise. Figure 5 showsthe array factor. Only two terms of (eq. 1.12)are enough to produce this result. Comparedwith the rectangular grid array, the higher side-lobe level for a uniform distribution is around -13 dB whilst for the concentric circular arraythe higher sidelobe level was around -18 dB. Asit can be observed from fig. 8, the sidelobe lev-els are 30 dB below the main lobe.

Therefore, based on the array factor config-uration, in some applications the synthesis tech-nique can explore its symmetry in a simplermanner.

The source distributions for both arrays aregiven in fig. 6. The feed system of the circulararray is simpler than the one of the rectangulargrid since several elements have the same exci-tation.

1.5. Conclusions

During this COST 296 action time, the«Fourier Relation» was successfully applied totwo dimensional antenna arrays to control theradiation pattern that is one of the main toolsfor Mitrigation of Ionospheric Effects on RadioSystems. The common field application makesthe research suitable for collaboration with oth-er COST actions as was done with COST 284and COST IC 0603.

2. Spectrum occupancy

2.1. Introduction

A long-term joint UK–Swedish–Germanproject has been undertaken on the measure-ment and analysis of HF spectral occupancy

over northern Europe. Measurements that re-sulted from this project have been used to fur-ther investigate spectral occupancy in the frameof COST 296. In this COST action the researcheffort focused on two areas: a) procedures forstatistically modelling spectral occupancy, withfinal stable-day and stable-night models fornorthern Europe, using calibrated monopole an-tennas (Economou et al., 2005) correspondingto weekly occupancy measurements; b) investi-gation into the possible application of artificialneural networks to predict spectral occupancyin the HF spectrum (1.6-30MHz). In particular,a study of the development of ITU allocationmodels for the diurnal variation of HF spectraloccupancy over Sweden is made (Haralambousand Papadopoulos, 2007; Haralambous et al.,2008). Furthermore the application of NeuralNetworks as a means of optimising the reliabil-ity of HF groundwave communication systemsby forecasting the detrimental effect of interfer-ence from other users is examined (Haralam-bous and Papadopoulos, 2008). This paper alsopresents atmospheric noise measurements overthe HF band during the 29 March 2006 total so-lar eclipse in Antalya (Tulunay, E. et al.,2006b).

2.2. Measurements during the 29 March 2006total solar eclipse week in the easternMediterranean region

Measurements over the HF band during the29 March 2006 total solar eclipse in Antalya(36° N, 30° E) Turkey were conducted from thechannel occupancy and atmospheric noisepoints of view.

The whole HF band ranging from 1 to 30MHz has been swept using 10 kHz peak and200 Hz average detectors of a certified EMI re-ceiver (HP-8542E) equipped with a calibratedactive monopole antenna (HE-011) (MCM4,2006 (p. 31-35); Tulunay et al., 2006a; 2006b;Tulunay E., 2007).

Figure 7 shows the atmospheric noise varia-tion almost at the time the total solar eclipse.The results indicate that during the total eclipsethe noise level exhibited a different pattern.Qualitatively, «the eclipse» values somehow

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represent the characteristic behavior of thenight-time. After the total eclipse the atmos-pheric noise level returned back to its pre-eclipse pattern both in magnitude and configu-ration (MCM4, 2006 (p. 31-35).

2.3. Measurement of HF spectral occupancyover Europe

For the purpose of taking occupancy meas-urements the HF spectrum was divided into 95allocations, which are shared by twelve differ-ent types of user. These allocations are based

Fig. 7. The atmospheric noise level on the time of the total eclipse.

Fig. 8. Examples of measured day and night congestion at the -117 dBm signal threshold level.

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on the ITU frequency allocations for Region 1ITU WARC (1979), but include some variationmodifications as they were interpreted in ac-cordance to the measurement of spectral occu-pancy. The measure of occupancy used is con-gestion, which is defined as the probability ofplacing at random, a bandpass filter of a givenbandwidth in a given ITU defined frequencyallocation, such that the RMS value of the fil-ter output signal exceeds a predefined thresh-old level.

2.3.1. Measurement system

The rural measurement sites were situatedat Baldock (UK), Linköping and Kiruna (Swe-den) and Munich (Germany). The measurementreceiver was the Rohde and Schwarz R&SESH3, and the calibrated active measurementantenna at each site was a low-angle monopole(R&S HE010). The system at each site, and the

measurement procedure have been describedpreviously Gott, G.F. et al. (1997). At each site,during a weekly congestion measurement, thereceiver frequency was incremented througheach frequency allocation, using typically a1kHz step, a 1 kHz measurement bandwidthand a 1s dwell time. The fraction of the alloca-tion spectral width for which the RMS signallevel at each step exceeds a defined field-strength threshold level defines the occupancyor congestion for that frequency allocation, forthe corresponding threshold level, measure-ment bandwidth, time of day, and sunspot num-ber. Figure 8 shows examples of HF spectraloccupancy at all sites where different types ofuser appear in different colour.

Diurnal measurements of occupancy wereobtained once a week provided that no othermeasurement campaigns were in progress. us-ing a 90 ms dwell time at each increment. TheHF spectrum was monitored in less than anhour by employing a variable frequency incre-ment algorithm.

The model for stable-day is:

yk = Ak + (B0 + B1fk + B2 f2k )20 log10(E)

+(C10 + C11fk C12 f2k )log10(BW)

+(C20 + C21fk)[log10(BW2)]2

+(D10 + D11fk + D12 f2k)cos(qw)

+(D20 + D21fk + D22 f2k)sin(qw)

+(D30 + D31fk + D32 f2k)cos(2qw)

+(D40 + D41fk + D42 f2k)sin(2qw)

+(G10 + G11fk + G12 f2k)cos(qlong)

+(G20 + G21fk + G22 f2k)cos(qlat)

+(G30 + G31fk + G32 f2k)sin(qlat)

+(H10 + H11fk + H12 f2k)SSN

+(H20 + H21fk + H22 f2k)SSN cos(qw)

+(H30 + H31fk + H32 f2k)SSN sin(qw)

+(J10 + J11fk + J12 f2k)SSN cos(qlong)

+(J20 + J21fk + J22 f2k)SSN cos(qlat)

+(J30 + J31fk + J32 f2k)SSN sin(qlat)

The model for stable-night is:

yk = Ak + (B0 + B1fk + B2 f2k )20 log10(E)

+(C10 + C11fk C12 f2k )log10(BW)

+(C20 + C21fk)[log10(BW2)]2

+(D10 + D11fk + D12 f2k)cos(qw)

+(D20 + D21fk + D22 f2k)sin(qw)

+(D30)cos(2qw)

+(D40 + D41fk + D42 f2k)sin(2qw)

+(G10 + G11fk + G12 f2k)cos(qlong)

+(G20 + G21fk + G22 f2k)cos(qlat)

+(G30 + G31fk + G32 f2k)sin(qlat)

+(H10 + H11fk + H12 f2k)SSN

+(H20 + H21fk + H22 f2k)SSN cos(qw)

+(H30 + H31fk + H32 f2k)SSN sin(qw)

+( J11fk + J12 f2k)SSN cos(qlong)

+(J20 + J21fk + J22 f2k)SSN cos(qlat)

+(J30 + J31fk + J32 f2k)SSN sin(qlat)

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This compromise does not affect signifi-cantly the resulting congestion values, based onRMS signal measurements. Figure 9 shows adiurnal congestion measurement for allocationsresiding in the upper and lower regions of theHF spectrum.

2.4. Models of HF spectral occupancy over asunspot cycle

The statistical occupancy models are basedon weekly measurements made since 1990,which apply to stable-day and stable-nightionospheric conditions when using a calibrat-ed monopole antenna. Congestion measure-ments for every frequency allocation weremade at each site, typically every 14 days, forboth stable-day and stable-night ionosphericconditions.

These conditions corresponded to two peri-ods, each of duration about three hours, cen-tered in time on local midday and on local mid-night, and give rise to very different occupancycharacteristics.

The models may be used in conjunctionwith frequency predictions to advise operatorson the occupancy they may encounter, and howthis varies with field-strength threshold level,frequency, time, bandwidth, location andsunspot number.

This may result in the use of a frequencywhich is suboptimum for propagation, butwhere the estimated occupancy is acceptable. Itis anticipated that such occupancy models mayalso be useful to communication system design-ers, to HF ground-wave users (who may choosefrequencies to avoid sky-wave interference),and to study groups who are concerned with thedetermination of international frequency as-signments.

2.4.1. Models

In each case yk is the model index functionfor the kth frequency allocation (k=1, 2,…, 95),fk is the centre frequency of allocation k (MHz),E is the field-strength threshold (V/m), BW isthe measurement filter bandwidth (kHz), SSN

is the sunspot number, θw defines week of year(2π[week-0.5]/52-where week varies in therange 1 to 52), θlong represents (2π_longi-tude/360) (longitude in degrees), θlat represents(2π_latitude/360), and A,B,…, J are estimatedmodel coefficients. Longitudes west of theGreenwich Meridian are entered as negativevalues.

The minimum field-strength threshold forwhich the models apply has been determinedfrom measurements of background atmospher-ic noise.

The sunspot number is based on the month-ly average, published by the World Data Centreat the Rutherford Appleton Laboratories. It waschosen to model this parameter over two cyclesto permit the extrapolation properties of themodel in time to be investigated. When futurevalues of congestion are to be estimated, it isnecessary to estimate the future sunspot num-ber.

2.4.2. Goodness of fit

An important consideration is goodness offit of the model to the experimental data, wherethe difference between each of the measuredand fitted congestion values is referred to as aresidual. Statistically, goodness of fit may bedefined by the residual scaled deviance Dwhich is equal to twice the difference betweenthe maximum achievable log likelihood andthat attainable under the fitted model (Maccul-lah and Nelder, 1989). In the analysis, theresidual mean deviance d is used d = D/(R-p)where R is the number of experimental conges-tion values, and p is the number of independ-ently estimated model parameters.

The scaling parameter is unity for the logis-tic model.

The addition of further significant parame-ters to a model improves the fit, and the good-ness of fit is indicated by the closeness of theresidual mean deviance d to unity. The valuesof residual mean deviance for the stable-dayand stable-night models are 7.8 for day and 8.2for night, which signify very good fit to the ex-perimental data.

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2.4.3. Extrapolation in time and space

To investigate the ability of the models toestimate future congestion values, a stable-dayfour-site model was determined independentlyfor 355,134 congestion measurements madeover the period 1990 to 1998 inclusive.

This model was then used to estimate sta-ble-day congestion values for each of the years1999, 2000 and 2001, using estimated sunspotnumber. Modelled and measured congestionvalues were then compared for the extrapolatedperiods.

The accuracy of extrapolation is very good,and is essentially equivalent for all the threeyears 1999, 2000 and 2001, even although thesunspot number is increasing rapidly over thisperiod. This accuracy is in part due to the mod-elling only of the systematic components of thecongestion data. This exercise has been repeat-ed using a smaller data set for the model, andextrapolating over a greater time. A stable-daythree-site model was derived from 219,671measurements made over the period 1990 to1995, which cannot include the Kiruna meas-urements.

This model was then used to estimate sta-ble-day congestion values for Baldock,Linköping and Munich for each year 1996 to2001 inclusive. The results again show that thetime-extrapolation properties of the model arevery good.

For extrapolation in space a stable-daythree-site model was determined for conges-tion measurements made over the period 1990to 2001, including data from Baldock,Linköping and Munich, but excluding datafrom Kiruna. The 45,280 congestion valuesmeasured at Kiruna (corresponding to fouryears of operation), were then estimated by themodel by entering the latitude and longitudeof the Kiruna site, and comparing estimatedand measured congestion values. Similarly,three further three-site models were deter-mined, excluding data from Linköping, Mu-nich and Baldock in turn. In each case, allmeasured congestion values at the excludedsite were estimated and compared with meas-ured values.

Very good extrapolation in space was

achieved for Kiruna and Munich, and very goodinterpolation for Linkoping.

The ability to extrapolate to Baldock wasless good: however this may be expected asthe measurements from Kiruna, Linkopingand Munich have little dependence on longi-tude.

2.5. Neural network prediction of the diurnalvariation of HF spectral occupancy

The aim of this work was to investigate thepossible application of artificial neural net-works to predict the diurnal variation of spec-tral occupancy in the HF spectrum. In particu-lar, a preliminary study for the development ofa single ITU allocation model for the diurnalvariation of HF spectral occupancy overLinköping (Sweden) was made. Furthermorethe model specification was extended in fre-quency to cover the whole of the HF spectrum(all ITU allocations) and in latitude by includ-ing diurnal measurements taken at Kiruna(Sweden). The dataset of diurnal occupancymeasurements used for the model developmentwas taken over a period of six years (April 1994to January 2000).

The model may be used to predict the occu-pancy that may be experienced by an HF radiosystem situated over Sweden, for a given set ofparameters for the particular ITU allocation.The prediction of spectral occupancy in the HFspectrum can be viewed as a multivariate re-gression problem consisting of a nonlinearmapping from a set of input variables describ-ing current ionospheric conditions onto a singleoutput variable representing the likelihood ofan occupied channel. Neural Networks can pro-vide an elegant solution to this problem sincewith a suitable network complexity they can ap-proximate any nonlinear mapping to an arbi-trary degree of accuracy.

2.5.1. Model development

In the preliminary work, only measurementsat Linköping for allocation 72 which is dedicat-ed to Broadcast users (21.450 - 21.870 MHz)

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was considered in the modelling process so thecongestion values per measurement taken intoaccount were 120. The total number of meas-urement sessions carried out is 197 which cor-responds to a total of 23640 congestion valuesfor the corresponding allocation. In this workthe Levenberg-Marquardt backpropagationneural network algorithm was used, since it ap-pears to be the fastest method for training mod-erate-sized feed-forward networks.

The variation of occupancy of the HF spec-trum due to skywave signals is primarily depen-dant on prevailing ionospheric conditions. Theinput parameters for modeling congestion wereselected so as to represent the known variationsthat give rise to the most characteristic proper-ties of the Ionosphere as a communicationschannel. Solar activity has an impact on ionos-pheric dynamics which in turn influence theelectron density of the ionosphere. Thus solar

activity is proved to be highly correlated withcongestion. This long-term variation was in-cluded as a separate input parameter with a run-ning mean value of the daily sunspot number(R) which is a well-established index of solaractivity. After a thorough investigation a 50-dayrunning mean value of the daily sunspot num-ber R50 was found to be the optimum parame-ter to represent the long-term variation of con-gestion since it achieves the minimum RootMean Squared Error (RMSE). A short-termstrong dependency between interference andthe hour of the day is clearly evident by observ-ing fig. 9. We therefore include hour numbers inthe inputs to the Neural Network.

The hour number, hour, is an integer in therange 0 � hour � 23. In order to avoid unreal-istic discontinuity at the midnight boundary,hour was converted into its quadrature compo-nents according to

Fig. 9. Typical diurnal congestion variation in the upper and lower part of the HF spectrum.

Fig. 10. Examples of diurnal measured and predicted congestion in allocation 72 (21.450-21.870 MHz).

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(2.1)

and

(2.2)

A seasonal variation is described by day num-ber daynum in the range 1 � daynum � 365.This variation is due to the response of the crit-ical frequency of the F2 layer, which acts as theprincipal reflector of radiowaves in the iono-sphere for long-distance transmission, to theseasonal change in extreme ultraviolet (EUV)radiation from the Sun. Again to avoid unreal-istic discontinuity between December 31st andJanuary 1st daynum was converted into itsquadrature components according to

(2.3)

and

(2.4)

Signal threshold level was also incorporatedas an input parameter (ST) since it is obviousfrom fig. 9 that it has a profound effect on meas-ured congestion. This is quite reasonable sinceincreasing the threshold would normally corre-spond to fewer channels exceeding its value sothis would result in a lower congestion value.The network used was a fully connected two-lay-

2365

cosday cosdaynum

π= c m

2365

sinday sindaynum

π= c m

224

coshour coshourπ= b l

sinhour sinhour

224

π= b l er neural network, with 6 input, 11 hidden and 1output neurons. Both its hidden and output neu-rons had logistic sigmoid activation functions.The number of hidden neurons was determinedby trial and error.

This network was trained using the Leven-berg-Marquardt backpropagation algorithm for afixed number of epochs. There was no concernfor overfitting since the number of free parame-ters of the network was very small compared tothe number of examples used for its training. Allinputs to the network were normalized settingthe minimum value of each input to -1 and itsmaximum value to 1. No normalization wasneeded for its outputs since they were already inthe interval (0,1).

The experiments were carried out using 10random splits of the whole data set into trainingand test sets. More specifically, for each split 20out of the 197 measurement sessions were ran-domly selected to form the test set, and the re-maining 177 were used to form the training set;all 120 congestion values of each session weretreated as a group and were placed either in thetraining or in the test set. The results reportedhere were obtained by averaging the results ofall 10 splits. In order to determine the signifi-cance of each of the model inputs the modellingprocedure was repeated five times, with each ofinput parameters being excluded each time. Theincrease in the RMSE with respect to the fullparameter model was used as a quantitative

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L in k o p in g

K i ru n a

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(a) 2.500-2.850 MHz (b) 15.100-15.600 MHz

Fig. 11. Typical diurnal variation of congestion in the upper and lower HF spectrum.

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measure of the impact of each parameter to themodel performance.

The RMSE and the correlation coefficientbetween the network predictions and the meas-ured congestion values was 0.0284 and 0.93 re-spectively. Both the low RMSE value and theclose to unity correlation coefficient valuesshow that the trained neural network can suc-cessfully predict congestion in the allocationunder consideration.

2.5.2. Predicting the diurnal variation of HFspectral occupancy over Sweden

In this work the neural network approach wasapplied for the prediction of the temporal varia-tion of congestion within a frequency allocationas it was described before and extended to encap-sulate the spatial and frequency dependence by

including congestion measurements covering theentire HF spectrum from two measurement sitesin Sweden. Examples of typical variation ofmeasured occupancy at the two sites with time-of-day are given in fig. 11 for allocations residingin the lower and upper regions of the HF band.The variation of occupancy with time-of-day wasfound to differ significantly across the HF band.Allocations in the lower portion of the HF bandexhibit different characteristics to those residingin the upper portion of the band. An example oftypical occupancy encountered in the lower por-tion of the HF band is given in fig. 11a, fromwhich significant diurnal variation of congestioncan be observed, peaking during night-time. Con-versely, in the upper portion of the HF band acomplete reversal of diurnal variation is observedas shown in fig. 11b, which again shows signifi-cant diurnal variation, but in this case occupancyis highest during day-time.

Fig. 12. Long-term and seasonal variation of congestion.

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5.950 - 6.200 MHz 7.100 - 7.300 MHz 9.500 - 9.900 MHz

11.650 - 12.050 MHz 13.600 - 13.800 MHz 15.100 - 15.600 MHz

17.550 - 17.900 MHz 21.450 - 21.850 MHz 25.670 - 26.100 MHz

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During years of low solar activity, the lowerfrequencies tend to be utilized more, while dur-ing years of high solar activity the higher fre-quencies are also used. This is demonstrated infig. 12 where congestion measured at Linköpingis plotted (with dots) for Broadcast allocationsdistributed across the HF spectrum togetherwith the 50-day running mean of the dailysunspot number (depicted as a continuous linein the background).

This figure shows that congestion is signifi-cantly higher for high sunspot number periodsin allocations 72 (21.450 - 21.850 MHz) and 86(25.670 - 26.100 MHz).

The same figure also demonstrates the sea-sonal variation of congestion in each allocation.This is attributed to the seasonal variation of thecritical frequency of the F2 layer, which acts asthe principal reflector of radiowaves in the ion-osphere for long-distance transmission, due toits response to seasonal change in extreme ul-traviolet (EUV) radiation from the Sun. Bothsolar cycle and seasonal variation are manifest-ed differently in each allocation underlying thedifferent occupancy characteristics at each fre-quency. In allocation 22 (5.950 - 6.200 MHz)the increasing sunspot number appears to ex-

hibit an increasing amplitude of seasonal varia-tion whereas in allocation 27 (7.100 - 7.300MHz) it seems to have a decreasing effect onthe average congestion level. In allocations 42(11.650 - 12.050 MHz), 48 (13.600 - 13.800MHz) and 53 (15.100 - 15.600 MHz) residingin the middle of the HF spectrum the solar cy-cle effect appears as an increasing average anda decreasing amplitude in the seasonal conges-tion variation.

2.5.3. Model development

A Neural Network was trained to predict thecongestion in each allocation based on the inputparameters. The neural networks used were ful-ly connected two-layer networks with 7 input(including a binary parameter to indicate thesite of the measurement) and 1 output neurons.Both their hidden and output neurons had logis-tic sigmoid activation functions. A differentnumber of hidden neurons was used for each al-location due to their difference in complexityand occupancy characteristics. The optimumnumber of hidden neurons was determined byforward selection. Each network was trained

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Predicted

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Fig. 13. Examples of diurnal measured and predicted congestion over Sweden.

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using the Levenberg-Marquardt backpropaga-tion algorithm for a fixed number of epochs(100). There was no worry of overfitting sincethe number of free parameters of the networkswas very small compared to the number of ex-amples used for their training. All inputs to thenetworks were normalized setting the mean val-ue of each input to 0 and its standard deviationto 1. The experiments were carried out using a10-fold cross-validation procedure.

The 268 measurement sessions were splitinto 10 parts of almost equal size and the pre-dictions for each part were obtained using aneural network trained on the examples of theother 9 parts. Both the low RMSE value andthe close to unity correlation coefficient valuesfor most allocations, demonstrated that thetrained neural networks can successfully pre-dict congestion. This is also demonstrated byexamples of measured and predicted conges-tion values (fig. 13).

2.6. Using neural networks for short-termforecasting the likelihood of interferenceto groundwave users in the HF spectrum

In this study a Neural Network approach wasproposed for the short-term forecasting of thelikelihood of interference experienced by HFgroundwave communication systems. In particu-lar this section describes the development of neu-ral network models to indicate the degree of spec-tral congestion in frequency allocations in thelowest part of the HF spectrum (1.6 to 4 MHz) 1hour in advance, as a function of the present con-gestion level, time of day, season, and field

strength threshold. This study was a continuationof previous work (Haralambous et al. 2007),where Neural Networks were used for the predic-tion of interference when there is no means ofmeasuring it. In this paper the possibility forshort-term forecasting of the same parameter isexplored in the context of near real time channelevaluation (RTCE), which implies recent meas-urements of the target model parameter incorpo-rated as inputs to the neural network. This ap-proach is applicable in the case of a system whichis capable of measuring interference and can usethat information to obtain a short-term forecast ofthe measured parameter 1 hour in advance.

2.6.1. Model parameters

The parameters used to describe the diurnaland seasonal variation were again sinusoidalcomponents identical to those described in Sec-tion 2.5.1. Regarding the effect of solar activity afurther investigation revealed that the congestionvariation due to the long-term variation of solaractivity is to a large extent described by the cur-rent value of congestion Q(h) (where h is the cur-rent hour) which was included as an additionalmodel input. Of course this implies that the sys-tem should be able to measure the current con-gestion value in order to forecast the next con-gestion value Q(h+1) 1 hour in advance. Thischaracteristic poses a significant requirement onthe system in question but on the other hand al-lows for the model to operate without externaldata to express the solar activity conditionswhich would necessitate a provision of an updat-ed solar index figure. Signal threshold level was

Fig. 14. Examples of diurnal measured and predicted congestion over Sweden.

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PredictedMeasured

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also incorporated as an input parameter since ithas a profound effect on measured congestion.

2.6.2. Results

In this study each neural network wastrained to forecast the congestion Q(h+1) of agiven allocation 1 hour in advance based on thesinhour (for h+1), coshour, sinday, cosday, cur-rent congestion value Q(h) and signal thresholdparameters. All networks used had exactly thesame structure. They were fully connected two-layer neural networks, with 6 input, 5 hiddenand 1 output neurons. Both their hidden and out-put neurons had logistic sigmoid activationfunctions. The number of hidden neurons wasdetermined by trial and error. More specifically,networks with 3 to 15 hidden neurons were triedand our choice was based on the fact that inmost cases there was no significant reduction inthe RMSE when increasing their number tomore than 5. These networks were trained usingthe Levenberg-Marquardt backpropagation al-gorithm for a fixed number of epochs (100).

2.7. Conclusions

Models of HF occupancy over northern Eu-rope have been studied for a complete sunspotcycle. Very good accuracy of fit is achieved tothe very large experimental data set. The accura-cy with which the models may be extrapolated intime and in space has also been shown to be verygood. In particular, the extrapolation using themodels in both time and in space to estimate con-gestion at Kiruna is considered excellent, espe-cially given the high latitude of the site and therapidly changing sunspot number over the peri-od of extrapolation. Neural network models havebeen developed to describe the diurnal variationof occupancy within frequency allocations of theHF spectrum. The models were developed fromextensive diurnal occupancy measurements tak-en over a period of six years. The remarkableagreement between the neural network predictedvalues and observed congestion data signifies theability of the resulting models to provide a quan-titative description of the diurnal, seasonal and

long-term trend in the variability of congestion.The proposed networks require the day number,hour, 50-day running mean of the daily sunspotnumber and signal threshold as inputs, and pre-dict the corresponding congestion value, whichindicates the likelihood of interference under thegiven conditions.

Finally measurements over the HF bandduring the 29 March 2006 total solar eclipse inAntalya revealed the variation of atmosphericnoise under the eclipse conditions.

Acknowledgements

The authors are grateful to Prof G.F. Gott,Prof P.J. Laycock and P.R. Green of the Univer-sity of Manchester for providing relevant back-ground experience, and to M. Bröms, S. Bobergand Bengt Lundborg (FOI Swedish DefenceResearch Agency, Linköping, Sweden) for sup-plying the measurement data for the develop-ment of the neural networks.

REFERENCES

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AZEVEDO, J.A. (2007): Antenna pattern control of planar ar-rays for long-range communications, IRI/COST 296Workshop on Ionosphere Modeling, Forcing andTelecommunications, (Prague, Czech Republic).

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