Influence of Terrain on Multipath Propagation of Fm Signal

Journal of ELECTRICAL ENGINEERING, VOL. 56, NO. 5-6, 2005, 113–120

INFLUENCE OF TERRAIN ON MULTIPATH PROPAGATION OF FM SIGNAL

J´an Klima ∗ — Mari´an Moˇzucha ∗∗

FM signal propagating through the troposphere interacts with the terrain as a reflecting plane. These reflected signals are not included into calculations and predictions of the field strength. The reason is simple — it is too difficult for processing, and demanding high quality data. For recent capabilities of computers and resolution level of digital terrain models this is not an irresolvable problem. In the report the authors show a practical demonstration how to include the reflected FM signals into the field strength calculations as well as the comparison with standard methods of field strength predictions. K e y w o r d s: digital terrain model (DTM), reflections, diffraction, multipath propagation

1 INTRODUCTION Here GRF represents a set of points of the terrain, z is the height in a point located in coordinates [x,y], A digital terrain model, as a discrete field of repre- KN F M is the curvature of the terrain as it is seen from sentative and positionally expressed points of the terrain the transmitter, FF M is the form, γF M is the slope, AF M and its approximation equations securing its continuity is the aspect, and δexp F M is irradiation — all from the [8] can serve, besides many other tasks, as a tool for lo- direction of the transmitter. cating, testing and calculating the reflecting planes for We will come from the known fact that the received propagating FM signals. When calculating the reflected field strength (E) of the radio signal propagated above a FM signals we cannot distinguish all, only statistically vertically dissected terrain can oscillate by ∆E = ±6 dB important directions expressed on the chosen resolution level. That is why measuring the field strength of FM sig- due to the reflected signals (Fig. 1). nal is a measurement of an integral quantity — it means The existence of reflection planes σI [1] between the of all possible inducted streams on the receiving antenna. transmitter Tx and receiver Rx is taken without testing An antenna constructed in the form of antenna field re- reflections in 3D dimensional space. The main reasons ceiving FM signals from different directions and summing are: them separately does not exist but we can find these di- – there is no exact procedure how to calculate statisti- rections iteratively. cally important reflected signals, In radiocommunication literature there are attempts – it is assumed that these reflections can be neglected to sum up direct and reflected waves [2], mainly those (though practice shows the opposite), reflected from determined shapes of obstacles — build- – it is difficult to describe the shapes and other parame- ings. Terrain with its irregular shape was not dealt with ters of all important obstacles on a huge area (though in these calculations. We will proceed from the assump- it is not a problem to get statistical values). tion that thanks to the additional field strength of FM In some special cases, the terrain with its configuration signal reflected from the terrain — not only on the line and reflection parameters can become a massive reflect- between the transmitter and receiver — we can get better predicted results. We will also assume that we can ing plane, this is why we are to predict with some sta- express that shape of objects of majority of obstacles on tistical error. If we considered a valley with dimensions the terrain with statistical methods, so we will get most responding to the 3D dimensions of the first Fresnel el- of reflected planes. As for the terrain, most calculation lipsoid (Fig. 2), then we could get an extreme increase of methods count with reflections only on a vertical pro- the field strength [10]. file though it does not correspond with reality. To take all reflections into accounts we can use effective values of morphometric parameters of the terrain such as elevation, 2 INPUT CONDITIONS AND PRESUMPTIONS form (convex, concave or linear), slope, aspect and angle of irradiation: 1. We have a terrain GRF (1) defined as a continuous topographic plane with continuous changes of its mor-

GRF = z, KN F M ,FF M , γF M , AF M , (δexp)F M . (1) phometric parameters, in the form of a digital terrain ∗ Department of Physics, Faculty of Natural Sciences, Universitu of Matej Bel, Tajovsk´eho 74, 974 01 Bansk´aBystrica, ∗∗ E-mail: [email protected]; Trans World Radio–Slovakia, Banˇselova 17, 821 04 Bratislava 2, Slovakia, E-mail: [email protected]

ISSN 1335-3632 c 2005 FEI STU 114 J. Klima — M. Moˇzucha: INFLUENCE OF TERRAIN ON MULTIPATH PROPAGATION OF FM SIGNAL

Tx Tx Rx a) Rx Tx Rx s 1 s s 2 3 b) d c)

Fig. 1. Reflection planes σ . Fig. 2. Valley with dimension of the first Fresnel zone a) side view, b) upper view, c) profile view.

T Tx x R N x L O A1 d LN d LN d A3 0 d exp Rx A2

Fig. 3. Multipath of FM signal from transmitter Tx to receiver Fig. 4. Equal size of the angle of incident δexp and angle of Rx . reﬂection δ0 in the same plane.

model (DTM) deﬁned by approximation equation 3 GEOMETRIC EXPRESSION

z = f(x,y) . (2) The impact angle δexp is equal to the angle of reﬂec- tion δ0 , so the reﬂected signal will be in the same plane, (Fig. 4).

2. We have a known and deﬁnite set of objects (for- The normal N~ of the terrain in point Ai[xi,yi,zi] is est, water planes, urban objects etc) creating the land expressed as: cover with its height and geometric (morphometric)

parameters. N~ = {Nx, Ny, Nz} , (3) 3. We will work with radio FM signal from the frequency band h87.5, 108i (MHz). where 4. Important interactions between the terrain and FM

signal are mathematically described by geometric and Nx = |N~ | cos αN = sin γN · cos AN , wave optics. N = |N~ | cos β = sin γ · sin A , 5. Only important and steady reﬂections will be taken y N N N into account. The neglected reﬂections are expressed Nz = |N~ | cos γN = cos γN by means of statistics (included in the mean values of

the field strength). where cos αN , cos βN , cos γN are direction angles (Fig. 5) 6. Calculation of the field strength as a sum of direct which are expressed through relations and reflected signals in huge areas (Fig. 3) is still in- sufficiently examined, hence there is a problem how to −zx −zy cos αN = , cos βN = , verify the outputs. 2 2 2 2 zx + zy + 1 zx + zy + 1 7. DTM is created by means of interpolation, smoothing q q 1 and various generalization methods — a lot of infor- cos γN = . 2 2 mation is lost due to these processes. The angle of re- zx + zy + 1 flection can be rapidly changing in a real terrain, while q

there is a smooth terrain in DTM. where zx and zy are partial derivatives of function (2). 8. We do not know the reﬂection ratio of the terrain and The unit vector |N~ | = 1 is expressed by equation its land cover, hence it would be best to ﬁnd them 2 2 2 iteratively. cos αN + cos βN + cos γN = 1 . (4) Journal of ELECTRICAL ENGINEERING 56, NO. 5–6, 2005 115

In the sense of Fig. 4, let us deﬁne the plateau σLN where ~ ~ zt both vectors L and N are placed. We want to ﬁnd the g L Ni angle between these vectors. We will use the dot product a b g za L L N of the two vectors L~ and N~ [8]: yt b AL N a ~ ~ ◦ xt N ya L · N = cos δLN = sin δexp δLN + δexp = 90 . (7) t xa n In scalar form

L~ · N~ = N L + N L + N L Fig. 5. Unit vectors N~ and L~ . x x y y z z = cos αN cos αL + cos βN cos βL + cos γN cos γL =

−zx −zy sin γL ·cos AL + sin γL ·sin AL 2 2 2 2 Tx g L n zx + zy + 1 zx + zy + 1 q q 1 d 0 g R a) FM x + cos γL . (8) d exp 2 2 zx + zy + 1 Ai q Tx g L n From (7) and (8) we can get d exp Rx b) g FM

d 0 (−zx∆xat) + (−zy∆yat) + ∆zat = sin δexp . (9) A 2 2 2 2 2 i zx + zy + 1 ∆xat + ∆yat + ∆zat q p Fig. 6. Reﬂections.

From relation (8) we can work with angles AL and γL , FM signal represented by the electromagnetic wave and γF M , AF M , γ0, A0 , in sense of Fig. 6. interacting with the terrain in a given point Ai[xi,yi,zi] can be expressed in a similar way: ◦ ◦ ◦ ◦ ◦ γN < 45 , γF M < 45 , γ0 > 0 , AL = h0 , 360 ), L~ = {Lx, Ly, Lz} , (5) ◦ ◦ ◦ ◦ (10) AF M = h0 , 360 ) , A0 = h0 , 360 ) where ◦ ◦ where AF M = 180 −AL +AN = 180 −AL +arctg zy/zx , Lx = cos αL = sin γL · cosAL , AL is the direction of the FM signal towards the south Ly = cos βL = sin γL · sin AL, (Fig. 5):

Lz = cos γL = cos γL , ~ 2 2 2 2 2 for |L| = 1 Lx + Ly + Lz = 1 . (6) γF M = γN cos AF M = arctg zx + zy cos AF M , q ya − yt Direction angles cos αL , cos βL , cos γL are expressed in A = arctg , L x − x a similar way, see Fig. 5: a t z − z γ = arctg a t , xa − xt L ~ cos αL = |L| 2 2 2 (xa − xt) + (ya − yt) + (za − zt) AN = zy/zx , p ∆xat = , ~ 2 2 2 ∆x2 + ∆y2 + ∆z2 |L| = (xt − xa) + (yt − ya) + (zt − za) , (11) at at at p 2 2 2 p ya − yt |O~ | = (xa − xr) + (ya − yr) + (za − zr) . (12) cos βL = 2 2 2 (xa − xt) + (ya − yt) + (za − zt) p p ∆y = at , Here O~ is the vector of FM signal reflected from the 2 2 2 ∆xat + ∆yat + ∆zat terrain (Fig. 4). p za − zt cos γL = All cases of the behaviour of FM signal are derived 2 2 2 (xa − xt) + (ya − yt) + (za − zt) from the laws of reflection and are implemented into the p ∆z developed software application, with consideration of the = at . 2 2 2 visibility of the reflected FM signal. ∆xat + ∆yat + ∆zat p 116 J. Klima — M. Moˇzucha: INFLUENCE OF TERRAIN ON MULTIPATH PROPAGATION OF FM SIGNAL

A2 E2 E 3 Etotal A3 E5 Rx

A = T E1 1 x E1 E E 2 E 4 E5 b) 4 E3 a) A5 A4

Fig. 7. Principle of summing of the ﬁeld strength of FM signals: a) in space, b) graphically.

rections we get signals of various ﬁeld strengths, and this will be expressed in their summing and adding to the ﬁeld

Tx strength from the direct FM signal by summing x,y,z Border of visibility Rx components of particular vectors E~ representing the size and direction of the field strength: a) Potential b) reflection plane 2 2 2 E = Xi + Yi + Zi . (13) qX X X Fig. 8. Potential reflection plateau on a planar terrain, with curvature of the Globe a) visible from Tx , b) visible from Rx . On the basis of experiences gained while developing module “Reflections”, a phase shift was also implemented into calculations. To get them we have to calculate the angles of A and γ see the Appendix). Then Input data (DTM,Tx),ranges (radius,angle) and methods 2πd E = f P , d R cos i , (14) i t i i λ

i Creating ray (angle,radius) between i Map output Tx [xt,yt,zt] and Rxi[xri,yri,zri] E0 = f P1, |L~ | (15) Angle Radius Potential and real Testing of visibilityof terrain from Tx reflectionplanes where Pt is the power of transmitter (kW), di is the sum of the incident and reflected trajectories of the signal Aspect of reflection (di = |L~ |+|O~ |) (km), and Ri is the reflection ratio of the Creating ray (angle,radius) between angle A0 towards Rxi (horiz.position) Rxi [xti,yti,zti] and Rxj[xrj,yrj,zrj] terrain reflection plateau (to be continued in Appendix). According to (III of Appendix), the sum of all signals g Reflection angle 0 received by the antenna is expressed by relation Testing of visibilityof terrain from Rxj j towards Rxi (vertical position)

Radius 2 2 2 Testing reflection planes for Rxi and Angle between E = Xi + X0 + Yi + Y0 + Zi + Z0 . angle of incident don Rxi direct and refleted qX X X signals (16) j E i.j Calculation of field strength of direct FMsignal onR xi Angle Total field strength E of FM 5 LIMITATIONS signal Summing of field strength of direct and reflected signals on Rxi In the developed software application including the testing reflection planes (Fig. 8) and calculation of re- Map output flected signals (Fig. 9) some limitations were accepted: – only points that are within the Fresnel zone were accepted [7], with possibility of setting also 1/3 of the Fig. 9. Calculation algorithm of reflected signals. first Fresnel zone, – only points within an angle of 15◦ from the receiving 4 SUMMING UP antenna are considered in order to make the same conditions as during a measurement of the signal, Summing FM signals from individual directions will be – relative to a given resolution level, the exact place of made as scalar summing of angular differences (Fig. 7). incidence of FM signal on the terrain was not calcu- Let us suppose that we have made measurements by lated within a pixel of DTM, for we count with inter- means of a directional antenna for the direction of trans- polated heights and its interpolated geometric (mor- mitter Tx . Further let us suppose that from various di- phometric) parameters, Journal of ELECTRICAL ENGINEERING 56, NO. 5–6, 2005 117

– the reﬂectivity ratio had to be found by means of S n dS iteration. a ,, , r r 6 DECISIVE AREA OF PROPAGATION r Tx Rx AND REFLECTION OF RADIO WAVES, FRESNEL ZONES

During the transfer of a radio wave from one space dS n point to another we can ask a question whether the whole a , inﬁnite space or only a ﬁnite part of it takes part in the r r,, R transfer.

Tx r1 r2 Rx Fresnel showed that we could specify a certain area; behind its boundaries all the obstacles have no influence on the distribution of the field. This area is called a S “decisive area” for the propagation of energy (or for the propagation of radio waves). For the specification of the dimensions of the decisive Fig. 10. Decisive area for propagation of radio waves. wave and its shape the Huyghens principle is used. This principle says that every element of the S plane which bounds the transmitter is becoming a secondary source transmitting a spherical wave and the total field in the area of receiving is given by the sum of these elementary waves (Fig. 10). R3 R 2 As the shape of plane S can be arbitrary, we can have R1 it as an infinitely big plane orthogonal to the trajectory of the direct wave (connection between Tx and Rx ), Fig. 10. The distance of this plane from the point of Tx is r1 and from point of Rx is r2 (r1 +r2 = r). We can calculate the field strength for this chosen area in a point of Tx on the basis of the known Kirchhoff solution or Kottler solution S of discontinuities of derivations on a outline curve in a form of:

− ′′ r1 r2 Rx jkr (P ) j (S) 1 + cos α e Tx 1.zone E = E ′′ S (17) λ ZS 2 r 2.zone 3.zone where r′′ is the distance of the elementary plane of dS of the Fig. 11. Deﬁnitions of Fresnel zones. plane of S from the point of Tx , α is the angle between the vertical and the plane of S (P) E with the direction to the point of Rx , E 0 k is the wave number, 2 λ is the wavelength. 1 For the present, let us consider the ﬁeld strength in every point of the plane of S in the form

0 1/3 1 23 4 5 6 ′ S/S1 −jkr (S) e E = K ′ (18) Fig. 12. Changes of the field strength in point receiver during r enlargening of impermeable (shading) obstacle. where K is some unknown constant value, r′ is the distance of point Tx of from the elementary plane dS , – a forest was not considered as a reflection plane, for Fig. 10 a,b. its diffusive and absorption impacts By inserting (18) into (17) we will get – urban objects were considered as a reflection plane un- ′ ′′ −jk(r +r ) der special conditions (sufficient height, suitable as- (P ) j 1 + cos α e etc E = K ′ ′′ dS . (19) pect, ), λ ZS 2 r + r 118 J. Klima — M. Moˇzucha: INFLUENCE OF TERRAIN ON MULTIPATH PROPAGATION OF FM SIGNAL

Fig. 13. Visibility from Tx and Rx , and reﬂection planes.

′ ′′ ′ λ The phase of the wave on the way of (r +r ) is ψ = k(r + (r1 + r2) ≤ n , by the simple modification we will get a ′′ 2 r ). The phase of the wave on the way of (r1 + r2 = r) relation for calculating its radius: is ψ0 = k(r1 + r2). To bound the “decisive area” for the propagation of nλr r R = 1 2 (22) radio waves, Fresnel was proceeding this way: he asked a n r r question whether all elementary planar radiators of dS on a plane of S contribute to the total value of the field When we transfer plane S , then circles with radius strength in a point of R with the same amount or not. x R describe the surface of an ellipsoid. The areas of the To solve it, he divided plane S into the so-called Fresnel n zones. Their dimension is specified with these conditions: space between two neighbouring ellipsoids (Fig. 11b) are spatial Fresnel zones.

π(n − 1) ≤ ψ − ψ0 ≤ nT ; n = 1, 2, 3,... Though the areas of individual Fresnel zones SF = 2 2 r1r2 π Rn + Rn−1 = nλ r in plane S are equal, the ampli- or tude of field strength in point Rx decreases with increasing number of the Fresnel zone n, for the term (1+cos α) ′ ′′ is decreasing and the distance (r′ + r′′) is increasing. So, (n − 1)λ/2 ≤ (r + r ) − (r1 + r2) ≤ nλ/2 . (20) the resultant field in point Rx is basically created by the secondary radiators that lay in the area of approx. the Every Fresnel zone includes secondary radiators on first eight to twelve zones. In a certain sense we can call this area as decisive area for propagation of radio waves plane S , their phases in the point of Rx being different by about π at the utmost. The neighbouring Fresnel that are propagating from Tx to Rx . zones create an antiphase field in point Rx (with a phase If we want to separate the field of the first Fresnel different by π at the utmost). zones, we will hide the connection line Tx –Rx by a thin From relations (19) it is seen that intersections of Fres- obstacle impermeable for radio waves, and we will cut it nel zones with plane S have a circular shape. The radii of around the connection line Tx –Rx to get a circle aper- individual zones Rn , n = 1, 2, 3,... can be determined ture. We will gradually magnify the area of this aperture. ′ ′′ (P ) from the conditions: r ≫ λ, r ≫ λ, Rn ≫ r. Then it In point Rx we will measure the field strength E . is possible to write: The result of this experiment is shown in Fig. 12 as a E(P ) S dependence on the ratio , where E0 is the field 2 E0 S1 ′ 2 2 Rn r = r + R =∼ r1 + , strength in point R during the propagation of radio 1 n 2r x q 1 (21) waves in a free space (without shading obstacle). S is R2 ′′ 2 2 ∼ n the area of the circular aperture in the shading obstacle r = r2 + Rn = r2 + . q 2r2 and S1 is the area of the first Fresnel zone. The smallest aperture in the shading obstacle where If we insert these relations into the equation of the (P ) ′ ′′ (P ) E S1 external boundary of the n-th Fresnel zone (r + r ) − E = E0 , E = 1, has a size of 3 . The radius is 0

Journal of ELECTRICAL ENGINEERING 56, NO. 5–6, 2005 119

7 RESULTS E(dBmV/m)

110 As it is seen in Fig. 13, reﬂection planes represent a) quite a small portion from the area visible from both the 100 transmitter Tx and receiver Rx , and are quite scattered.

90 7.1 Exactness y= 0.9714x+ 2.1309 R2 = 0.9185 80 Comparing the predicted field strength according to 70 ITU-R and according to the new method with the mea- 70 80 90 100 110 sured data showed that the new method is quite exact E(dBmV/m) and with good input DTM and land cover it provides E(dBmV/m) better results that standard methods, Fig. 14 (see cor- 110 relation coefficient). In some cases, comparison between b) the measured values and predicted values where reflec- 100 tions were included did not show a sufficient change. In 15 % of cases there was an improvement by more than 90 1 dB, in 9 % of cases by more than 2 dB. y= 0.9987x+ 0.103 80 R2 = 0.9361 7.2 Time 70 70 80 90 100 110 The time of calculations seems to be the biggest disad- E(dBmV/m) vantage in comparison with classical calculations by standard methods (ITU-R 370 and others). The new method Fig. 14. Exactness of a) standard methods and b) the new method. counts the visibility of the terrain from every possible re-

tn(s) ceiver, and makes tests of all suitable points of the terrain 6000 on reﬂections. These operations are quite time consum- 5000 ing, with an increase of the test area the calculation time

4000 increases exponentially (Fig. 15).

3000 7.3 Effectiveness 2000 1000 The effectiveness of terrain reflection plateau tracing 0 depends on geometric parameters of DTM. In the case of 0 20 40 60 80 a planar terrain and with low density of urban objects tn(s) between the transmitter and receiver, using the new pre- Fig. 15. Exactness of a) standard methods and b) the new method. diction method is useless. Results will be almost identical with standard methods. In other cases it depends on how big the differences given by the relation: are between the predicted and measured field strengths. The new method could be used in special cases as an 1 λr1r2 adjunct to the standard methods. Rmin = . (23) r3 r1 + r2 7.4 Importance The shading area does not have a practical influence By means of this new method it is possible to find on the field strength E(P ) when the aperture in this area sources of unexpected mistakes in predictions made by includes approximately the first eight Fresnel zones. standard methods. In the point of receiving Rx mutual compensation oc- curs of the fields of the neighbouring Fresnel zones, and the results of calculation show that in the first Fresnel 8 CONCLUSION zone one half of the total energy of the radio wave is transferred. Finally, we can say that a decisive contribu- Implementation of reflection phenomena in predictions tion to field strength in point Rx is brought by secondary of the field strength of FM signal is possible, with good sources that lay in a the pace of 1/3 of the first Fresnel results. On the other hand, it has big requirements — P 1 E( ) good quality DTM and time for calculations. For practical zone (n = /3), when E = 1. This area is called the 0 purposes it is suitable in the case of a small range of minimum Fresnel zone and its radius is given by relation input data, for example a small city — it allows to make (23). calculations more effectively. In the case of calculation 120 J. Klima — M. Moˇzucha: INFLUENCE OF TERRAIN ON MULTIPATH PROPAGATION OF FM SIGNAL

of terrain reﬂections within a huge area we have to cope Appendix with unknown reﬂectivity of the land cover.

References 2 2 dar2 = (xr − xa) + (yr − ya) , (I) p [1] CERNOHORSKˇ Y,´ D.—NOVA´ CEK,ˇ Z.: Antennas and Propa- 2 2 2 dar3 = (xr − xa) + (yr − ya) + (zr − za) , (II) gation of Radiowaves (Antény a ˇs´ıˇren´ırádiových vln), FEI VUT, p Ustav´ radioelektroniky, Brno, 2001. (in Czech) cos Aar = (xr − xa)/dar2 , (III) [2] GROSSKOPF, R. : Feldstärkevorhersage mit Berücksichtung sin Aar = (yr − ya)/dar2 , (IV) von Mehrwegeausbreitung, Rundfunktechnik Mitteilungen (München) 33 (1989), 155–161. (in German) cos γar = dar2/dar3 , (V) [3] GROSSKOPF, R. : Field Strength Prediction in the VHF and UHF Range Including Multipath Propagation, Proc. 7th Inter- sin γar = (zr − za)/dar3 , (VI) national Conference on Antennas and Propagation (ICAP 1991), Xi = Ei cos γar cos Aar , (VII) York, Conference Publication, 333, vol. 2, pp. 965–967, London, 1991. Yi = Ei cos γar sin Aar , (VIII) [4] ITU–R.: Propagation over Irregular Terrain with and without Zi = Eisinγar , (IX) Vegetation, Repor 1145, Geneva (CD), 2000. 2 2 [5] ITU–R.: VHF and UHF Propagation Curves for Land Mobile dtr2 = (xr − xt) + (yr − yt) , (X) Services. Recommendation 529, Report 567-3, Geneva (CD), p 2 2 2 2000. dtr3 = (xr − xt) + (yr − yt) + (zr − zt) , (XI) [6] ITU–R.: Propagation Statistics Required for Broadcasting Ser- p vices Using the Frequency Range 30 to 1000 MHz. Rec. 616, cos Atr = (xr − xt)/dtr2 , (XII) Rep. 239-6, Geneva (CD), 2000. sin Atr = (yr − yt)/dtr2 , (XIII) [7] KLIMA, J. : Measurement and Assessment of Slovak Repub- lic Territory Coverage by Television and Radio Broadcasting cos γtr = dtr2/dtr3 , (XIV) Signal, Technical Regulation of Telecommunications TPT-R5. sin γtr = (zr − zt)/dtr , (XV) Ministry of Transport, Posts and Telecommunications of Slovak 3 Republic (Meranie a posudzovanie pokrytia územia Slovenskej X0 = E0 cos γtr cos Atr , (XVI) republiky telev´ıznym a rozhlasovým signálom. Technickýpred- pis telekomunikáci´ı. TPT-R5. Bratislava: Ministerstvo dopravy, Y0 = E0 cos γtr sin Atr , (XVII) pôˇst a telekomunikáci´ıSR, 2001. (in Slovak) Z0 = E0 sin γtr . (XVIII) [8] KRCHO, J. : Modeling of Georelief and its Geometrical Struc- ture using DTM; Positional and Numerical Accuracy, Bratislava: QIII, 2001. Ján Klima graduated from the Faculty of Electrical Engi- ˇ [9] MOZUCHA, M. : The Barrier Effects of Georelief on the Radio neering, Slovak University of Technology, Bratislava, in 1971 FM Signal Propagated in Geographical Sphere (PhD. thesis, in and received the PhD degree in the theory of electromagnetism Slovak), Bratislava: Faculty of Natural Sciences of Comenius University, 2003 (Bariérovéefekty georeliéfu pri ˇs´ıren´ı rozhla- from the same university in 1979. Since 1991 till now he has sového FM signálu v prostred´ıgeografickej sféry. been a member of the international TWG HCM of Vienna [10] RAIDA, J.et al : Multimedia Textbook of Electromagnetic Agreement, now Agreement 2003. At present he is an asso- Waves and Microwave Technology (Multimediáln´ı uˇcebnice e- ciate professor at the Physics Department of the University lektromagnetických vln a mikrovlnnétechniky), Brno, Institute of Mathias Bel in BanskáBystrica. He cooperates also with of radio electronics FEI VUT, 2001. (in Czech) PTT Research Institute in BanskáBystrica. His professional [11] BLAUNSTEIN, N.—GILADI, R.—LEVIN, M.: Characteris- domains are the theory of electromagnetic fields, radio waves tics’ Prediction in Urban and Suburban Environments, IEEE propagation, frequency spectrum engineering and human ex- Trans. Veh. Technol. 47 (1998), 225–234. posure to electromagnetic fields. ¨ [12] KURNER, T.—CICHON, D.—WIESBECK, W.: Characteris- Marián Moˇzucha graduated from the Faculty of Natu- tics’ Prediction in Urban and Suburban Environments, IEEE ral Sciences, Comenius University, Bratislava, in 1995 and re- Trans. Veh. Technol. 46 (1997), 739–747. ceived the PhD degree in cartography and geoinformatics from [13] TONG, F.—AKAIWA, Y. : Effects of Beam Tilting on Bit-Rate the same university in 2004. At present he works for Trans Selection in Mobile Multipath Channel, IEEE Trans. Veh. Tech- nol. 46 (1997), 257–261. World Radio — Slovakia in Bratislava. His professional do- main is cartography programming connected with radio wave Receivd 26 November 2004 propagation.