Modeling of Propagation in Mobile Wireless Communication: Theory, Simulation and Experiment

Transcription

1 Modeling of Propagation in Mobile Wireless Communication: Theory, Simulation and Experiment MAGDALENA SALAZAR-PALMA* TAPAN K. SARKAR**, WALID M. DYAB**, MOHAMMAD N. ABDALLAH**, M. V. S. N. PRASAD*** *Dept. Signal Theory and Communications, College of Engineering, Charles the Third University of Madrid, Spain, **Electrical & Computer Eng. Dept., Syracuse University, NY, USA *** National Physical Laboratory, New Delhi, India IEEE Northern Australia Section James Cook University, Townsville, Australia, August 15, 2017

2 Objective 2 To illustrate that an electromagnetic macro modeling can properly predict the path loss exponent in a mobile cellular wireless communication system. Path loss exponent in a cellular wireless communication system is 3, preceded by a slow fading region, and followed by the fringe region where the path loss exponent is 4. Size of these regions is determined by the height of the base station antenna. Theoretical analysis: Radiation from a vertical dipole over a horizontal imperfect ground plane: Sommerfeld & Schelkunoff. Numerical analysis. Experiments: Okumura et al. and more extensive experimental data from different base stations.

3 Objective 3

4 Index 4 Theory Sommerfeld formulation. Theory Analysis of the reflected field. Theory Field near the interface. Numerical analysis Field near an earth-air interface. Experimental data. What type of wave is it? Some quotations. Conclusions. References.

5 Theory Sommerfeld Formulation 5 Dipole of moment Idz oriented along the z-direction and located at (x, y, z ) over an imperfect ground plane of complex relative dielectric constant ε. ( x, y, z ) Dipole moment Idz R 1 ( xyz,, ) z k = ω µε y z ( µ, ε, k ) medium (1) Air x ( x, y, z ) θ R 2 Image ρ medium (2) Earth ( µ, εε, k ) jσ ε = εr ωε k = ω µεε

6 Theory Sommerfeld Formulation Hertz vector potential u Π : In medium 1: In medium 2: Ι dz jωε Electric and magnetic field: E Η 6 ( k ) ( ) ( ) ( ) 1 Π 1z = δ x x' δ y y' δ z z' ( 2 k 2 ) + Π = 2 2z 0 ( ) 2 = Π + k Π = jωε ε Π i i i i ( ) i 0 i i ˆz 0 z

7 Theory Sommerfeld Formulation 7 Boundary condition: At interface, z=0, tangential electric and magnetic field components must be identical, thus: Π1z Π2z Π1z Π2z = ε = ε y y x x Π1z Π2z = y z y z which may be further written as: Π Π 1z = ε Π 1z Π2 2z = z z z Π1z Π2z = x z x z

8 Theory Sommerfeld Formulation Solution: ( ) ( ) exp jk ( ( )) 1R1 J 0 λρ ε λ k1 λ k Π 1z = P + exp λ k z z' λdλ R λ k1 ε λ k1 + λ k2 Π = 2z ( ) ( ) λρ exp λ λ ' J0 k2 z k1 z 2P ε λ k + λ k λdλ for > 2 2 Real λ k 1,2 0, where P I dz jω4πε = ρ = ( x x' ) 2 + ( y y' ) 2 R 2 ( ) 2 1 = ρ + z z' 0

9 Theory Sommerfeld Formulation 9 Medium 1, i.e., air: First term: direct line-of-sight (LOS) contribution from the dipole antenna source, i.e., spherical wave originating from the source to the observation point. Second term: complementary solution or reflection term (reflection from the imperfect ground plane). This term is the strongest one near the surface of the earth and exponentially decays as we go away from the interface. Addition of both: ground wave, as per IEEE Standard Definitions. Medium 2, i.e., ground: Partial transmission of the wave from medium 1 into medium 2. Our interest is in medium 1.

10 Theory Sommerfeld Formulation In medium 1: where and ( g ) Π =Π +Π = P g + direct reflected 1z 1z 1z 0 s ( ) Π z = P exp jk R R = P g direct , is a spherical wave from the source. 2 2 ( λρ ) exp λ ( + ') J 0 k1 z z reflected ε λ k1 λ k 2 Π 1z = P λdλ = Pg ε λ k1 λ k + 2 λ k1 is a superposition of plane waves resulting from the reflection of the plane waves into which a spherical wave from the image point can be expanded. s

11 Theory Sommerfeld Formulation 11 This can be seen from the identity: where 2 2 ( jkr ) ( λρ ) exp λ ( + ') = R λ k1 exp J k z z ( ) 2 R = + z+ z 2 2 ρ ' λdλ The term under the integral sign can be recognized as a multiple plane wave decomposition of the spherical wave source. Upon reflection of the plane waves from the dipole source, the amplitude of each wave must be multiplied by the reflection coefficient R( λ) as given by the following expression.

12 Theory Sommerfeld Formulation Reflection coefficient: 12 R ( λ ) ε λ k λ k = ε λ k + λ k When ε, i.e., the earth behaves as a perfect conductor, the reflected wave is simply a spherical wave originating at the image point. The reflection coefficient takes into account the effects of the ground plane in all the waves decomposition of the spherical wave and sums it up as a ray originating from the image of the source but multiplied by a specular reflection coefficient R( θ ), where θ is interpreted as the angle of the incident wave to the ground, as shown in the figure of chart 4.

13 Theory Analysis of the Reflected Field 13 There are two forms to express mathematically equivalent. First one: reflected Π1 z which are exp( jk R ) k J0( λρ ) exp λ k1 ( z z' ) λ + Π = P 2 λdλ P g g reflected z R2 0 λ k1 ε λ k1 + λ k 2 [ ] where g 1 is the spherical wave originating from the image of the source, and g sv is the correction factor characterizing the effects of the ground. This is the form that has been use by most researchers. sv

14 Theory Analysis of the Reflected Field Second one: 2 2 ( ) ( ) exp ( ') reflected exp jk1r J λρ λ k z z + 2 Π 0 1 1z = P + 2ε λdλ P g G R 2 0 ε λ k1 + λ k 2 14 [ ] useful when both transmitter and receiver are close to the ground, since the reflection coefficient is 1 for grazing angle of incidence, where θ π/2. Then, the direct term g 0 cancels the image term g 1 leaving only the correction factor G sv. This is the form that has been used by us, as we will see later on. sv

15 Theory Analysis of the Reflected Field 15 Let us focus in the first expression. The objective will be to compute g sv, and from it, to obtain the reflected expressions of Π1 z and Π1z. This is not a trivial problem. Many researchers tried to work out different ways of doing it, from Sommerfeld in 1909 and later on, in 1926, to Norton, Stratton, Wait, Baños, Tyras, Miller et al., Brekhovskikh, Sarkar, Hill and Wait, Karawas, King, Ishimaru, Collin, and so on. The main difficulty is how to choose the integration path with respect to the poles and how to choose and use the asymptotic expansions. In the process, the controversy of a surface wave arising from the poles and a possible error in a sign in Sommefeld formulation came through, with contributions by Ott, Sommerfeld, Kahan and Eckart, Epstein, Baños, Weyl, and, finally, Schelkunoff who clarified the topic showing that there was no such surface wave and no error in a sign.

16 Theory Analysis of the Reflected Field 16 The best way to obtain a solution is to transform the Bessel function of the first kind and zeroth order to a combination of Hankel functions of the first and second kinds and zeroth order. Then, the path of integration may be modified which can be shown to be advantageous. Using the method of steepest descent one gets, for ε >> 1 ( jk R ) ( jk R ) 3 exp 1 1 exp 1 2 ε cos θ 1 2ε 1 Π1z P + + R1 R2 ε cos θ 1 jkr ε cosθ + 1 When ε the previous expression goes properly into the form of a source plus an image term due to a vertical electric dipole located above a perfectly conducting ground plane....

17 Theory Analysis of the Reflected Field However, when θ π 2 17, it becomes ( ) ( ) exp jk1r1 exp jk1r2 2ε Π1z P + exp ( jk1r2) R1 R2 jk1r2 where it can be seen that the third term may be higher than the first two terms. For example, if both the transmitter and the receiver are close to the ground, then R1 = R2 ρ, z 0 z' and the Hertz potential will be determined just by the third and higher order terms. Also, note that the dominant term 2 behaves as 1/ R. This is due to a poor convergence in the vicinity of θ π 2.

18 Theory Field Near the Interface 18 For that reason we prefer to use the second expression for the reflected reflected Hertz potential, Π1 z, together with a modified saddle point method, and a better asymptotic expansion, which constitute a novel approach to this problem. Sommerfeld introduced the parameter W or numerical distance as: 2 cosθ ε sinθ W = jk1r2 1 + ε + 1 ε + 1 In what follows, without giving more details about the novel approach (which can be found in the reference), we are going to show the expressions obtained for GsV, close to the interface, as a function of W.

19 Theory Field Near the Interface 19 For ε, θ π 2, and W small, [ ] ( z+ z' ) ε ( z + z ' ) exp [ jk ] 1R2 π 2π kj ε 1 1 GsV exp jk1r2 2 k 2 1j 1.5 R2 R2 R2 and three facts can be recognized: A variation of the Hertz potential as which will give a field variation of 1 Π R 15 ρ 1z 15 2 equivalently, a path loss exponent of 3. A height gain effect: see the (z+z ) term. No dependence with the ground parameters. 1 if z+z << ρ, or

20 20 For ε, θ π 2, and W large, G sv Theory Field Near the Interface + ε 2 ε exp R 2 jk1r 2 [ ] ( z z' jk R ) and four facts can be recognized: A term with a variation of the Hertz potential as 1/R 2, which is recognized as a Norton surface wave, and will give a path loss exponent of 4. A higher order term with a variation as 1/R 3. A height gain effect for both terms. A dependence with the ground parameters for both terms.

21 Theory Field Near the Interface 21 In summary, the expressions for the total Hertz potential near the interface for ε and θ π 2 are: exp( jk R ) exp( jk R ) exp( jk R ) P j2 π k ( z+ z'), W < R1 R2 R2 Π1z exp( jk1r1) exp( jk1r2) exp( jk1r2) ε ε 2 R1 R2 R2 jk1r2 P + 2 ( z+ z') 1, W > 1 where we can recognize two distinct regions: the first one, closer to the dipole, with a path loss exponent of 3, height gain, and no dependence with the ground parameters; the second one, further away from the dipole, with a path loss exponent of 4, height gain and dependence with the ground parameters.

22 Numerical Analysis Field Near an Earth- Air Interface 22 Since a number of approximations have been done in the mentioned theory to arrive to the previous conclusions, in order to confirm the theoretical results, a numerical analysis with a Method of Moments code based on a rigorous Sommerfeld formulation without any approximation, has been performed. The code used is AWAS (see references). Results coincide with the theoretical predictions and show other interesting features. First we run an example based on the classical experiment by Okumura et al. and then further explore the behavior in the proximity of the source dipole, and the dependence with the source dipole height, and with the type of imperfect ground.

23 Numerical Analysis Field Near an Earth- Air Interface Comparison with Okumura et al. experiment. 23 Variation with distance of magnitude of E z from a half-wavelength dipole located 140 m from the ground at an operating frequency of 453 MHz. The height of the observation point was 3 m from an urban ground with a permittivity of ε r = 4, and a 4 conductivity of σ = 2 10 mhos/m. Okumura s results: triangles. Hata s fitted curve: blue line. AWAS, free space: red line. AWAS, imperfect ground: line with dots.

24 Numerical Analysis Field Near an Earth- Air Interface 24 Further analysis for points closer to base station were done to check for the existence of the so called slow fading region, which is, in fact, the near field region (displaying an interference pattern), which is followed by a smooth region. Interference region (near field) clearly shows up. It can be seen that there is no height gain within that region. Actually, the closer the antenna to the ground, the strongest the field is. Smooth region: Starts at 4H H TX RX as shown in another paper (see references). λ Exhibits height gain. Two distinct subregions: first one, 30 db per decade; second one, 40 db per decade.

25 Numerical Analysis Field Near an Earth- Air Interface 25 Power loss of 30 db/ decade Practical heights of cellular towers (10~20m) Power loss of 40 db/ decade f=1 GHz; Receiver: 2 m above earth; Earth parameters: same as before. Distances which are very close to the tower where the approximation θ π/2 is not valid Effective Cell Radius (from 100 m to 2 km)

26 Numerical Analysis Field Near an Earth- Air Interface 26 Variation of magnitude of E z from a half-wavelength dipole as a function of distance, at an operating frequency of 900 MHz. The height of the observation point was 2 m. Five different types of ground have been used, with different parameters.

27 Experimental Data 27 Experimental data from 6 cellular wireless base station antennas operating in dense-urban, urban and suburban environment in the city of Delhi at frequencies of 1800 MHz and 900 MHz. Special feature of the Delhi urban environment is that the houses are not uniformly spaced. First the 1800 MHz measurements. Then, the 900 MHz measurements. Two other experiments from other locations in India at 900 MHz.

28 Experimental Data 28 The Delhi 1800 MHz GSM base station transmitters belong to Idea Cellular Network. Have been monitored with Nokia GSM receiver (model 6150) generally used as a drive-in tool for planning cellular networks. Receiver sensitivity: 102 dbm. Base stations transmitting powers: +43 dbm. Receiving equipment installed in a vehicle along with the data acquisition system. Vehicle moved on a normal road at a permissible speed in the traffic and the downlink signal strength was monitored by the receiver. Gain of the transmitting antenna: 18 db.

29 Experimental Data 29 The Delhi 900 MHz experiments were carried with the help of Aircom International Limited, a UK company based in India. Base stations transmitting power: 43.8 dbm. Transmitting antennas gain: 2dBi. Gain of receiving antenna: 0 db Receiver: standard Nokia equipment used in drive-in tools for field trials.

30 For all Delhi measurements: Experimental Data 30 Position of the mobile determined from GPS receiver. This information with the coordinates of the base station was utilized to deduce the distance traveled by the mobile from the base station. The signal strength information recorded in dbm was converted into path loss values utilizing the gains of the antenna. Receiver height: 1.5 m. Data recorded with 512 samples in one second on a laptop computer and the number of samples collected for each site varied from to Measured r.m.s. (root mean squared) error: 1.5 db. Data averaged over a conventional range of 40λ.

31 Experimental Data 31 Google map showing location of the Delhi base stations: OM-1 and BJV are 1800 MHz base stations. UA, SNT, FBD and VKH are 900 MHz base stations.

32 Experimental Data 32 Photograph of a Delhi typical urban environment in this study.

33 Experimental Data 33 Photograph of a Delhi typical urban environment in this study.

34 Experimental Data 34 Clutter diagram of BJV & VKH base stations generated from the Aircom radio planning tool.

35 Experimental Data 35 Clutter diagram of FBD base station generated from the Aircom radio planning tool.

36 Experimental Data 36 Variation of path loss exponent with distance for OM-1 base station (1800 MHz). Base station height: 24 m. Beginning of smooth region: 864 m.

37 Experimental Data 37 Variation of path loss exponent with distance for BJV base station (1800 MHz). Base station height: 24 m. Beginning of smooth region: 864 m.

38 Experimental Data 38 Variation of path loss exponent with distance for UA base station (900 MHz). Base station height: 24 m. Beginning of smooth region: 432 m.

39 Experimental Data 39 Variation of path loss exponent with distance for SNT base station (900 MHz). Base station height: 18 m. Beginning of smooth region: 324 m.

40 Experimental Data 40 Variation of path loss exponent with distance for FBD base station (900 MHz). Base station height: 10 m. Beginning of smooth region: 180 m.

41 Experimental Data 41 Variation of path loss exponent with distance for VKH base station (900 MHz). Base station height: 13 m. Beginning of smooth region: 234 m.

42 Experimental Data 42 In the previous results the beginning of the fringe region, with a path loss exponent of 4, is not seen: the cell ends before such variation is evident. In order to confirm the existence of such region additional experiments are presented. Two results are shown: Base station AURNIA 19, located in an industrial area in the city of Aurangabad, in the Maharashtra state of western India. Base station PAJMSU17, located in the Panjim suburban region of the sea port of Goa, located in the western region of India.

43 Experimental Data 43 Variation of path loss exponent with distance for AURNIA 19 base station (900 MHz). Base station height: 50 m. Beginning of smooth region: 900 m.

44 Experimental Data 44 Variation of path loss exponent with distance for PAJMESU17 base station (900 MHz). Base station height: 50 m. Beginning of smooth region: 900 m.

45 From the measurements shown it may be concluded: 45 In all cases, most of the cell is in the near field region of the base station. Then, there is a region with a path loss exponent of 3, i.e., with a decay of the field as. Next, the region with a path loss exponent of 4, due to the Norton surface wave, follows. The question arises: what type of wave is such that decays as 1 15 ρ What Type of Wave Is It? 15 ρ in the intermediate region? 1

46 What Type of Wave Is It? 46 Following Van der Pol and other researchers, it can be concluded that such wave is a surface wave originated by a 2D infinite source as the secondary sources shown in the following diagram, which is precisely the situation in this problem.

47 What Type of Wave Is It? An optical analog situation: 47

48 What Type of Wave Is It? 48

49 What Type of Wave Is It? 49 Waves on a wet ground due to the partial reflectivity of the surface. The figure gives an impression on the physical propagation mechanism to be expected in cellular environments at frequencies where a wet earth represents a complex impedance surface.

50 Historical Note Kennelly-Heaviside Layer One remarkable Ionosphere experiment in history is Marconi s transatlantic transmission in 1901 It was not less than 30 years later when people understood the mechanism by which that claimed experiment was successful Sommerfeld formulation of the problem needs to be revisited due to its importance! 50 Rx Tx Surface waves First studied by Sommerfeld in 1909

51 Some Quotations 51 Dennis Gabor wrote [1972, IEEE Trans. Information Th. 1 st Issue]: The wireless communication systems are due to the generation, reception and transmission of electro-magnetic signals. Therefore all wireless systems are subject to the general laws of radiation. Communication theory has up to now been developed mainly along mathematical lines, taking for granted the physical significance of the quantities which are fundamental in its formalism. But communication is the transmission of physical effects from one system to another. Hence communication theory should be considered as a branch of physics. Thus it is necessary to embody in its foundation such physical data. Hence we can apply to our problem the well known results of the theory of radiation by the Maxwell-Poynting theory.

52 IEEE SPECTRUM, October 2010, pp. 29

53 Conclusions The theory of field propagation from an antenna over an imperfect ground plane has been outlined. It shows that, after the near field region, a region with a path loss exponent of 3 and no depedence with the ground parameters should be expected, followed by a region with a path loss exponent of 4. Theory has been confirmed by both, a numerical code based on the theory without approximations, and experimental data. For propagation modeling it is sufficient to carry out a physics-based macro modeling instead of a fine detailed micro model of the environment. 53

54 Conclusions 54 In a cellular communication system, within the cell it is the path loss exponent of 30 db per decade with distance which is predominant and therefore, since most of the cell is not within the far field region, the resultant field strength inside a cell cannot be predicted by using ray tracing, diffraction theory or by using the reflection coefficient method. Note that the free space fields provide an asymptotic rate of decay of 20 db per decade which is not predicted by the theory of propagation over an imperfect ground. Only the use of the accurate Sommerfeld formulation provides a rate of decay of 30 db per decade and, in the fringe area, 40 db per decade.

55 References 55 A. R. Djordjevic, M. B. Bazdar, T. K. Sarkar, and R. F. Harrington, AWAS Version 2.0: Analysis of Wire Antennas and Scatterers, Software and User 's Manual, Artech House, Norwood, MA, USA, A. De, T. K. Sarkar, and M. Salazar-Palma, Characterization of the Far-Field Environment of Antennas Located over a Ground Plane and Implications for Cellular Communication Systems, IEEE Antennas and Propagation Magazine, vol. 52, no. 6, pp , November-Dececember 2010,. T. K. Sarkar, W. Dyab, M. N. Abdallah, M. Salazar-Palma, M. V. S. N. Prasad, S. W. Ting, S. Barbin, Electromagnetic Macro Modeling of Propagation in Mobile Wireless Communication: Theory and Experiment, IEEE Antennas and Propagation Magazine, vol. 54, no. 6, pp , November-December T. K. Sarkar, W. Dyab, M. N. Abdallah, M. Salazar-Palma, M. V. S. N. Prasad, S. Barbin, S. W. Ting, Physics of Propagation in a Cellular Wireless Communication Environment, The Radio Science Bulletin, no. 343, pp. 5-21, December W. M. Dyab, T. K. Sarkar, M. Salazar-Palma, A Physics-Based Green s Function for Analysis of Vertical Electric Dipole Radiation over an Imperfect Ground Plane, IEEE Transactions on Antennas and Propagation, vol. AP-61, no. 8, pp , August 2013.

56 References 56 T. K. Sarkar, W. M. Dyab, M. N. Abdallah, M. Salazar-Palma, M. V. S. N. Prasad, S. W. Ting, Application of the Schelkunoff Formulation to the Sommerfeld Problem of a Vertical Electric Dipole Radiating over an Imperfect Ground, IEEE Transactions on Antennas and Propagation, vol. AP-62, no.8, pp , August M. N. Abdallah, W. Dyab, T. K. Sarkar, M. V. S. N. Prasad, C. S. Mishra, A. García Lampérez, M. Salazar-Palma, S. W. Ting, Further Validation of an Electromagnetic Macro Model for Analysis of Propagation Path Loss in Cellular Networks Using Measured Drive Test Data, IEEE Antennas and Propagation Magazine, vol. 56, no.4, pp , July-August W. M. Dyab, T. K. Sarkar, M. N. Abdallah, M. Salazar-Palma, Green s Function Using Schelkunoff Integrals for Horizontal Electric Dipoles over an Imperfect Ground Plane, IEEE Transactions on Antennas and Propagation, vol. AP-64, no. 4, pp , April 2016 M. N. Abdallah, T. K. Sarkar, M. Salazar-Palma, V. Monebhurrun, Where Does the Far Field of an Antenna Start? [Stand on Standards], IEEE Antennas and Propagation Magazine, vol. 58, no. 5, pp , September-October 2016.

57 Food for Thoughts 57 As long as I live, so long do I learn! (Sri Ramakrishna)

58 Lake Michigan in Chicago Thank you for your attention!