1. Introduction to the Propagation of Radio Waves ............... 1
1.1. Introduction ............................................... 1
1.1.1. Propagation Mechanisms .............................. 1
1.1.2. Propagation Environment ............................. 3
1.1.3. Antennas ............................................ 4
1.1.4. Selectivity ......................................... 4
1.1.5. Propagation Modelling ............................... 5
1.2. Overview of the Book ....................................... 5
2. The Earth's Atmosphere ...................................... 13
2.1. Structure ................................................. 13
2.1.1. The Homosphere ..................................... 13
2.1.2. The Heterosphere ................................... 15
2.1.3. The Ionosphere ..................................... 15
2.2. Atmospheric Composition ................................... 20
2.2.1. Major Atmospheric Constituents ..................... 20
2.2.2. Minor Atmospheric Constituents ..................... 20
2.2.3. Aerosols ........................................... 21
2.3. Atmospheric Parameters .................................... 22
2.3.1. Atmospheric Pressure ............................... 22
2.3.2. Temperature ........................................ 22
2.3.3. Relative Humidity .................................. 23
2.3.4. Water Vapour Partial Pressure ...................... 24
2.3.5. Dew Point .......................................... 25
2.3.6. Saturation Vapour Pressure ......................... 25
2.3.7. Water Vapour Density ............................... 26
2.4. Weather Phenomena ......................................... 26
2.4.1. Sunshine Duration .................................. 26
2.4.2. Solar Radiation .................................... 26
2.4.3. Evaporation ........................................ 26
2.4.4. Condensation ....................................... 27
2.4.5. Solidification and Melting ......................... 27
2.4.6. Superfusion ........................................ 27
2.4.7. Reverse Sublimation ................................ 27
2.4.8. Wind ............................................... 28
2.4.9. Turbulence ......................................... 28
2.4.10.Advection .......................................... 29
2.4.11.Subsidence ......................................... 29
2.4.12.Nebulosity ......................................... 30
2.4.13.Meteors ............................................ 30
2.4.14.Fog and Mist ....................................... 30
2.4.15.Precipitations ..................................... 32
2.4.16.Clouds ............................................. 32
2.4.17.Auroras and Auroral Activity ....................... 33
References ................................................ 33
3. Electromagnetic Waves and Propagation Characteristics ....... 35
3.1. Basic Properties of Electromagnetic Waves ................. 35
3.1.1. Electromagnetic Parameters characterising
Wave Propagation ................................... 35
3.1.2. Maxwell's Equations ................................ 36
3.1.3. Propagation Velocity (Phase Speed) ................. 38
3.1.4. Wavelength and/or Frequency ........................ 39
3.1.5. Characteristic Impedance of the Propagation
Medium ............................................. 39
3.1.6. Poynting Vector .................................... 40
3.1.7. Refractive Index ................................... 40
3.1.8. Wave Polarisation .................................. 41
3.1.9. Depolarisation ..................................... 43
3.1.10.Cross-Polarisation ................................. 43
3.1.11.Cross-Polarisation Discrimination or Decoupling
Ratio .............................................. 43
3.1.12.Cross-Polarisation Isolation ....................... 44
3.2. Propagation Mechanisms .................................... 44
3.2.1. Reflection ......................................... 44
3.2.2. Transmission ....................................... 49
3.2.3. Diffraction ........................................ 49
3.2.4. Diffusion .......................................... 51
3.2.5. Guiding ............................................ 51
3.3. Main Physical Phenomena and Frequency Dependence .......... 52
3.3.1. Path Propagation ................................... 52
3.3.2. Fresnel Ellipsoids ................................. 53
3.3.3. Free-Space Attenuation ............................. 54
3.3.4. Variability ........................................ 56
3.3.5. Frequency Selectivity .............................. 59
References ................................................ 66
4. Ionospheric Links ........................................... 69
4.1. Introduction .............................................. 69
4.2. Ionospheric Refraction .................................... 69
4.3. Trajectory Calculation .................................... 78
4.4. Ionospheric Forecasts ..................................... 81
4.4.1. Long-Term Forecasts ................................ 81
4.4.2. Medium-Term Forecasts .............................. 89
4.4.3. Short-Term Forecasts ............................... 90
4.5. Conclusion ................................................ 91
References ................................................ 91
5 Terrestrial Fixed Links ...................................... 93
5.1. Introduction .............................................. 93
5.2. Radioelectric Parameters of the Atmosphere ................ 94
5.2.1. Refractive Index ................................... 94
5.2.2.. Modified Refractive Index ......................... 95
5.2.3. Reference Atmosphere for Refraction ................ 97
5.2.4. Vertical Gradient of the Refractive Index .......... 98
5.2.5. Variability of the Refractive Index ................ 98
5.3. Refraction ............................................... 100
5.3.1. Trajectories of Radio Waves ....................... 100
5.3.2. Radius of Curvature of the Paths of Radio Waves ... 100
5.3.3. Effective Earth Radius ............................ 102
5.3.4. Effects of Refractivity Variations ................ 103
5.4. Experimental Results on the Refractive Index ............. 105
5.4.1. Refractivity ...................................... 105
5.4.2. Refractivity Gradient ............................. 105
5.4.3. Cumulative Distribution of the Refractivity
Gradient .......................................... 106
5.4.4. Cartography ....................................... 107
5.5. Modelling of the Cumulative Distributions of the
Refractivity Gradient .................................... 108
5.5.1. Evaluation of the Median .......................... 109
5.5.2. Percentage of Time that the Gradient is lower
than the Median ................................... 109
5.5.3. Percentage of Time that the Gradient is higher
than the Median ................................... 110
5.6. Main Propagation Mechanisms .............................. 111
5.6.1. Line-of-Sight Propagation ......................... 113
5.6.2. Tropospheric Scatter .............................. 114
5.6.3. Duct Propagation .................................. 119
5.6.4. Reflection at Elevated Layers ..................... 122
5.6.5. Diffraction ....................................... 124
5.7. Experimental Results ..................................... 127
5.7.1. Tropospheric Scatter .............................. 128
5.7.2. Duct Propagation .................................. 128
5.7.3. Reflection at Elevated Layers ..................... 128
5.7.4. Spherical Diffraction and Superrefraction ......... 129
5.7.5. Daily Variation of the Path Loss .................. 129
5.7.6. Seasonal Variation of the Path Loss ............... 130
5.7.7. Statistical Distribution of the Path Loss ......... 131
5.7.8. Experimental Results on Propagation Mechanisms .... 133
5.8. Influence of Rain on Propagation ......................... 134
5.8.1 Experimental Device ................................ 135
5.9. Propagation Modelling .................................... 142
5.9.1. First Order Complex Polynomial Model or
Greenstein Model .................................. 143
5.9.2. Two-Ray Model with Fixed Delay .................... 144
5.9.3. Normalised Two-Ray Model .......................... 144
5.10.Performance Prediction ................................... 144
5.10.1.Quality Prediction ................................ 144
5.10.2.Signature of a Radio System ....................... 146
References ............................................... 148
6. Satellite Links ............................................ 153
6.1. Introduction ............................................. 153
6.2. Free-Space Attenuation ................................... 153
6.3. Phenomena associated to the Refractive Indexes ........... 154
6.3.1. Troposphere ....................................... 154
6.3.2. Ionosphere ........................................ 155
6.3.3. Refraction ........................................ 157
6.3.4. Delay and Propagation Time Distortion ............. 158
6.3.5. Direction of Arrival .............................. 161
6.3.6. Rotation of the Polarisation Plane ................ 161
6.3.7. Scintillations .................................... 161
6.4. Attenuation by Atmospheric Gases ......................... 162
6.5. Hydrometeor Attenuation .................................. 164
6.5.1. Attenuation due to Clouds and Fog ................. 164
6.5.2. Rain Attenuation .................................. 166
6.6. Depolarisation Attenuation ............................... 169
6.7. Building Penetration Loss ................................ 170
6.8. Attenuation due to the Local Environment ................. 171
6.8.1. Effects of Buildings .............................. 171
6.8.2. Effects of Vegetation ............................. 171
References ............................................... 173
7. Mobile Radio Links ......................................... 175
7.1. Introduction ............................................. 175
7.2. Types of Models .......................................... 177
7.2.1. Theoretical Models ................................ 177
7.2.2. Empirical or Statistical Models ................... 177
7.2.3. Semi-Empirical Models ............................. 179
7.3. Uses of Models ........................................... 179
7.4. Macrocell Models ......................................... 179
7.4.1. Rural Models ...................................... 180
7.4.2. Mountainous Model ................................. 182
7.5. Small Cell Models ........................................ 184
7.5.1. COST-CNET Model ................................... 184
7.5.2. Lee Model ......................................... 190
7.6. Microcell Models ......................................... 192
7.6.1. Introduction ...................................... 192
7.6.2. MicroG-CNET Model ................................. 192
7.7. Ray Launching Model ...................................... 196
7.8. Building Penetration Loss Models ......................... 199
7.9 Indoor Propagation Models ................................. 202
7.9.1 Empirical Models ................................... 202
7.9.2 Deterministic Models ............................... 203
7.10.Broadband Models ......................................... 204
7.10.1.Introduction ...................................... 204
7.10.2.Path Loss Models .................................. 205
7.10.3.Representation Models ............................. 216
7.10.4.Ray Models ........................................ 221
7.10.5.Geometrical Models ................................ 222
7.10.6.Uses of Broadband Models in Simulation Software ... 224
References ............................................... 226
Appendices .................................................... 231
A. The Sun and the Solar Activity ............................. 233
A.l. Introduction ............................................. 233
A.2. The Photosphere .......................................... 234
A.2.1. Granulation ....................................... 235
A.2.2. Sunspots .......................................... 235
A.2.3. The Magnetic Fields of Sunspots ................... 236
A.3. The Chromosphere ......................................... 237
A.3.1. Plages ............................................ 237
A.3.2. Prominences and Filaments ......................... 237
A.3.3. Fibrils ........................................... 238
A.4. The Solar Corona ......................................... 238
A.5. The Solar Wind ........................................... 238
A.6. The Magnetosphere ........................................ 239
A.7. Solar Activity ........................................... 240
A.7.1. Wolf Number ....................................... 240
A.7.2. Radio Flux at the 10.7 cm Wavelength .............. 242
A.7.3. Correlation of the Wolf Number and the Solar
Radio Flux ........................................ 242
A.8. Solar Flares ............................................. 243
A.8.1 Solar Radio Emissions .............................. 244
A.8.2 Corpuscular Radiation .............................. 245
A.8.4 Emissions of Shock Waves ........................... 245
References ............................................... 245
В. Microphysical Properties of Hydrometeors ................... 247
B.l. Rain and Drizzle ......................................... 247
B.2. Snow ..................................................... 250
B.3. Hail ..................................................... 251
B.4. Fog ...................................................... 253
References ............................................... 254
С. The Frequency Spectrum ..................................... 257
C.l. Introduction ............................................. 257
C.2. Frequency Bands .......................................... 257
C.2.1. ELF Waves ......................................... 257
C.2.2. VLF Waves ......................................... 258
C.2.3. LF Waves .......................................... 259
C.2.4. MF waves (300-3000 kHz) ........................... 259
C.2.5. HF waves .......................................... 260
C.2.6. VHF Waves ......................................... 261
C.2.7. UHF waves ......................................... 262
C.2.8. SHF Waves ......................................... 262
C.2.9. EHF Waves ......................................... 263
C.2.10.Sub-UHF waves ..................................... 264
C.2.11.Infrared and Light Waves .......................... 265
C.3. IMT-2000 Frequency Allocation ............................ 266
C.4. Frequency Bands used in Satellite Communications
(COST255 2000) ........................................... 266
C.5. P, L, S, X, K, Q, V and W band (Freeman) ................. 267
References ............................................... 269
D. Cross-Polarisation induced by the Atmosphere ............... 271
D.l. Introduction ............................................. 271
D.l.l. Cross-Polarisation Discrimination ................. 271
D.l.2. Cross-Polarisation Isolation ...................... 272
D.2. Cross-Polarisation Discrimination Models ................. 273
D.2.1. Cross-Polarisation caused by Rain ................. 273
D.2.2. Cross-Polarisation caused by Ice Particles ........ 277
D.2.3. Cross-Polarisation caused by Dust and
Sandstorms ........................................ 277
D.2.4. Cross-Polarisation in Clear Atmosphere ............ 278
References ............................................... 279
E. Fresnel Equations .......................................... 281
E.l. Introduction ............................................. 281
E.2. Horizontal Polarisation .................................. 282
E.3. Vertical Polarisation .................................... 283
E.4. Unspecified Polarisation ................................. 284
E.5. Multiple Reflections and Transmissions ................... 285
F. Ionospheric and Geomagnetic Disturbances associated with
Solar Events ............................................... 287
F.l. Introduction ............................................. 287
F.2. Sudden Ionospheric Disturbances .......................... 288
F.2.1. Sudden Enhancement of Atmospherics ................ 289
F.2.2. Sudden Enhancements of Signals .................... 291
F.2.3. Sudden Phase Anomalies at Very Low Frequencies .... 293
F.3. Polar Cap Absorption ..................................... 298
F.4. Geomagnetic Disturbances ................................. 299
F.5. Ionospheric Storms ....................................... 302
F.6. Auroras .................................................. 303
F.7. Conclusion ............................................... 304
References ............................................... 305
G. Investigation Methods of the Ionosphere .................... 307
G.l. Vertical or Oblique Bottomside Sounding .................. 307
G.2. Vertical Topside Sounding ................................ 308
G.3. Backscatter Sounding ..................................... 309
G.4. Incoherent Scatter Sounding .............................. 309
G.5. Riometers ................................................ 310
G.6. Low Frequency and Very Low Frequency Receivers ........... 310
References ............................................... 311
H. The Terrestrial Magnetic Field and the Magnetic Indexes .... 313
H.l. The Terrestrial Magnetic Field ........................... 313
H.2. Magnetic Indexes ......................................... 315
H.2.1. KIndex ............................................ 315
H.2.2. KP Index .......................................... 315
H.2.3. AP Index .......................................... 316
H.2.4. AA Index .......................................... 316
H.2.5. Dst Index ......................................... 316
H.2.6. AE Index .......................................... 316
References ............................................... 317
I. Rain Attenuation ........................................... 319
I.1. Introduction ............................................. 319
I.2. Statistical Models for Rain Attenuation .................. 319
I.2.1. Assis-Einloft Model ............................... 319
I.2.2. Brazilian Model ................................... 321
I.2.3. Bryant Model ...................................... 323
References ............................................... 324
J. Vegetation Attenuation ..................................... 325
J.l. Introduction ............................................. 325
J.2. Vegetation Attenuation Models ............................ 325
J.2.1. Exponential Decay Model (EXD Model) ............... 325
J.2.2. Modified Exponential Decay Model (MED Model) ...... 326
J.2.3. Rice Model ........................................ 327
J.2.4. ITU-R Model ....................................... 327
J.2.5. Al-Nuami - Hammoudeh Model ........................ 328
J.2.6. Stephens Model .................................... 328
J.2.7. Radiative Transfer Models ......................... 329
J.2.8. MIMICS Model (Michigan MICrowave Scattering) ...... 333
J.2.9. Karam-Fung Model .................................. 334
J.3. Experimental Results ..................................... 335
J.3.1. Fixed Link Measurements ........................... 336
J.3.2. Mobile Link Measurements .......................... 339
References ............................................... 343
К. Diffraction Models ......................................... 345
K.l. Diffraction by a Single Knife Edge ....................... 345
K.2. Diffraction by Multiple Knife Edges ...................... 348
K.2.1. Theoretical Methods ............................... 348
K.2.2. Approximate Methods ............................... 352
K.3. Diffraction by a Single Rounded Obstacle ................. 364
K.3.1. Wait Method ....................................... 364
K.3.2. ITU-R Method ...................................... 366
References ............................................... 368
L. Mobile Radio Measurements .................................. 369
L.l. Measurement of the Field Strength ........................ 369
L.2. Measurement of the Impulse Response ...................... 370
L.3. Measurement of the Directions of Arrival ................. 372
L.4. AMERICC Propagation Channel Sounder ...................... 373
References ............................................... 373
M. Directions of Arrival ...................................... 375
M.l. Introduction ............................................. 375
M.2. Experimental Determination of Directions of Arrival ...... 375
M.3. Mathematical Modelling of the Signal ..................... 376
M.4. Determination Methods of the Directions of Arrival ....... 378
M.4.1. Linear Methods .................................... 378
M.4.2. Non-Linear or High Resolution Methods ............. 382
References ............................................... 390
N. Geographical Databases ..................................... 391
N.l. Introduction ............................................. 391
N.2. Digital Terrain Model .................................... 391
N.3. Global Land Use Data ..................................... 392
N.4. Local Data ............................................... 394
N.4.1. Building Contours ................................. 395
N.4.2. Communication Lines ............................... 396
N.4.3. Raster Data ....................................... 396
N.4.4. Local Land Use Data ............................... 397
N.5. GLOBE Terrain Data ....................................... 398
N.6. Building Height .......................................... 399
N.7. Street Width ............................................. 399
N.8. Indoor Data .............................................. 400
N.9. Future Developments ...................................... 400
References ............................................... 400
О. Determination of the Electromagnetic Field after
Interaction with Structures ................................ 403
O.l. Introduction ............................................. 403
O.2. Geometrical Optics Method ................................ 403
О.З. Geometrical Theory of Diffraction ........................ 405
O.4. Uniform Theory of Diffraction ............................ 407
O.5. Finite Difference in Time Domain Method .................. 409
O.6. Moment Method ............................................ 411
O.7. Parabolic Equation Method ................................ 413
References ............................................... 414
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