Mobile Radio Propagation Models

Mobile Radio Propagation Models

• Challenges in mobile radio channel

• Empirical formulas and models for predicting signal strength at mobile stations

Mobile Radio Channel

• Wireless medium between the tower and mobile station.

• Also known as wireless transmission media.

• Transmitter (base station) and a moving receiver.

• Challenges:

  • Mobility of the user: changes signal strength as the user moves.

  • Changing surroundings: terrain, buildings, vehicles vary by environment (rural vs. urban).

  • Multipath propagation: signals arrive via multiple paths (direct, reflected).

  • Attenuation or fading: signal strength decreases with distance.

Multipath Propagation

• Signals reach the mobile station via multiple paths (direct and reflected).

• The signals can be in phase or out of phase, leading to constructive or destructive interference.

Factors Affecting Mobile Radio Channel

• Mobility of the user.

• Changing surroundings (buildings, terrain).

• Multipath propagation.

• Fading (rapid signal fluctuations).

• Path loss (average signal attenuation over distance).

• Shadowing (signal attenuation due to obstacles).

• Doppler shift (frequency shift due to relative motion).

Types of Fading

• Large-scale fading: due to distance from the transmitter, path loss, and shadowing.

• Small-scale fading: due to multipath propagation and Doppler effect, leading to rapid amplitude and phase changes.

Need for Propagation Models

• Predict radio signal behavior in different environments.

• Network planning, coverage estimation, capacity, and interference analysis.

• Handover design: estimate signal strength and interference levels.

• Approaches: empirical, analytical, or simulation-based.

Types of Propagation Models

• Empirical Models:

  • Derived from real-world measurement data.

  • Examples: Lee model, Okumura model, Hata model, Ibrahim and Parsons model, COST 231 model.

  • Used when physical details are unknown or hard to model.

• Analytical Models:

  • Based on theory and geometry.

  • Examples: free space path loss model, two-ray model, flat earth model, ray-tracing models (computationally intensive).

• Statistical Models:

  • Use probabilistic behavior of fading.

  • Examples: Rayleigh fading model (no line of sight), Rician, and Nakagami models.

• Environment-Based Models:

  • Indoor models (Wi-Fi, mmWave).

  • Outdoor models (urban, rural, satellite).

  • Satellite: free space and two-ray models.

• Modern Techniques:

  • AI and machine learning.

  • Gather data from real networks, predict signal quality, optimize beamforming.

Basic Concept

• Mobile radio channels are dynamic.

• Propagation models are essential for wireless network design.

• Types: empirical, analytical, statistical, or deterministic.

• Modern models use AI and machine learning for real-time data analysis.

Free Space Path Loss Model

• Simplest model: direct line of sight between transmitter and receiver.

• No obstructions, reflections, or scattering.

• Calculates power loss as signal propagates through space.

• Assumptions:

  • Line of sight.

  • No obstacles.

  • No reflection, multipath, diffraction, or scattering.

  • Isotropic antennas (radiate energy in all directions).

  • Spreading loss only.

  • No atmospheric attenuation or absorption.

  • No interference.

Equations

• Power density at distance $d$: $P<em>d = \frac{P</em>t G_t}{4 \pi d^2}$

  • $P_t$: transmitted power

  • $G_t$: gain of transmitting antenna

• Effective area of receiving antenna: $A = \frac{\lambda^2 G_r}{4 \pi}$

  • $\lambda$: wavelength

  • $G_r$: gain of receiving antenna

  • $c = f \lambda$

• Received power: $P<em>r = \frac{P</em>t G<em>t \lambda^2 G</em>r}{(4 \pi d)^2}$

• Path loss: $PL = \frac{P<em>t}{P</em>r} = \frac{(4 \pi d)^2}{G<em>t G</em>r \lambda^2}$

• Path loss in dB: $PL<em>{dB} = 10 \log</em>{10}(\frac{P<em>t}{P</em>r}) = -10 \log<em>{10}(G</em>t) - 10 \log<em>{10}(G</em>r) + 20 \log<em>{10}(f) + 20 \log</em>{10}(d) + K$

  • $K = -147.56$ (constant)

• Simplified equation (distance in km, frequency in MHz): $PL<em>{dB} = 32.44 + 20 \log</em>{10}(f<em>{MHz}) + 20 \log</em>{10}(d_{km})$

• Simplified equation (distance in meters, frequency in Hz): $PL<em>{dB} = 20 \log</em>{10}(d) + 20 \log_{10}(f) - 147.55$

Observations

• Path loss increases with distance and frequency.

• Frequency and distance dependent.

• Applications: satellite communication, microwave line of sight links, initial link budget for 5G, LTE, and Wi-Fi.

• Limitations:

  • Not suitable for indoor or urban environments.

  • Reflection, diffraction, and scattering are not considered.

  • Antenna gains and atmospheric effects are not considered.

  • Assumes perfect line of sight.

Example Calculation

• Access point on ceiling, laptop 200 meters away, frequency 2.4 GHz.

• Calculate path loss.

• Path Loss Calculation

  • $PL = 32.44 + 20 \log<em>{10}(f</em>{MHz}) + 20 \log<em>{10}(d</em>{km})$

  • $PL = 32.44 + 20 \log<em>{10}(2400) + 20 \log</em>{10}(0.2)$

  • $PL = 32.44 + 20(3.38) + 20(-0.699)$

  • $PL = 32.44 + 67.6 - 13.98$

  • $PL = 86.06 \text{ dB}$

• Assuming transmitted power is 200 milliwatts: $P<em>t(dBm) = 10 \log</em>{10}(200) = 23 \text{ dBm}$

• Received power: $P<em>r = P</em>t - PL = 23 \text{ dBm} - 86.06 \text{ dB} = -63.06 \text{ dBm}$

• Receiver card needs to detect at least -75 dBm signal.

Other factors

• Conductivity and dielectric constants of the earth.

  • Poor Dry ground $10^{-3}$

  • Average ground $5 \cdot 10^{-3}$

  • Good ground $2 \cdot 10^{-2}$

  • Seawater: 5

  • Freshwater $10^{-3}$

• Curved Reflecting Surfaces can make make the angle of reflection and incidence different.

Two-Ray Model

• More realistic: considers direct line of sight and ground-reflected path.

• Two paths for signal propagation:

  • Direct path

  • Reflected path

• Interference may be constructive or destructive.

• Depends on distance between transmitter receiver and height of transmitter and receiver.

• Assumptions:

  • Ground surface is flat and smooth.

  • Ideal reflection (no absorption).

  • Line of sight signal and ground reflected ray dominate.

    • Both antennas above the ground.

• Accurate for large-scale signal strength over several kilometers with cell towers > 50 meters.

Equation

• Received power: $P<em>r = \frac{P</em>t G<em>t G</em>r h<em>t^2 h</em>r^2}{d^4}$

  • $h_t$: height of transmitting antenna

  • $h_r$: height of receiving antenna

• Power falls off at 40 dB per decade.

• In dB: $PL<em>{dB} = 40 \log</em>{10}(d) - 10 \log<em>{10}(G</em>t) - 10 \log<em>{10}(G</em>r) - 20 \log<em>{10}(h</em>t) - 20 \log<em>{10}(h</em>r)$

Key Points

• Accounts for constructive and destructive interference.

• Depends on distance and height of transmit receiver.

• Applicable in urban and rural environments.

• Antenna placement can minimize destructive interference.

Limitations

• Flat earth assumption.

• Only considers one ground reflection.

Flat Earth Model

• Earth is flat, ground reflects radio waves perfectly.

• Considers direct and ground-reflected rays.

• Antennas at finite heights above the flat ground plane.

• Transmitter gain and receiver gain are 1.

• $PL<em>{dB} = 40 \log</em>{10}(d) - 20 \log<em>{10}(h</em>t) - 20 \log<em>{10}(h</em>r)$

• Applications: cellular network coverage planning, minimizing dead zones, interference management, capacity optimization.

• Limitations: terrain variations not considered, only one ground reflection.

Egli Model

• Terrain-based propagation model for urban and suburban environments.

• Developed by John Egli, based on UHF and VHF television transmission.

• Based on real-world measurements.

• Applicable to point to point communication (radio and TV broadcast).

• Estimates median path loss.

• Assumptions:

  • Rural and suburban areas.

  • Frequency range: 30 MHz to 3 GHz.

  • Vertically polarized antenna.

  • Significant antenna height.

  • Line of sight not strictly required.

Formula

• Takes into effect the heights and gains of the antennas

• $\frac{G<em>b G</em>m h<em>b h</em>m}{d^2} \beta$

  • $\beta = (\frac{40}{f_{MHz}})^2$

  • $PL<em>{dB} = -40 \log</em>{10}(d) + 10 \log<em>{10}(G</em>b) + 10 \log<em>{10}(G</em>m) + 20 \log<em>{10}(h</em>b) + 20 \log<em>{10}(h</em>m) + 10 \log_{10}(\beta)$

Limitations

• Does not account for signal loss due to trees and vegetation.

• Only considers one ground reflection.

Lee's Model

• Designed for cellular systems (800-900 MHz).

• Real-world measurements to empirical equations.

• Offers a reference distance-based path loss formula.

• Correction factors for environment, antenna height, power, and frequency.

• Two Modes:

  • Area to area mode: when detailed path profile is not available.

  • Point to point mode:

• Path profile: graphical numerical representation of the physical terrain obstacles.

Assumptions

• Detailed field measurements were done for the following;

  • Transmitter power: 10 watts

  • Transmitting base antenna base station antenna gain is six dBd.

  • Frequency, 900 megahertz.

  • Out of the transmitter is 30.5 meters, and out of the receiver is three meters

• Distance must be greater than 1 kilometer.

• Transmitter antenna gain: 6 dBd

• Transmitting power: 10 watts

• Omnidirectional antenna height: 30.5 meters.

• Area to Area Mode
  * Medium transmission loss is at the range of 1 kilometer
  * The slope of the path loss curve is gamma in dB per decade

Equation for Area to Area

• Medium path loss at a distance d : $L= L<em>0 + \gamma \log(d) + f</em>0$
  * $L<em>0$ is median transmission loss * $\gamma$ is the gamma of path loss curves. * $f</em>0$ is the adjustment factors to match field measured areas and areas.

Some Reference

• For open rural areas where Loss $L_0$ = 91.3 dB and slope $\gamma$ is 43.5 dB/decade

• Suburban areas a where Loss $L_0$ = dB and slope $\gamma$ dB/decade

Adjustment Factor

• $f<em>0= f</em>1 f<em>2 f</em>3 f<em>4 f</em>5$

• $f_1 = \frac{\text{actual base station antenna height}}{30.5}$

• $f_2 = \frac{\text{actual power transmitted in watt}}{10}$

• $f_3 = \frac{\text{actual gain factor of the base station antenna in dB}}{6}$

• $f_4 = \frac{\text{actual mobile antenna height in meters }}{3}$

  • If antenna is greater than 3 meters must be squared$\text{actual mobile antenna height in meters }^2$

• If antenna is less than 3 meters then height should not be squared.

• $f_5 = \frac{{\text actual frequency in use}}{900}^2$

Point To Point Calculation Factor

• $L<em>{50}= \text{loss} + 20\log</em>{10}(h_e/30)$

• Calculate The height and draw a slope

Okumura-Hata Model

• Empirical prediction model based on measurements in Tokyo city.

• Frequencies: 200 MHz to 2 GHz.

• No assumptions of plain earth or other models.

• Divided prediction area into open area, suburban area, and urban area.

Formulas for different Locations:

• Open Areas a + b log(r) - e

• Suburban Areas a + b log(r) - c

• Urban Areas a + b log(r) - d

Where

• a = 69.55 + 26.15 log(frequency carrier) -13.82 log(Base antenna high)

• b = 44.9 -6.55 log( base station antenna height)

• c= 2 (log 5 frequency carrier divide 28 the hold square) + 5.4 (factor for some area the carrier frequency is being adjusted again)

• d= 4.78 log (F sub c) squared -18.33 log (frequency carrier) + 40.94 (Open and suburban area)

• e =(factor area factor ) depends on three: height of the mobile station is also considered in factor e.(3.2 log(11.75)squared - 4.97 larger series used frequencies greater than 300 MHz use factor 8.29 (factor(1.5) - 1.1 Large Mobile antenna heights are also involved here) Medium and smaller city 1.1 log ( frequency ) -7 times .7 ( 1.56 ( log f - 0.8 ( medium or small sizes)

Limitations

• The model is limitation is that the frequency range is between one fifty megahertz and 1,500 megahertz.

• Base Should Be between 30 meters and 200.

• Mobile Needs to be from 1 and 10 meters.

• Distance always greater than 1.

Ibrahim and Parsons Model

• Field trials around London city.

• Concentration on urban propagation loss.

• Integrates with previous measurements to render the fraction effects on each 0.5 km square data.

• Divided the whole area into squares, with each square having h, u, and l parameters.

Parameters

• h: terrain height

  • Defined as the actual height of a peak basin plateau valley found in square Or the arithmetic mean of the minimum and maximum heights found in the square if it does not contain any such feature.

• u: degree of urbanization

  • *defined by 4 more floors building site percentage in square building site occupied by four or more square buildings 2 - 95 *urban environment - is one that focuses Street is used in buildings and London London so that's for the urban area

• l: land factor

  • percentage in squares is is actual percentage in squares is and actual buildings or

Some Factors and Formula

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