1. A Survey of Various Propagation Models for Mobile Communication
Tapan K Sarkar, Zhong Ji, Kyungjung Kim, Abdellatif Medouri, and Magdalena Salazar-Palma
IEEE Antenna and Propagation Magazine, Vol. 45, No. 3, June 2003
Presented by Lu-chuan Kung

2. Outline Mobile radio propagation Models for Path Loss
Empirical (statistical) models
Site-specific (deterministic) models
Models for Small-scale Fading
Impulse-Response Models

3. Mobile Radio Propagation
EM wave
Radio Wave Propagation:
Reflection
Diffraction
Scattering
Multi-path channel impulse response

4. Basic Definitions Path Loss Power-Delay Profile
Friis free-space equation
Metrics (dBm, mW)
P(dBm) = 10 * log[ P(mW) ]
Power-Delay Profile
Take spatial average of |hb(t;τ)|2 over a local area

5. Basic Definitions Time-Delay Spread First-arrival delay (τA)
Mean excess delay
RMS delay

6. Inter-symbol Interference
Slide from R. Struzak

7. Basic Definitions Coherence Bandwidth Doppler spread Coherence Time
Range of frequency over which channel is “flat”
Relation to delay spread
Doppler spread
Measure spectral broadening caused by motion of the mobile
Coherence Time
Time duration over which channel impulse response is invariant

8. Models of Path Loss Log-distance Path Loss Model Log-normal Shadowing
Xσ: N(0,σ) Gaussian distributed rv

9. Models for Path Loss Empirical Models
Okumura Model
L50: median of propagation path loss
LF: free-space propagation loss
Amu(f,d): median attenuation
G(hte), G(hre): gain factors for BS and mobile antenna
GAREA: environment gain
Applicable frequncies: 150 MHz to 1920 MHz (typically is extrapolated up to 3000 MHz)
Disadvantage: slow response to rapid changes in terrain

10. Models for Path Loss Empirical Models
Dual-slope model
P1=PL(d0): the path loss at d0
dbrk: Fresnel breakpoint
Lb: basic transmission-loss parameter
n1,n2: slopes of the best-fit line before and after dbrk

11. Models for Path Loss Empirical Models: Indoor Case
Indoor Log-distance path loss model
FAF(q): floor attenuation factor
WAF(p): wall attenuation factor

12. Models for Path Loss Empirical Models: Indoor Case
Indoor Log-distance path loss model
γ ranges from 1.5 to 4
γ depends on frequency and building materials

13. Site-specific Path Loss Models Ray-tracing
Ray-tracing Technique
Assume energy is radiated through infinitesimally small tubes, often called rays
Model signal propagation via ray propagation

14. Ray-tracing Technique: Image Method
Images of a source serve as secondary sources
N reflecting planes
N first-order images
N(N-1) two-reflection images
N(N-1)(N-1) three-reflection images
Efficient but cannot handle complex environments

15. Ray-tracing Technique: Brute-force Method
Considers a bundle of transmitted rays
Generates reflecting and refracting rays when hits an object
Generates a family of diffracting rays when hits a wedge

16. Ray-tracing Model 2-D Ray-tracing model 3-D model
Each ray is a ray sector of sector angle φ
Smallerφprovides higher accuracy
3-D model
Each ray tube occupy the same solid angle
Antenna patterns are incorporated

17. Site-specific Path Loss Model: FDTD Models
Ray-tracing fails for complex lossy structures with finite dimentions
Finite-Difference Time-Domain (FDTD) method
Solve Maxwell’s equations numerically
Complete solution for all points in the map
Requires large computational resources

18. Site-specific Path Loss Model: Artificial Neural-Network Models
Artificial Neural-Network Models (ANNs)
Use neural network models to predict path loss from noisy measurements
Pros:
Better accuracy than statistical model
Better computational efficiency than other site-specific models
Cons:
Slow convergence
Unpredictable solutions during learning

19. Models for Small-Scale Fading
Rayleigh fading
Assume a large number of scattering sources
By Central Limit Theorem, signal is a Gaussian rv with random phase between 0~2π
The power (envelope) of this random Gaussian vector is Rayleigh distributed

20. An Example of Rayleigh Fading
A typical Rayleigh fading envelope at 900MHz, mobile unit velocity = 120km/hr

21. Models for Small-Scale Fading
Ricean Distribution
A: peak amplitude of the dominant signal
I0(): modified Bessel function of the first kind
Add a dominant LOS signal to Rayleigh fading
Ricean factor: K=A2/2σ2

22. Models for Small-Scale Fading
Log-normal Fading
m: median value
σ: standard deviation

23. Models for Small-Scale Fading
Suzuki Model
Combines log-normal and Rayleight distributions

24. Models for Small-Scale Fading
Nakagami Model
r: envelope amplitutde
Ω=<r2>: time-averaged power of received signal
m: the inverse of normalized variance of r2
Get Rayleigh when m=1

25. Impulse-Response Models
Complete characterization of the linear system
Model the effect of multi-path fading
Measurement-based Models
Statistical Models
Deterministic Models

26. Impulse-Response Models Measurement-based Models:
Direct Pulse Measurement
Minimum resolvable delay = probing pulse width Tbb
Subject to interference and noise

27. Impulse-Response Models: Measurement-based Models
Spread-spectrum Sliding Correlator

28. Impulse-Response Models: Measurement-based Models
Swept-frequency measurements
Pros:
Provide both amplitude and phase information
Cons:
Require hardwired synchronization between TX and RX
Need fast sweeping times but reduces time resolution

29. Impulse-Response Models: Statistical Models
Two-ray Rayleigh Fading Model
α1 & α2: independent Rayleigh r.v.
θ1 & θ2 ~ Uni[0, 2π]
τ: time delay between the two rays

30. Impulse-Response Models: Statistical Models
SIRCIM Model
Based on measurements at 1300MHz in 5 factory and other buildings
Model power-delay profile as a piecewise function
For LOS:
For OBS:

31. Conclusion With propagation models, we can
Provide installation guidelines
Mitigate interference
Design better wireless system