Path loss

1. Path Loss ve Shadowing

2. Wireless Channels
• Radyo kanallarının modellenmesi tipik olarak istatistiksel olarak
gerçekleştirilir. Bu istatistiksel modelleme yaklaşım modellenecek olan
haberleşme sistemi ve spekturm için yapılmış olan ölçümlere dayandırılır.
• Wireless radio channel modeling is typicaly done in a statistical fashion
based on measurements made specificaly for an intended communication
system or spectrum allocation.
• Yayılım modelleri geleneksel olarak verilen uzaklıkta vericiden alınan
sinyalin ortalama gücünün tahmin edilmesini sağlamaktadırlar. Bu uzaklıkta
laınacak olan sinyal gücü bulunan ortama göre değişmektedir.
• Radio propagation models have focused on predicting the average received
signal strength at a give distance from the transmitter, as well as the
variability of the signal strength in close proximity to a particular location.

3. Wireless Channels
• Kablosuz kanalların temel karekteristikleri zaman ve frekansa göre değişimler
gösterebilmektedirler.
• Main characteristics of wireless channels may have been variations of the
channel strength over time and frequency.
• Large-scale propagation models: verici ile arasındaki mesafe için ortalama sinyal
gücünün tahmin edilmesinin sağlayan yayılım modelleri vericinin kapsama
alanının belirlenmesinde efektif biçimde kullanılmaktadır ve large scale
propagation modelleri olarak adlandırılırlar. Bu modeller yol kaybını büyük
nesnelerin gölgeleme etkilerini ve uzaklığı fonksiyonu olarak farz eder ve
frekanstan bağımsızdır.
• Large-scale propagation models: propagation models that predict the mean signal
strength for an arbitrary transmitter receiver seperation distance are usefull in
estimating the radio coverage area of a transmitter and are called large scale
propagation models. These models assume the the path loss as a a function of
distance and shadowing by large objects, typically frequency independent.

4. Wireless Channels
• Models of large-scale effects
• The most appropriate path loss model depends on the location of the receiving antenna
• L1, free space loss is likely to give an accurate estimate of path loss.
• L2, a strong line-of-sight is present, but ground reflections can significantly influence path loss.
The plane earth loss model appears appropriate.
• L3, plane earth loss needs to be corrected for significant diffraction losses, caused by trees cutting
into the direct line of sight.
• L4, a simple diffraction model is likely to give an accurate estimate of path loss.
• L5, loss prediction fairly difficult and unreliable since multiple diffraction is involved.

5. Wireless Channels
• Small-scale propagation models: kısa mesafelerde veya kısa sürelerde
alınan sinyal üzerindeki hızlı dalgalanmaları karakterize eden yayılşım
modellerine small-scale yayılım veya kayıp modelleri adı verilir.
• Smale-scale propagation models: propagation models that
characterize the rapid fluctuations of the received signal strength over
very short travel distances or short time durations are called small-
scale propagation or fading models.

6. Wireless Channels
Bu derste larg-scale yayılım modelleri incelenecektir
In this lecture, large-scale propagation models will be
studied.

7. Free Space Propagation Model
• This model is used to predict received signal strength when the
transmitter and receiver have a clear, un obstacled, line of sight path
between them. The path loss then depends on how much of this
power is captured by the receiving antenna.
• If effective aperture of the antenna is Ar, then the power which can
be delivered to the receiver is simply

8. Free Space Propagation Model
• The relation between the transmit and receive power with non-isotropic
antennas with Gt and Gr gains is given by (Friis free space equation)
• Pt is transmitted power
• Pr is receivedpower at distance d
• Gt is transmitter antenna gain
• Gr is receiver antenna gain
• d is T-R seperation in meters

9. Free Space Propagation Model
• λ is related to the carrier frequency by
• fc is the carrier frequency in Hertz and c is the speed of the light in
meters/sec
• Then, free space received signal strength at distance d

10. Path Loss
• The path loss for free space model when antenna gains are included is given by
• The dB path gain is defined as the negative of the dB path loss
• PG=-PL=10log10(Pr/Pt) which is generally a negative number
𝑃𝐿 𝑑𝐵 = −10log[
𝐺 𝑇 𝐺𝑟 𝜆2
(4𝜋)2 𝑑2
]
• Frain hufer distance (Far field): df=2D2/λ where D is the largest physical dimension
of the antenna
• The free space model is valid for values of d which are in the far field of the
transmitting antenna.
• To be in the far field region df must satisfy
• df>>D----D>> λ/2 then df >> λ

11. • Recall the received power at the output of the receiving antenna
• The term (4πd/λ)2is known as the free space path loss and it may be
given in dB (assume Gr=Gt=1 or 0 dB)
•
Free SpacePath Loss

12. • Example: Find df for an antenna with maximum dimension of 1 m and
operating frequency of 900 MHz?
• D=1m fc =900 MHz  λ=c/f λ=3x108/900x106=1/3 m
• df=2D2/λ2/(1/3)=6 m
df>>D and df>> λ
Example: Pt=50 watt fc=900 MHz Gt=Gr=1 find Pr for d=100 m and d=10 km?
Pr =50x1x1x(1/3)2/(4xπ2x1002)=3.5x10-6 watt(dBm)=10log(3.5x10-3)
=-24.5 dBm
Pr(d)= Pr (d0)+20xlog(d0/d) Pr(10 km)=-24.5+20xlog(100/10000)=-24.5-40=-
64.5 dBm
Free SpacePath Loss

13. • Example: Determine the isotropic free space loss at 4 GHz for the
shortest path to a geosynchronous satellite from earth (35,863 km).
• PL=20log10(4x109)+20log10(35.863x106)-147.56dB
• PL=195.6 dB
• Suppose that the antenna gain of both the satellite and ground-based
antennas are 44 dB and 48 dB, respectively
• PL=195.6-44-48=103.6 dB
Free SpacePath Loss

14. Basic Propagation Mechanisms
• Reflection, diffraction and scattering are the three basic propagation mechanism
which impact propagation in a mobile communication systems.
• Reflection occurs when a propagation electromagnetic wave impinges upon an
object which has very large dimensions when compared to the wavelength of the
propagation wave.
• Diffraction occurs when the radio path between the transmitter and receiver is
obstructed by a surface that has sharp irregularities. The secondary waves
resulting from the obstructing surfaces are present throughout the space and
even behind the obstacle, giving rise to a bending of waves, even when a line of
sigth path does not exist between T-R.
• Scattering occurs when the medium throug which the wave travels consists of
objects with dimensions that are small compared to the wavelength and where
the number of obstacles per unit volume is large.

15. Basic Propagation Mechanisms

16. Transmit and Receive Signal Models
• Frequency range: 0.3-3GHz (UHF) and 3-30 GHz (SHF)
• Real signals
• Complex signal models are used for analytical simplicity
• We model the transmitted signal as
• 𝑠 𝑡 = ℛ 𝑢 𝑡 𝑒 𝑗2𝜋𝑓𝑐 𝑡 = 𝑥 𝑡 cos 2𝜋𝑓𝑐 𝑡 − y 𝑡 sin 2𝜋𝑓𝑐 𝑡
• u(t)=x(t)+jy(t) is a complex baseband signal

17. Ground Reflection (Two-Ray Model)
• This model has been found to reasonably accurate for predicting the large
scale signal strength over distances of several kilometers for mobile radio
systems taht use tall towers (over 50m), as well as LOS microcell channels
in urban environments.
• Free space propagation does not apply in a mobile radio environment
• Besides distance and frequency, path loss also depends on the antenna
heights
• Consider the signal transmission over a smooth, reflecting, and flat plane
•
•

18. Ground Reflection (Two-Ray Model)
• For 2-ray models, the received power at a distance d from the
transmitter can be expressed as
• The patho loss for 2-ray model can be expressed in dB as
• 𝑃𝐿 𝑑𝐵 = 40logd − (10log𝐺𝑡 + 10log𝐺𝑟 + 20logℎ 𝑡 + 20logℎ 𝑟)

19. Ground Reflection (Two-Ray Model)
• Example: Determine the critical distance for the two-ray model in an urban
microcell (ht = 10m, hr = 3 m) and an indoor microcell (ht = 3 m, hr = 2 m)
for fc = 2 GHz.
• dc = 4hthr/λ = 800 meters for the urban microcell and 160 meters for the
indoor system. A cell radius of 800 m in an urban microcell system is a bit
large: urban microcells today are on the order of 100 m to maintain large
capacity. However, if we used a cell size of 800 m under these system
parameters, signal power would fall off as d2 inside the cell, and
interference from neighboring cells would fall off as d4, and thus would be
greatly reduced. Similarly, 160 m is quite large for the cell radius of an
indoor system, as there would typically be many walls the signal would
have to go through for an indoor cell radius of that size. So an indoor
system would typically have a smaller cell radius, on the order of 10-20 m.

20. Ground Reflection (Two-Ray Model)
• Received Power versus Distance for Two-Ray Model.

21. Path Loss Models
• By using path loss models to estimate the received signal level as a function
of distance, it becomes possible to predict the SNR for a mobile
communication system.
• Log distance path loss model: Both theoratical and measurement based
propagationmodels indicate that average received signal power decreases
logaritmically with distance whether in outdoor or indoor radio channels.
• The average large sclae path loss for an arbitrary T-R seperation is
expressed as:
• 𝑃𝐿 𝑑𝐵 = 𝑃𝐿 𝑑0 + (10nlog
𝑑
𝑑0
)  n path loss exponent, 𝑑0 close in
reference distance, d T-R seperation

22. Path Loss Models
• Log normal shadowing model: Log distance path loss model is not valid for
ecery environment. Measurements have shown that at any value of d the
path loss at a particular location is random and distributed log normally
(normal in dB) about the mean distance dependent value.
• 𝑃𝐿 𝑑𝐵 = 𝑃𝐿 𝑑0 + 10nlog
𝑑
𝑑0
+ Xσ  Xσ zero mean Gaussian
distributed RV in dB with standard deviation σ (also in dB)
• The log normal distribution describes the random shadowing effects which
occur over a large nukmber of measurement locations which have the
same T-R seperation, but have different levels of cluster on the propagation
path. This phenameon is referred to log normal shadowing.

23. Path Loss Models
• The probability that the received signal level will exceed a certain
value Z can be calculated from the cumulative sensitivity function of
• 𝑝(𝑃𝑟(𝑑) > 𝑍) = 𝑄(𝑍 − 𝑃𝑟(𝑑)/𝜎) where Q is a function
• 𝑄 𝑍 = 1/ 2𝜋( 𝑍
∞
exp
𝑥2
2
𝑑𝑥) = 1/2[1 − erf(𝑍/ 2)]=1-Q(-Z)
• 𝑝(𝑃𝑟 𝑑 < 𝑍) = 𝑄(𝑃𝑟 𝑑 − 𝑍/𝜎)

24. Examples
• Distance from transmitter 100m, 200m, 1000m, 3000m
• Measured received power 0dBm, -20dBm, -35 dBm, -70 dBm
• Estimate the received powers taking reference 100m
• Compute the variance between estimated and measured values
• Solution:
• Pr(d0)=0 dBm