Path-loss and Shadowing (Large-scale Fading)ย ยท Path-loss and Shadowing (Large-scale Fading) PROF....
Transcript of Path-loss and Shadowing (Large-scale Fading)ย ยท Path-loss and Shadowing (Large-scale Fading) PROF....
Path-loss and Shadowing(Large-scale Fading)
PROF. MICHAEL TSAI
2016/04/08
Multipath
2
3
4
Friis Formula
TX Antenna
EIRP=๐๐ก๐บ๐ก
๐
Power spatial density๐
๐2
1
4๐๐2
๐ด๐
ร
ร
RX Antenna
โ ๐๐=๐๐ก๐บ๐ก๐ด๐4๐๐2
5
Antenna Aperture
โข Antenna Aperture=Effective Area
โข Isotropic Antennaโs effective area ๐จ๐,๐๐๐ โ๐๐
๐๐
โข Isotropic Antennaโs Gain=1
โข ๐ฎ =๐๐
๐๐๐จ๐
โข Friis Formula becomes: ๐ท๐ =๐ท๐๐ฎ๐๐ฎ๐๐
๐
๐๐ ๐ ๐ =๐ท๐๐จ๐๐จ๐
๐๐๐ ๐
6
๐ท๐ =๐ท๐๐ฎ๐๐ด๐4๐๐2
Friis Formula
โข๐๐
๐๐ ๐ ๐ is often referred as โFree-Space Path Lossโ (FSPL)
โข Only valid when d is in the โfar-fieldโ of the transmitting antenna
โข Far-field: when ๐ > ๐ ๐, Fraunhofer distance
โข ๐ ๐ =๐๐ซ๐
๐, and it must satisfies ๐ ๐ โซ ๐ซ and ๐ ๐ โซ ๐
โข D: Largest physical linear dimension of the antenna
โข ๐: Wavelength
โข We often choose a ๐ ๐ in the far-field region, and smaller than any practical distance used in the system
โข Then we have ๐ท๐ ๐ = ๐ท๐ ๐ ๐๐ ๐
๐
๐
๐ท๐ =๐ท๐๐ฎ๐๐ฎ๐๐
๐
๐๐ ๐ ๐
7
Received Signal after Free-Space Path Loss
๐ ๐ = ๐น๐๐ ๐ฎ๐๐ฎ๐๐๐๐ โ
๐๐๐ ๐ ๐
๐๐ ๐ ๐ ๐ ๐๐๐ ๐๐๐ ๐๐๐
phase difference due to propagation distance
Free-Space Path Loss
Complex envelope
Carrier (sinusoid)
8
Example: Far-field Distance
โข Find the far-field distance of an antenna with maximum dimension of 1m and operating frequency of 900 MHz (GSM 900)
โข Ans:
โข Largest dimension of antenna: D=1m
โข Operating Frequency: f=900 MHz
โข Wavelength: ๐ =๐
๐=
๐ร๐๐๐
๐๐๐ร๐๐๐= ๐. ๐๐
โข ๐ ๐ =๐๐๐
๐=
๐
๐.๐๐= ๐. ๐๐ (m)
9
Example: FSPL โข If a transmitter produces 50 watts of power, express the transmit
power in units of (a) dBm and (b) dBW.
โข If 50 watts is applied to a unity gain antenna with a 900 MHz carrier frequency, find the received power in dBm at a free space distance of 100 m from the antenna. What is the received power at 10 km? Assume unity gain for the receiver antenna.
โข Ans:
โข ๐๐ ๐๐๐๐๐ ๐๐ = ๐๐ ๐ ๐ฉ๐พ = ๐๐ ๐๐๐ฆ
โข Received Power at 100m
๐ท๐(๐๐๐๐) =
๐๐ ร ๐ ร ๐ ร๐ ร ๐๐๐
๐๐๐ ร ๐๐๐
๐
๐๐ ร ๐๐๐ ๐ = ๐. ๐ ร ๐๐โ๐ ๐พ
= โ๐๐. ๐ (๐ ๐ฉ๐พ)
โข Received Power at 10km
๐ท๐ ๐๐๐๐ = ๐ท๐ ๐๐๐๐๐๐๐
๐๐๐๐๐
๐
= ๐. ๐ ร ๐๐โ๐๐ ๐พ
= โ๐๐. ๐ (๐ ๐ฉ๐พ) 10
Two-ray Model
TX Antenna
๐
๐
๐
๐ฅ ๐ฅโฒ
RX Antenna
โ๐กโ๐
๐บ๐
๐บ๐๐บ๐
๐บ๐
๐2โ๐๐๐ฆ ๐ก =
๐ ๐๐
4๐
๐บ๐๐บ๐ ๐ ๐ก exp โ๐2๐๐๐
๐+๐ ๐บ๐๐บ๐ ๐ ๐ก โ ๐ exp โ
๐2๐ ๐ฅ + ๐ฅโฒ
๐
๐ฅ + ๐ฅโฒexp ๐2๐๐๐๐ก
Delayed since x+xโ is longer. ๐ = (๐ฅ + ๐ฅโฒ โ ๐)/๐
R: ground reflection coefficient (phase and amplitude change) 11
Two-ray Model: Received Power
โข ๐ท๐ = ๐ท๐๐
๐๐
๐ ๐ฎ๐๐ฎ๐
๐+
๐ฎ๐๐ฎ๐ ๐๐๐ โ๐๐ซ๐
๐+๐โฒ
๐
โข The above is verified by empirical results.
โข ๐ซ๐ = ๐๐ (๐ + ๐โฒ โ ๐)/๐
โข ๐ + ๐โฒ โ ๐ = ๐๐ + ๐๐๐ + ๐ ๐ โ ๐๐ โ ๐๐
๐ + ๐ ๐
12
l
x
xโ
xโ
x
Two-ray Model: Received Power
โข When ๐ โซ ๐๐ + ๐๐, ๐ซ๐ =๐๐ ๐+๐โฒโ๐
๐โ
๐๐ ๐๐๐๐
๐๐
โข For asymptotically large d, ๐ + ๐โฒ โ ๐ฅ โ ๐ , ๐ โ ๐, ๐๐๐๐ โ๐ฎ๐๐ฎ๐ , ๐ โ โ๐ (phase is inverted after reflection)
โข๐ฎ๐๐ฎ๐
๐+
๐ฎ๐๐ฎ๐ ๐๐๐ โ๐๐ซ๐
๐+๐โฒ
๐
โ๐ฎ๐๐ฎ๐
๐
๐
๐ + ๐๐๐ โ๐๐ซ๐ ๐
โข ๐ + ๐๐๐ โ๐๐ซ๐ ๐ = ๐ โ ๐๐๐ ๐ซ๐๐+ ๐๐๐๐๐ซ๐ = ๐ โ
๐๐๐จ๐ฌ ๐ซ๐ = ๐๐๐๐๐(๐ซ๐
๐) โ ๐ซ๐๐
โข ๐ท๐ โ๐ ๐ฎ๐๐ฎ๐
๐๐ ๐
๐๐๐ ๐๐๐๐
๐๐
๐๐๐ญ =
๐ฎ๐๐ฎ๐๐๐๐๐
๐ ๐
๐
๐๐ญ
13Independent of ๐ now
14
๐๐ =4โ๐กโ๐๐
โ๐ก
Could be a natural choice of cell size
Indoor Attenuation
โข Factors which affect the indoor path-loss:
โข Wall/floor materials
โข Room/hallway/window/open area layouts
โข Obstructing objectsโ location and materials
โข Room size/floor numbers
โข Partition Loss:
15
Partition type Partition Loss (dB) for 900-1300 MHz
Floor 10-20 for the first one,6-10 per floor for the next 3,A few dB per floor afterwards.
Cloth partition 1.4
Double plasterboard wall 3.4
Foil insulation 3.9
Concrete wall 13
Aluminum siding 20.4
All metal 26
Simplified Path-Loss Model
โข Back to the simplest:
โข ๐0: reference distance for the antenna far field (usually 1-10m indoors and 10-100m outdoors)
โข ๐พ: constant path-loss factor (antenna, average channel attenuation), and sometimes we use
โข ๐พ: path-loss exponent
16
๐๐ = ๐๐ก๐พ๐0๐
๐พ
๐พ =๐
4๐๐0
2
Some empirical results
17
Measurements in Germany Cities
Environment Path-loss Exponent
Free-space 2
Urban area cellular radio 2.7-3.5
Shadowed urban cellular radio
3-5
In building LOS 1.6 to 1.8
Obstructed in building 4 to 6
Obstructed in factories 2 to 3
Empirical Path-Loss Model
โข Based on empirical measurements
โข over a given distance
โข in a given frequency range
โข for a particular geographical area or building
โข Could be applicable to other environments as well
โข Less accurate in a more general environment
โข Analytical model: ๐ท๐/๐ท๐ is characterized as a function of distance.
โข Empirical Model: ๐ท๐/๐ท๐ is a function of distance including the effects of path loss, shadowing, and multipath.
โข Need to average the received power measurements to remove multipath effects Local Mean Attenuation (LMA) at distance d.
18
Example: Piecewise Linear Model
โข N segments with N-1 โbreakpointsโ
โข Applicable to both outdoor and indoor channels
โข Example โ dual-slope model:
โข ๐พ: constant path-loss factor
โข ๐พ1: path-loss exponent for ๐0~๐๐โข ๐พ2: path-loss exponent after ๐๐ 20
๐๐ ๐ =
๐๐ก๐พ๐0๐
๐พ1
๐๐ก๐พ๐๐๐
๐พ1 ๐
๐๐
๐พ2
๐0 โค ๐ โค ๐๐ ,
๐ > ๐๐.
Shadow Fading
โข Same T-R distance usually have different path loss
โข Surrounding environment is different
โข Reality: simplified Path-Loss Model represents an โaverageโ
โข How to represent the difference between the average and the actual path loss?
โข Empirical measurements have shown that
โข it is random (and so is a random variable)
โข Log-normal distributed
21
Log-normal distribution
โข A log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed:
โข ๐ฅ: the random variable (linear scale)
โข ๐, ๐2: mean and variance of the distribution (in dB)
22
๐๐ ๐ฅ; ๐, ๐2 =1
๐ฅ๐ 2๐exp โ
log ๐ฅ โ ๐ 2
2๐2
logarithm of the random variable
normalized so that the integration of the pdf=1
Log-normal Shadowing
โข Expressing the path loss in dB, we have
โข ๐ฟ๐: Describes the random shadowing effects
โข ๐ฟ๐~๐ต(๐, ๐๐)
(normal distribution with zero mean and ๐๐ variance)
โข Same T-R distance, but different levels of clutter.
โข Empirical Studies show that ๐ ranges from 4 dB to 13dB in an outdoor channel
23
๐๐ฟ ๐ ๐๐ต = ๐๐ฟ ๐ + ๐๐ = ๐๐ฟ ๐0 + 10๐พ log๐
๐0+ ๐๐
Why is it log-normal distributed?
โข Attenuation of a signal when passing through an object of depth d is approximately:
โข ๐ผ: Attenuation factor which depends on the material
โข If ๐ถ is approximately the same for all blocking objects:
โข ๐๐ก = ๐ ๐๐: sum of all object depths
โข By central limit theorem, ๐ ๐~๐ต(๐, ๐๐) when the
number of object is large (which is true).
24
๐ ๐ = exp โ๐ผ๐
๐ ๐๐ก = exp โ๐ผ
๐
๐๐ = exp โ๐ผ๐๐ก
Path Loss, Shadowing, and Multi-Path
25
Cell Coverage Area
โข Cell coverage area: expected percentage of locations within a cell where the received power at these locations is above a given minimum.
26
Some area within the cell has received power lower than ๐๐๐๐
Some area outside of the cell has received power higher than ๐๐๐๐
Cell Coverage Area
โข We can boost the transmission power at the BS
โข Extra interference to the neighbor cells
โข In fact, any mobile in the cell has a nonzero probability of having its received power below ๐ท๐๐๐.
โข Since Normal distribution has infinite tails
โข Make sense in the real-world: in a tunnel, blocked by large buildings, doesnโt matter if it is very close to the BS
27
Cell Coverage Area
โข Cell coverage area is given by
โข ๐ท๐จ โ ๐ ๐ท๐ ๐ > ๐ท๐๐๐
28
๐ช = ๐ฌ๐
๐ ๐น๐ ๐๐๐๐ ๐๐๐๐
๐ ๐ท๐ ๐ > ๐ท๐๐๐ ๐๐ ๐ ๐จ ๐ ๐จ
=๐
๐ ๐น๐ ๐๐๐๐ ๐๐๐๐
๐ฌ ๐ ๐ท๐ ๐ > ๐ท๐๐๐ ๐๐ ๐ ๐จ ๐ ๐จ
1 if the statement is true, 0 otherwise. (indicator function)
๐ช =๐
๐ ๐น๐ ๐๐๐๐ ๐๐๐๐
๐ท๐จ๐ ๐จ =๐
๐ ๐น๐ ๐
๐๐
๐
๐น
๐ท๐จ ๐๐ ๐ ๐ ๐ฝ
Cell Coverage Area
โข Q-function:
29
๐๐ด = ๐ ๐๐ ๐ โฅ ๐๐๐๐ = ๐๐๐๐๐ โ ๐๐ก โ ๐๐ฟ ๐
๐
๐ ๐ง โ ๐ ๐ > ๐ง = ๐ง
โ 1
2๐exp โ
๐ฆ2
2๐๐ฆ
Log-normal distributionโs standard deviation
z
Cell Coverage Area
โข Solving the equations yield:
โข ๐ =๐ท๐๐๐โ๐ท๐ ๐น
๐, ๐ =
๐๐๐ธ๐๐๐๐๐ ๐
๐
โข If ๐ท๐๐๐ = ๐ท๐ ๐น
30
๐ถ = ๐ ๐ + exp2 โ 2๐๐
๐2๐
2 โ ๐๐
๐
average received power at cell boundary (distance=R)
๐ถ =1
2+ exp
2
๐2๐
2
๐
Example
โข Find the coverage area for a cell with
โข a cell radius of 600m
โข a base station transmission power of 20 dBm
โข a minimum received power requirement of -110 dBm.
โข path loss model: ๐๐(๐) = ๐๐ก๐พ๐0
๐
๐พ, ๐พ = 3.71,๐พ = โ31.54 ๐๐ต, ๐0 = 1, shadowing
standard deviation ๐ = 3.65 dB
โข Ans:
โข ๐ท๐ ๐น = ๐๐ โ ๐๐. ๐๐ โ ๐๐ ร ๐. ๐๐ ร ๐๐๐๐๐ ๐๐๐ = โ๐๐๐. ๐ ๐ ๐ฉ๐
โข ๐ =โ๐๐๐+๐๐๐.๐
๐.๐๐= ๐. ๐๐, ๐ =
๐๐ร๐.๐๐ร๐.๐๐๐
๐.๐๐= ๐. ๐๐
โข ๐ช = ๐ธ ๐. ๐๐ + ๐๐๐ โ๐. ๐๐ ๐ธ โ๐. ๐๐๐ = ๐. ๐ (not good)
โข If we calculate C for a minimum received power requirement of -120 dBm
โข C=0.988!
31
๐ถ = ๐ ๐ + exp2 โ 2๐๐
๐2๐
2 โ ๐๐
๐
๐ =๐ท๐๐๐โ๐ท๐ ๐น
๐, ๐ =
๐๐๐ธ๐๐๐๐๐ ๐
๐
Example: road corners path loss
32
5 m
40 m
10 m
Radio: Chipcon CC2420IEEE 802.15.4, 2.4 GHzTX pwr: 0 dBm
8 dBi peak gainomni-directionalantenna
Intel-NTU Connected Context Computing Center
โข Compare the path-loss exponent of three different locations:
1. Corner of NTU_CSIE building
2. XinHai-Keelong intersection
3. FuXing-HePing intersection
Link Measurements โPath loss around the corner building
33
1 2 3
Passing-by vehicles
Occasionally Frequently Frequently
Buildings Around
No Few buildings
Some high buildings
Intersection Narrow Wide Wide
34