23
EELE 6333: Wireless Commuications Chapter # 2 : Path Loss and Shadowing (Part Two) Spring, 2012/2013 EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 1 / 23
EELE 6333: Wireless Commuications
Chapter # 2 : Path Loss and Shadowing
(Part Two)
Spring, 2012/2013
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 1 / 23
Outline
1 Empirical Path Loss Models
2 Simplified Path Loss Model
3 Shadow Fading
4 Combined Path Loss and Shadowing
5 Outage Probability under Path Loss and Shadowing
6 Cell Coverage Area
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 2 / 23
Empirical Path Loss ModelsIntroduction ...1
Most mobile communication systems operate in complexpropagation environments that cannot be accurately modeled byfree-space path loss or ray tracing.
Path loss models have been developed over the years to predict pathloss in typical wireless environments such as large urban macrocells,urban microcells, and inside buildings.
These models are mainly based on empirical measurements:
Over a given distance.In a given frequency range.In a particular geographical area or building.
Applications of these models are not always restricted toenvironments in which the empirical measurements were made⇒ the accuracy of such empirically-based models applied to moregeneral environments is somewhat questionable.
Many wireless systems use these models as a basis for performanceanalysis.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 3 / 23
Empirical Path Loss ModelsIntroduction ...2
Local mean attenuation (LMA)
Defined as average of the path loss at a given distance over severalwavelengths.
The average is used to remove the effect of the multipath on themodel.
Measurements are typically taken throughout the environment, andpossibly in multiple environments with similar characteristics.
Empirical path loss
The average of the LMA measurements at distance d , averaged over allavailable measurements in the given environment.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 4 / 23
Empirical Path Loss ModelsThe Okumura Model ... 1
One of the most common models for signal prediction in large urbanmacrocells.
Applicable over distances of 1-100 Km and frequency ranges of150-1500 MHz.
The empirical path loss formula of Okumura at distance dparameterized by the carrier frequency fc is given by:
PL(d)dB = L(fc , d) + Amu(fc , d)− G (ht)− G (hr )− GAREA
where:
L(fc , d) is free space path loss at distance d and carrier frequency fc .Amu(fc , d) is the median attenuation in addition to free space pathloss across all environments.G (ht)/G (hr ) is the base station/mobile antenna height gain factor.GAREA is the gain due to the type of environment.
The values of Amu(fc , d) and GAREA are obtained from Okumura’sempirical plots.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 5 / 23
Empirical Path Loss ModelsThe Okumura Model ... 2
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 6 / 23
Empirical Path Loss ModelsThe Okumura Model ... 3
Okumura derived empirical formulas for G (ht) and G (hr ) as
Main disadvantage of this model is its slow response to rapid changein the terrain.
Okumura’s model has a 10− 14 dB empirical standard deviationbetween the predicted and the measured pathloss values.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 7 / 23
Empirical Path Loss ModelsHata Model
The Hata model is an empirical formulation of the graphical pathloss data provided by Okumura.
Valid over roughly the same range of frequencies, 150-1500 MHz.
Simplifies calculation of path loss since it is a closed-form formula.
The standard formula for empirical path loss in urban areas underthe Hata model is
PL,urban(d)dB = 69.55 + 26.16 log10(fc)− 13.82 log10(ht)− a(hr ) +(44.9− 6.55 log10(ht)) log10(d)
where a(hr ) is a correction factor for the mobile antenna heightbased on the size of the coverage area.
The Hata model well-approximates the Okumura model fordistances d > 1 Km
Does not model propagation well in current cellular systems withsmaller cell sizes and higher frequencies.Indoor environments are also not captured with the Hata model.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 8 / 23
Empirical Path Loss ModelsPiecewise Linear (Multi-Slope) Model ... 1
A common empirical method for modeling path loss in outdoormicrocells and indoor channels.
This approximation relates dB attenuation with the log-distance.
Piecewise linear model represents an approximation to differentmeasurements.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 9 / 23
Empirical Path Loss ModelsPiecewise Linear (Multi-Slope) Model ... 2
A piecewise linear model with N segments must specify N − 1breakpoints d1, · · · , dN−1 and the slopes corresponding to eachsegment s1, · · · , sN .
Different methods can be used to determine the number andlocation of breakpoints to be used in the model.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 10 / 23
Empirical Path Loss ModelsIndoor Attenuation Factors ... 1
It is difficult to find generic models that can be accurately applied todetermine empirical path loss in a specific indoor setting. WHY ?!!
Indoor path loss models must accurately capture the effects ofattenuation across floors due to partitions, as well as between floors.
The attenuation per floor is greatest for the first floor that is passedthrough and decreases with each subsequent floor passed through,WHY?!!!
Because the number of attenuating floors increases due to thescattering up the side of the building and reflections from adjacentbuildings.Ex. At 900 MHz, the attenuation when the transmitter and receiverare separated by a single floor ranges from 10-20 dB, whilesubsequent floor attenuation is 6-10 dB per floor for the next threefloors, and then a few dB per floor for more than four floors.
If the transmitter is located outside the building, the penetrationloss decreases by about 1.4 dB per floor at floors above the groundfloor. WHY ?!!!
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 11 / 23
Empirical Path Loss ModelsIndoor Attenuation Factors ... 2
The experimental data for floor and partition loss can be added toan analytical or empirical dB path loss model PL(d) as
PrdBm = PtdBm − PL(d)−∑Nf
i=1 FAFi −∑Np
i=1 PAFi
where FAFi represents the floor attenuation factor (FAF) for the ithfloor traversed by the signal, and PAFi represents the partitionattenuation factor (PAF) associated with the ith partition traversedby the signal. The number of floors and partitions traversed by thesignal are Nf and Np, respectively.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 12 / 23
Simplified Path Loss Model ... 1
The following simplified model for path loss as a function of distanceis commonly used for system design
Pr = PtK[d0d
]γwhere K is a unitless constant which depends on the antennacharacteristics and the average channel attenuation, d0 is a referencedistance for the antenna far-field, and γ is the path loss exponent.
PrdBm = PtdBm + KdB − 10γ log10
[dd0
].
The values for K , d0, and γ can be obtained to approximate eitheran analytical or empirical model.
d0 is typically assumed to be 1-10 m indoors and 10-100 m outdoors.
When the simplified model is used to approximate empiricalmeasurements ⇒ KdB = 20 log10
λ4πd0
(assuming omnidirectionalantennas).
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 13 / 23
Simplified Path Loss Model ... 2
K can be determined by measurement at d0 or optimized (alone ortogether with γ) to minimize the mean square error (MSE) betweenthe model and the empirical measurements.
The value of γ depends on the propagation environment.
The value of γ for more complex environments can be obtained via aminimum mean square error (MMSE) fit to empirical measurements.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 14 / 23
Simplified Path Loss Model ... 3
Ex. 2.3: Consider the set of empirical measurements of Pr/Pt
given in the table below for an indoor system at 900 MHz. Find thepath loss exponent γ that minimizes the MSE between the simplifiedmodel and the empirical dB power measurements, assuming thatd0 = 1 m and K is determined from the free space path gainformula at this d0. Find the received power at 100 m for thesimplified path loss model with this path loss exponent and atransmit power of 1 mW (0 dBm).
Distance from Transmitter M = PrPt
10m -70 dB
20m -75 dB
50m -90 dB
100m -110 dB
300m -125 dB
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 15 / 23
Simplified Path Loss Model ... 4
Solution
The MMSE error equation for the dB power measurements isF (γ) =
∑5i=1 [Mmeasured(di )−Mmodel(di )]2
where Mmeasured(di ) is the path loss measurement at distance di andMmodel(di ) = K − 10γ log10(d) is the path loss based on the simplifiedmodel at di .Using the free space path loss formula,K = 20 log10(.3333/(4π)) = −31.54 dB.⇒ F (γ) = (−70 + 31.54 + 10γ)2 + (−75 + 31.54 + 13.01γ)2 + (−90 +31.54 + 16.99γ)2 + (−110 + 31.54 + 20γ)2 + (−125 + 31.54 + 24.77γ)2
= 21676.3− 11654.9γ + 1571.47γ2
Differentiating F (γ) relative to γ and setting it to zero yieldsdF (γ)dγ = −11654.9 + 3142.94γ = 0⇒ γ = 3.71.
To find the received power at 100 m under the simplified path loss modelPr = Pt + K − 10γ log10
dd0
) = 0− 31.54− 10 ∗ 3.71 log10(100) =−105.74dBm
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 16 / 23
Shadow Fading
A signal transmitted through a wireless channel will typicallyexperience random variation due to blockage from objects in thesignal path.
This model has been confirmed empirically to accurately model thevariation in received power in both outdoor and indoor radiopropagation environments.
In the log-normal shadowing model the ratio of transmit-to-receivepower ψ = Pt
Pris assumed random with a log-normal distribution.
Models for path loss and shadowing can be superimposed to capturepower falloff versus distance along with the random attenuationabout this path loss from shadowing.PrPt
(dB) = 10 log10 K − 10γ log10dd0− ψdB
where ψdB is a Gauss-distributed random variable with mean zeroand variance σ2ψdB
.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 17 / 23
Combined Path Loss and Shadowing
Ex. 2.4: In Ex 2.3 we found that the exponent for the simplifiedpath loss model that best fits the measurements Table 2.3 wasγ = 3.71. Assuming the simplified path loss model with thisexponent and the same K = −31.54 dB, find σ2
ψdBdB, the variance
of log-normal shadowing about the mean path loss based on theseempirical measurements.
The sample variance relative to the simplified path loss model withγ = 3.71 isF (γ) =
∑5i=1 [Mmeasured(di )−Mmodel(di )]2
Thus⇒ σ2ψdB
= 15 [(−70 + 31.54 + 37.1)2 + (−75 + 31.54 + 48.27)2 + (−90 +
31.54 + 63.03)2 + (−110 + 31.54 + 74.2)2 + (−125 + 31.54 + 91.90)2]= 13.29
Thus, the standard deviation of shadow fading on this path isσψdB
= 3.65 dB.EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 18 / 23
Outage Probability under Path Loss and Shadowing
In wireless systems there is typically a target minimum receivedpower level Pmin below which performance becomes unacceptable(e.g. the voice quality in a cellular system is too poor tounderstand).
Outage probability pout(Pmin, d)
The probability that the received power at a given distance d , Pr (d),falls below Pmin : pout(Pmin, d) = p(Pr (d) < Pmin).
See Ex. 2.5 page 46.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 19 / 23
Cell Coverage Area
Cell Coverage Area
The expected percentage of area within a cell that has received powerabove a given minimum.
The transmit power at the base station is designed for an averagereceived power at the cell boundary.
Shadowing will cause some locations within the cell to have receivedpower below and above the average.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 20 / 23
Cell Coverage Area ... 2
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 21 / 23
Cell Coverage Area ... 3
The coverage area is given by:
where
See Ex. 2.6 and 2.7 pages 48-49.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 22 / 23
Next Lecture
The homework assignment will be available tomorrow’s night on thecourse webpage. The homework is due in one week.
In Next Lecture
Chapter 3: Statistical Multipath Channel Models.
EELE 6333: Wireless Commuications - Ch.2 Dr. Musbah Shaat 23 / 23
