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**Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss**

Wireless Communications Principles and Practice 2nd Edition T.S. Rappaport Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss 2006 UMAIR HASHMI Spring 2011

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**Reflection from Conductors**

A perfect conductor reflects back all the incident wave back. Ei = Er Өi = Өr ( E in plane of incidence) Ei = - Er Өi = Өr ( E normal to plane of incidence) 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

Propagation Model that considers both the direct (LOS) path and a ground reflected path between transmitter and the receiver. Reasonably accurate model for predicting large scale signal strength over distance of several kilometres. The E-field due to Line-Of-Sight is given by ELOS The E-field for the ground reflected wave is given by Eg The Total E-field is a sum of LOS and Reflected components, 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

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**Ground Reflection (Two-Ray) Model**

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**Ground Reflection (Two-Ray) Model**

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**Ground Reflection (Two-Ray) Model**

The path difference between the LOS path and the ground reflected path is represented by lambda 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

The phase difference and the time arrival delay between the two E-components is given by: When d becomes large, difference between d’ and d’’ becomes negligible and ELOS and Eg could be considered equal in magnitude 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

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**Ground Reflection (Two-Ray) Model**

Now sin(Ө) is approximately equal to Ө when Ө < 0.3 radians. 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

The received power Pr and Path Loss PL will be given by: 2006 UMAIR HASHMI Spring 2011

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**Ground Reflection (Two-Ray) Model**

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**Ground Reflection (Two-Ray) Model**

Example A mobile is located 5 km away from a BS and uses vertical lambda/4 monopole antenna with gain of 2.55 dB to receive cellular signals. The E-field at 1 km from the transmitter is measured to be 10-3 V/m. The carrier frequency is 900 MHz. Find length and gain of receiving antenna Find receiver power at the mobile using 2-ray ground reflection model assuming height of transmitting antenna is 50m and receiving antenna is 1.5 m. 2006 UMAIR HASHMI Spring 2011

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Diffraction Diffraction is a process that allows radio signals to propagate around curved surfaces and objects and to propagate behind obstructions. Visible Region Shadow Region Obstruction 2006 UMAIR HASHMI Spring 2011

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Diffraction geometry 2006 UMAIR HASHMI Spring 2011

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**Diffraction geometry Visible Region Shadow Region Obstruction**

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**Contribution of Huygen’s Secondary Sources at the Receiver**

Tx Rx Obstruction 2006 UMAIR HASHMI Spring 2011

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Fresnel Zone Geometry A transmitter and receiver separated in free space. An obstructing screen of height h is placed at a distance d1 from the transmitter and d2 from the receiver. The difference between the direct path and the diffracted path is called the excess path length Δ. Assuming h << d1,d2 and h>>λ 2006 UMAIR HASHMI Spring 2011

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Fresnel Zone Geometry 2006 UMAIR HASHMI Spring 2011

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Fresnel Zone Geometry Now tan x is approximately equal to x for x < 0.5 radians Fresnel – Kirchoff Diffraction Parameter v is given by 2006 UMAIR HASHMI Spring 2011

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Fresnel Zone Geometry The phase difference between LOS and diffracted path is a function of Height and Position of the obstruction Transmitter and Receiver Location FRESNEL ZONES Fresnel Zones represent successive regions where secondary waves have a path length from the transmitter to the receiver which are nλ/2 greater than the total path length of a LOS path The successive concentric circles on the plane have path length increment by λ/2. The successive circles are called Fresnel Zones and successive Fresnel Zones have the effect of producing constructive and destructive interference. 2006 UMAIR HASHMI Spring 2011

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**Fresnel Zone Geometry The radius of the nth Fresnel Zone is given by**

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**Knife-Edge Diffraction Model**

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**Knife-Edge Diffraction Model**

The receiver is at point R which is located in the shadowed region (called Diffraction Zone). The field strength at R is a vector sum of the fields due to all of the secondary Huygen;s sources in the plane. The Electric Field of a knife edge diffracted wave is The Diffraction Gain due to the presence of a knife edge is given by 2006 UMAIR HASHMI Spring 2011

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**Knife-Edge Diffraction Model**

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Fresnel Zone Geometry The Diffraction Gain for different values of v is: 2006 UMAIR HASHMI Spring 2011

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**Knife-edge diffraction loss (Summing Secondary Sources)**

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**Fresnel Zone Geometry EXAMPLE**

Compute the diffraction loss for the three cases in fig. when λ=1/3m, d1=1km, d2=1km and (a) h=25m, (b) h=0 (c) h= -25m. Compare the answers with the values obtained from the graph. 2006 UMAIR HASHMI Spring 2011

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**Fresnel Zone Geometry EXAMPLE**

Determine (a) Loss due to knife-edge diffraction and (b) the height of the obstacle required to induce 6 dB diffraction loss. Assume f = 900MHz 2006 UMAIR HASHMI Spring 2011

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Scattering When a wave impinges on a rough surface, the reflected wave is spread out (diffused) in all directions due to scattering. The dimensions of the objects inducing Scattering are comparable to λ To judge if a surface is smooth or rough (if we will have reflection or scattering) when a wave impinges upon that surface, the Critical Height hc is given by hc = λ / ( 8 sin Өi) If maximum protuberance hmax < hc : Smooth Surface hmax > hc : Rough Surface The reflected E-Fields for h > hc is given by : 2006 UMAIR HASHMI Spring 2011

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**Radar Cross Section Model (RCS Model)**

The Radar Cross Section (RCS) of a scattering object is defined as the ratio of the power density of the signal scattered in the direction of the receiver to the power density of the radio wave incident upon the scattering object. The bistatic radar equation is used to compute the propagation of a wave travelling in free space that impinges on a distant scattering object and then reradiated in the direction of the receiver. The objects are assumed to be in the Far-Field region (Fraunhofer region) PR (dBm) = PT (dBm) + GT (dBi) + 20 log λ + RCS [dB m2 ] – 30 log (4 pi) – 20 log dT – 20 log dR 2006 UMAIR HASHMI Spring 2011

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**Radar Cross Section Model (RCS Model)**

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**SUMMARY What is Large Scale Path Loss? Free space Propagation Model**

Friis Free space propagation model Relating power to Electric field The three Basic Propagation mechanisms Reflection Reflection coefficients Polarization rotation Brewster angle Reflection from perfect conductors Ground Reflection (Two Ray Model) 2006 UMAIR HASHMI Spring 2011

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SUMMARY Diffraction Fresnel Zone Geometry Knife Edge Diffraction Multiple Knife edge Diffraction Scattering Rough Surface Scattering Radar Cross section Now we know all the propagation mechanisms and can use them to predict path loss in any environment 2006 UMAIR HASHMI Spring 2011

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**Log-Distance Path Loss Model**

Radio Propagation Models Log-distance Path Loss Model Received Power decreases logarithmically with distance, whether in outdoor or indoor radio channels Reference distance should be in the far field region of the antenna 2006 UMAIR HASHMI Spring 2011

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**Log-Distance Path Loss Model**

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Log-Normal Shadowing Surrounding environment clutter not considered in previous model. Received power can vary at quite a significant value at 2 points having same T-R separation distances. Path Loss (PL) is random and distributed log-normally about the mean distance-dependent value. 2006 UMAIR HASHMI Spring 2011

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Log-Normal Shadowing Log-Normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation distance. This phenomenon is called the log-normal shadowing. Implies that measured signal levels at specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean. 2006 UMAIR HASHMI Spring 2011

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Log-Normal Shadowing 2006 UMAIR HASHMI Spring 2011

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Log-Normal Shadowing 2006 UMAIR HASHMI Spring 2011

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**Determination of Percentage of Coverage Area**

The percentage of useful service area i.e. the percentage of area with a received signal level that is greater or equal to a threshold value. 2006 UMAIR HASHMI Spring 2011

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**Determination of Percentage of Coverage Area**

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**Determination of Percentage of Coverage Area**

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**Determination of Percentage of Coverage Area**

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**Determination of Percentage of Coverage Area**

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**Determination of Percentage of Coverage Area**

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**Determination of Percentage of Coverage Area**

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**Outdoor Propagation Models Longley Rice Model**

Point to point communication 40 MHz to100 GHz Different kinds of terrain Median Tx loss predicted by path geometry of terrain profile & Refractivity of troposphere Diffraction losses predicted by? Geometric losses by? 2006 UMAIR HASHMI Spring 2011

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**Outdoor Propagation Models Longley Rice Model**

Operates in 2 modes Point-to-point mode Area mode prediction Modification Clutter near receiver Doesn’t determine corrections due to environmental factors 2006 UMAIR HASHMI Spring 2011

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**Outdoor Propagation Models Durkin’s Model**

Computer simulator described for field strength contours of irregular terrain Split into 2 parts, first reconstructs radial path profile & second calculates path loss Rx can move iteratively to establish contour Topographical database can be thought of as 2-dimensional array Each array element corresponds to a point on map & elevation Radial path may not correspond to discrete data points thus interpolation 2006 UMAIR HASHMI Spring 2011

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**2-D Propagation Raster Model**

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**Representing Propagation**

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**Positive height difference**

Height reconstructed by diagonal, vertical & horizontal interpolation methods Reduced to 1 D Now determine whether LOS – difference btw heights and line joining Tx & Rx Positive height difference 2006 UMAIR HASHMI Spring 2011

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Algorithm for LOS 2006 UMAIR HASHMI Spring 2011

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**Then checks first Fresnel Zone clearance **

If terrain profile fails first Fresnel Zone Clearance a) non LOS b) LOS but inadequate Fresnel Zone Clearance 2006 UMAIR HASHMI Spring 2011

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**Non-LOS Cases a) Single Diffraction Edge b) Two Diffraction Edges**

a) Three Diffraction Edges a) More than three Diffraction Edges Method sequentially tests for each Angles btw pine joining Tx & Rx and each point on reconstructed profile. Max angle (di,hi) Angles between line joining Tx & Rx and Tx Antenna to every point on reconstructed profile For single diffraction di=dj 2006 UMAIR HASHMI Spring 2011

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**Multiple Diffraction Computation**

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**Okumura’s and Hata’s Model**

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**Hata’s Model Empirical formulation of graphical path loss data**

Valid from 150 MHz to 1500 MHz. Urban Area Propagation loss as a standard and supplied correction equations for application to other situations hte=30 m to 200m, hre=1m to 10m Compares very closely with Okumura model as long as d doesn’t exceed 1km Well suited for large cell communications but not PCS 2006 UMAIR HASHMI Spring 2011

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**PCS Extension to Hata Model**

Hata’s model to 2GHz 2006 UMAIR HASHMI Spring 2011

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ASSIGNMENT Review the Outdoor Propagation Models presented in the slides showing their salient features and how they differentiate from each other. 2006 UMAIR HASHMI Spring 2011

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Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss

Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss

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