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**EELE 5490, Fall, 2009 Wireless Communications**

Ali S. Afana Department of Electrical Engineering Class 5 Dec. 4th, 2009

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**Outline Review Free space propagation Reflection: Diffraction**

Received power is a function of transmit power times gains of transmitter and receiver antennas Signal strength is proportional to distance to the power of -2 Reflection: Cause the signal to decay faster. Depends on the height of transmitter and receiver antennas Diffraction Scattering 2

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**Diffraction Diffraction occurs when waves hit the edge of an obstacle**

“Secondary” waves propagated into the shadowed region Water wave example Diffraction is caused by the propagation of secondary wavelets into a shadowed region. Excess path length results in a phase shift The field strength of a diffracted wave in the shadowed region is the vector sum of the electric field components of all the secondary wavelets in the space around the obstacle. Huygen’s principle: all points on a wavefront can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wavefront in the direction of propagation. 3

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Diffraction

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Diffraction geometry Derive of equation 5

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Diffraction geometry 6

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Diffraction geometry Fresnel-Kirchoff distraction parameters, 4.56 7

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Diffraction Loss

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Fresnel Screens Fresnel zones relate phase shifts to the positions of obstacles 10

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**Fresnel Zones Bounded by elliptical loci of constant delay**

Alternate zones differ in phase by 180 Line of sight (LOS) corresponds to 1st zone If LOS is partially blocked, 2nd zone can destructively interfere (diffraction loss) How much power is propagated this way? 1st FZ: 5 to 25 dB below free space prop. LOS -10 -20 -30 -40 -50 -60 0o 90 180o dB Obstruction Tip of Shadow 1st nd Obstruction of Fresnel Zones 11

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**Fresnel diffraction geometry**

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**Knife-edge diffraction**

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**Knife-edge diffraction loss**

Gain 14

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**Multiple knife-edge diffraction**

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**Scattering Rough surfaces Nearby metal objects (street signs, etc.)**

Lamp posts and trees, scatter all directions Critical height for bumps is f(,incident angle), Smooth if its minimum to maximum protuberance h is less than critical height and rough if greater than that. Scattering loss factor modeled with Gaussian distribution Nearby metal objects (street signs, etc.) Usually modeled statistically 16

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Propagation Models Large scale models predict behavior averaged over distances >> Function of distance & significant environmental features, roughly frequency independent Breaks down as distance decreases Useful for modeling the range of a radio system and rough capacity planning, Experimental rather than the theoretical for previous three models Path loss models, Outdoor models, Indoor models Small scale (fading) models describe signal variability on a scale of Multipath effects (phase cancellation) dominate, path attenuation considered constant Frequency and bandwidth dependent Focus is on modeling “Fading”: rapid change in signal over a short distance or length of time. 17

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Free Space Path Loss Path Loss is a measure of attenuation based only on the distance to the transmitter Free space model only valid in far-field; Path loss models typically define a “close-in” point d0 and reference other points from there: Log-distance generalizes path loss to account for other environmental factors Choose a d0 in the far field. Measure PL(d0) or calculate Free Space Path Loss. Take measurements and derive empirically. 18

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**Typical large-scale path loss**

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**Log-Normal Shadowing Model**

Shadowing occurs when objects block LOS between transmitter and receiver A simple statistical model can account for unpredictable “shadowing” PL(d)(dB)=PL(d)+X0, Add a 0-mean Gaussian RV to Log-Distance PL Variance is usually from 3 to 12. 20

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Questions?

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