diffraction

EE 552/452, Spring, 2007 Wireless Communications (and Networks): 

EE 552/452, Spring, 2007 Wireless Communications (and Networks) Zhu Han Department of Electrical and Computer Engineering Class 7 Feb. 6 th , 2007

Outline: 

EE 552/452 Spring 2007 Outline Review Free space propagation 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 Homework Conference, moving of classes Project, TI toolboxes Diffraction Scattering Practical link budget model

Diffraction: 

EE 552/452 Spring 2007 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.

Diffraction geometry: 

EE 552/452 Spring 2007 Diffraction geometry Derive of equation 4.54-4.57

Diffraction geometry: 

EE 552/452 Spring 2007 Diffraction geometry

Diffraction geometry: 

EE 552/452 Spring 2007 Diffraction geometry Fresnel-Kirchoff distraction parameters, 4.56

Fresnel Screens: 

EE 552/452 Spring 2007 Fresnel Screens Fresnel zones relate phase shifts to the positions of obstacles Equation 4.58 A rule of thumb used for line-of-sight microwave links 55% of the first Fresnel zone is kept clear.

Fresnel Zones: 

EE 552/452 Spring 2007 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. Obstruction of Fresnel Zones  1st 2nd 0 -10 -20 -30 -40 -50 -60 0 o 90 180 o dB Tip of Shadow Obstruction LOS

Fresnel diffraction geometry: 

EE 552/452 Spring 2007 Fresnel diffraction geometry

Knife-edge diffraction: 

EE 552/452 Spring 2007 Knife-edge diffraction Fresnel integral, 4.59

Knife-edge diffraction loss: 

EE 552/452 Spring 2007 Knife-edge diffraction loss Gain Exam. 4.7 Exam. 4.8

Multiple knife-edge diffraction: 

EE 552/452 Spring 2007 Multiple knife-edge diffraction

Scattering: 

EE 552/452 Spring 2007 Scattering Rough surfaces Lamp posts and trees, scatter all directions Critical height for bumps is f( ,incident angle) , 4.62 Smooth if its minimum to maximum protuberance h is less than critical height. Scattering loss factor modeled with Gaussian distribution, 4.63, 4.64. Nearby metal objects (street signs, etc.) Usually modeled statistically Large distant objects Analytical model: Radar Cross Section ( RCS ) Bistatic radar equation, 4.66

Measured results: 

EE 552/452 Spring 2007 Measured results

Measured results: 

EE 552/452 Spring 2007 Measured results

Propagation Models: 

EE 552/452 Spring 2007 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.

Free Space Path Loss: 

EE 552/452 Spring 2007 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 d 0 and reference other points from there: Log-distance generalizes path loss to account for other environmental factors Choose a d 0 in the far field. Measure PL(d 0 ) or calculate Free Space Path Loss. Take measurements and derive  empirically.

Typical large-scale path loss: 

EE 552/452 Spring 2007 Typical large-scale path loss

Log-Normal Shadowing Model: 

EE 552/452 Spring 2007 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. Reason for Gaussian

Measured large-scale path loss: 

EE 552/452 Spring 2007 Measured large-scale path loss Determine n and  by mean and variance Equ. 4.70 Equ. 4.72 Basic of Gaussian distribution

Area versus Distance coverage model with shadowing model: 

EE 552/452 Spring 2007 Area versus Distance coverage model with shadowing model Percentage for SNR larger than a threshold Equ. 4.79 Exam. 4.9

Questions?: 

EE 552/452 Spring 2007 Questions?