Fading

1. Fading Kevin BoldingElectrical EngineeringSeattle Pacific University

2. Signals fade • Received Signal Strength (RSS) varies over time and space • Slow Fading caused by large obstacles and terrain impairments • Appears as local rises/falls in RSS around a logarithmic curve

3. Multipath fading • Reflections and diffraction cause radio signals to follow different paths to the receiver • The received signals are summed at the receiver • The signal components will have various phases and amplitudes • This will cause positive and negative interference that varies based on the relative locations of the: • Source • Objects in the path • Receiver • As these objects move around, the interference pattern will change • The signal strength will vary significantly over small variations in the placement of these objects

4. Fading due to reflections • Multiple signal paths will result in multiple received signals • Each reflection path is longer than the direct path – a change in the path length results in a phase difference • Reflections off of the earth usually introduce a 180 degree phase shift • In the absence of reflecting objects other than the earth, the relationship of the various reflected signal depends on • The location and height of the transmitter and receiver • The wavelength (frequency) of the signal • Multiple reflections cause the RSS to vary with frequency

5. Fading due to multipath Doppler shift • If the receiver is moving relative to the transmitter, there will be a shift in frequency – Doppler shift • Frequency increases if moving closer • Frequency decreases if moving apart • At typical vehicle velocities, the Doppler shift is under 100Hz, which is not itself a problem • In a multipath situation, the relative velocity of the receiver varies depending on the geometry of the paths •  Different paths have different Doppler shifts, leading to slightly different frequencies • The received signal strength will vary over time as the alignment of the various signals changes • Multipath Doppler shift causes the RSS to vary over time

6. Doppler Shift • For E/M waves, the change in frequency (Doppler shift) is computed by: • vs,r is the relative speed of the receiver w.r.t. the transmitter. vs,r is positive when the receiver is moving away from the transmitter. • f0 is the frequency and 0 is the wavelength of the E/M wave.

7. Fading varies with time and frequency Amplitude of the channel attenuation in dB versus carrier frequency (in MHz) and time (in milliseconds).Normalized delay spread tm = 0.05 and normalized Doppler spread fD = 0.05.A time selective and frequency selective Rayleigh fading channel From: http://www.wirelesscommunication.nl/reference/chaptr03/channel.htm

8. Multipath fading http://en.wikipedia.org/wiki/Image:Rayleigh_fading_doppler_10Hz.svg Average RSS Fades “Deep” Fades An example of multipath fading from a moving receiver.

9. Multipath Fading Analysis • Some environments have a large number of scatterers • Ionosphere • Urban environments • If there are a large number of scattering objects, the received signal has phase and amplitude represented by a complex vector z with: • Randomly distributed Real part (Normal dist.) • Randomly distributed Imaginary part (Normal dist.) • Note: This assumes that only scattered rays are received. If scattered and the direct ray are both received, a different model applies.

10. Im Re Complex plane • Amplitude = sqrt (x2+y2) y z = x + iy amplitude phase x See http://www.wirelesscommunication.nl/reference/chaptr03/rayjava/rayjava.htm for an animation tool

11. Rayleigh Distribution • A random variable follows the Rayleigh distribution if it is a vector with its orthogonal components normally and independently distributed • The Real (x) and Imaginary (y) parts of the received signal are both normally distributed • The amplitude has a Rayleigh distribution PDF of a RayleighDistribution with variousVariances Mean Power < Mean Power > Mean Tail goes to infinity

12. Rayleigh PDF RSS, 4 MPH RSS, 40 MPH Rayleigh Fading with Moving Receiver • Rayleigh fading describes the change in RSS at various locations • A Rayleigh faded channel has significant RSS variations over very small distances • A moving receiver experiences this as RSS changes over a short period of time • A moving receiver also experiences Doppler shift, which increases the rate of fading

13. RSS, 4 MPH, Max Doppler = 10Hz Assume fade margin is setto some level. (Example: -15dB)  = ratio of margin to RMSmean (Example: -15dB =1/31.6 = 0.032)fd=Maximum Doppler shift(Example: 10Hz) Analysis using Rayleigh Model How often do fades exceed the fade margin?Analytically, compute theLevel Crossing Rate (Hz): How long is the averagefade duration for fadesbeyond the fade margin?Analytically, computethe Average Fade Duration (s):

14. Rician Fading • If the received signal is a combination of a single line-of-sight (dominant) ray and scattered rays, the RSS follows the Rice distribution • The Rice distribution has a parameter, v, that represents the degree of dominance of the primary ray • At v=0, the Ricean distribution is the same as the Rayleigh distribution v=0, Rayleigh Note that the meanchanges with v

15. Fading Summary • Obstructions cause fading through blockages, reflections and diffraction • Slow fading refers to deviations from free-space fading that occur over longer distances • Caused by large obstructions • Characterized by log-normal distribution • Fast fading refers to deviations that occur over very short distances • Caused by multipath • Characterized by Rayleigh or Ricean distributions