1. Characterizations and Modeling of the Wireless Channel
Lecture Note 3

2. Wireless channel disturbances
Additive noise, like thermal background noise
Multiplicative noise
Distortion due to time dispersion
Corruptive elements are in the forms of:
Multipath delay spread
Doppler spread due to motion
Signal fading of frequency-selective and non-frequency-selective variety

3. Multipath propagation environment
Wireless propagation channel contains objects (particles) randomly scattering the energy of transmitted signals
Scattered signals arrive at receiver out of step
These objects (particles) are called scatterers
Scatterers introduce:
Fading
Multipath delay spread
Doppler spread
Attenuation

4. Multipath delay spread
Scattering by randomly located scatterers gives rise to different paths with different path-lengths/propagation-delays, resulting in multipath delay spread
If the propagation channel doesn’t exhibit multipath delay spread, a point source (a single tone sinusoid) appears at front end of receiver as another point source
A multipath situation arises when a transmitted point source is received as multipoint source, with each of individually received points experiencing a different transmission delay
The effect of multipath propagation on digital transmission can be characterized by time dispersion and fading

5. Wireless channel time dispersion
The transmitted point source will be received as a smeared wave due to multipath delay spread
Non-overlapping scatterers give rise to distinct multi paths – characterized by their locations in scattering medium.
All scatterers are located on ellipses with transmitter (Tx) and receiver (Rx) as the foci. One ellipse is associated with one path length/delay
Signals reflected by scatterers located on the same ellipse experience the same propagation delay and thus signal components from these multi-paths are indistinguishable at the receiver
Signals that are reflected by scatterers located on different ellipses arrive a the receiver with different delays

6. Ellipsoidal portrayal of scatterer location

7. Flat fading vs. frequency-selective fading and ISI
If max difference in delay spread is small compared with symbol duration of transmitted signal, channel is said to exhibit flat fading
If difference in delay spread is large compared with the symbol duration of transmitted signal, the channel exhibits frequency-selective fading
In time domain, received signals corresponding to successive transmitted symbols through frequency-selective fading channel will overlap, giving rise to a phenomenon called inter-symbol interference (ISI)
ISI is a signal-dependent distortion
The severity of ISI increase with the width of delay spread.
ISI distortion in time domain can also be examined in frequency domain
ISI degrades transmission performance, which can be overcome by the channel equalization techniques

8. Background noise and AWGN
Inherent background noise can be approximated as thermal noise and treated as Additive White Gaussian (AWGN)
Digital transmission over practical wireless channels is mainly limited by interference or distortion other than AWGN

9. Wireless channel fading
The multipath components can affect the received signal strength constructively or destructively, depending on carrier frequency and delay differences among the multi paths
As a mobile station moves, the position of each scatterer w.r.t. transmitter and receiver may change
The overall effect caused by multipath delay spread, Doppler spread, attenuation, thermal noise, etc. is that the received signal level fluctuates with time, which is the phenomenon called fading

10. Line-of-Sight (LOS) vs. non-line-of-sight (NLOS)
The delay of Line-of-Sight (LOS) or direct path is the shortest path among the multi paths, having smallest propagation delay (often assumed to be zero); the delay of non-line-of-sight (NLOS) or reflected path has longer propagation delay

11. Multipath propagation & LOS

12. An example of two-path channel
Consider transmitting a single-tone sinusoid signal:

13. A wireless channel model with two propagation paths

14. Amplitude fluctuation of the two-path channel

15. Wireless channel fading analysis
When mobile station moves, alpha_1, alpha_2, and tau change with time and thus received signal amplitude and phase also change with time.
Assuming alpha_1 = 2 and alpha_2 = 1
Assuming alpha_1 = 1.1 and alpha_2 = 1.0, resulting in deeper fading

16. Effects of channel fading
When signal components from two paths add destructively, transmitted signal experiences deep fading with a small value of the amplitude alpha
During each deep fading, the instantaneously received signal power is very low, resulting in poor transmission quality (high transmission error rate)
Diversity and error-correction coding are effective to combat channel fading for better transmission accuracy
Channel fading is classified long-term fading or short-term fading:
Short-term fading is rapid fluctuations caused by the local multipath (e.g., Rayleigh fading)
Long-term fading is long-term slow variation in the mean level of received signal strength (e.g., Lognormal fading) caused by movement over large enough distance
Multipath propagation in wireless mobile environment yields fading dispersive channel
Signal propagation environment changes as the mobile station moves and /or as any surrounding scatterers move  the wireless channel is time-varying and can be modeled as a linear time-variant (LTV) system

17. Linear time-variant (LTV) channel model

18. Input/output model of Wireless Channel Linear time-invariant (LTI) channel model —Review “Channel impulse response”

19. Input/output model of Wireless Channel Linear time-variant (LTV) channel