1. The Wireless Channel
Lecture 3

2. Large and Small Scale Propagation Models
Area 2
Area 1
Transmitter
Log-normal
shadowing
Short-term
fading

3. Wireless Mulipath Channel
Channel varies at two spatial scales:
large scale fading
small scale fading

4. Large-scale fading In free space, received power attenuates like 1/r2.
With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated.
Time constants associated with variations are very long as the mobile moves, many seconds or minutes.
More important for cell site planning, less for communication system design.

5. Small-scale multipath fading
Wireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)
Multipath fading due to constructive and destructive interference of the transmitted waves.
Channel varies when mobile moves a distance of the order of the carrier wavelength. This is 0.3 m for Ghz cellular.
For vehicular speeds, this translates to channel variation of the order of 100 Hz.

6. Plan
We wish to understand how physical parameters such as carrier frequency, mobile speed, bandwidth, delay spread impact how a wireless channel behaves from the communication system point of view.
We start with deterministic physical model and progress towards statistical models, which are more useful for design and performance evaluation.

7. Physical Models
Wireless channels can be modeled as linear time-varying systems:
where ai(t) and i(t) are the gain and delay of path i.
The time-varying impulse response is:
Consider first the special case when the channel is time-invariant:

8. Impulse Rresponse Ccharacterization
t(t0) t0 t2
t(t2) t1
t(t1)
Time spreading property
Time variations property
Impulse response: Time-spreading : multipath
and time-variations: time-varying environment

9. Passband to Baseband Conversion
Communication takes place at [fc-W/2, fc+ W/2].
Processing takes place at baseband [-W/2,W/2].

10. Baseband Equivalent Channel
The frequency response of the system
Each path is associated with a delay and a complex gain.

11. Sampling

12. Multipath propagation
Signal can take many different paths between sender and receiver
due to reflection, scattering, diffraction
Time dispersion: signal is dispersed over time
interference with “neighbor” symbols Inter Symbol Interference (ISI)
The signal reaches a receiver directly and phase shifted
distorted signal depending on the phases of the different parts

13. The Effects of Multipath Propagation
• Due to the different paths taken by the multipath components, they may arrive at different times
• If the symbol period TS is smaller than the delay spread, i.e. TS < Tm, Inter-Symbol Interference (ISI) will occur
• The receiver cannot determine which symbol each multipath component belongs to:

14. The Effects of Multipath Propagation

15. Delay Spread
The Delay Spread Tm is defined as the difference between times-of arrival
of the first and last multipath components Typical values are as follows:

16. (Doppler shift)

17. Fading

18. Coherence Bandwidth
The Coherence Bandwidth Bc is a statistical measure of the range of frequencies over which the attenuation of the channel is approximately constant
Two frequency components f1 and f2 will experience similar attenuation if (f1 – f2) << Bc
Coherence Bandwidth is approximately related to the Delay Spread by:
Bc (Hz) = 1/Tm
e.g. in a particular factory environment,
Tm = 120ns, Bc = 1/(120 x 10-9) = 8.33 MHz

19. Coherence Bandwidth (2)
If the transmitted signal has a bandwidth (Bu) much smaller than the Coherence Bandwidth(Bc), i.e. Bu << Bc, all frequency components will be attenuated similarly.
This is called Flat Fading
Else, it will undergo Frequency-selective fading, with different components attenuated differently. This causes distortion of the signal

20. Channel Classification
Based on Time-Spreading
Flat Fading
BS < BC  Tm < Ts
Rayleigh, Ricean distrib.
Spectral chara. of transmitted
signal preserved
Frequency Selective
BS > BC  Tm > Ts
Intersymbol Interference
signal not preserved
Multipath components resolved
Signal
Channel
freq. BS BC

21. Channel Classification
Based on Time-Variations
Fast Fading
High Doppler Spread
TC < Ts
Slow Fading
Low Doppler Spread
TC> Ts
Signal
freq. BD BS
Doppler

22. Flat and frequency selective fading Channels

23. Classification of fading Channel

24. Statistical Multipath Model

25. The Multipath Model

26. The tapped delay line model

27. Time Varying Impulse Response

28. Linear Time Varying System

29. Received Signal Characteristics

30. Multipath resolvability

31. The tapped delay line model revised

32. Narrowband Model

33. Statistical Models

34. Statistical Models
Design and performance analysis based on statistical ensemble of channels rather than specific physical channel.
Recall that:

35. Additive Gaussian Noise
The discrete-time baseband-equivalent model

36. Rayleigh Model Rayleigh flat fading model: many small scattered paths
Complex circular symmetric Gaussian .
Rayleigh PDF:

37. Typical Rayleigh fading envelope @ 900 MHz

38. Rician Model Used when LOS or other dominant non fading path exist.
Characterized by Rician factor K that compare signal power of the non-fading path to variance of multipath.

39. Rician  Rayleigh

40. Distributions for Rayleigh and Rician fading channels

41. Nakagami model More practical model Rayleigh fading Rician fading
No fading, Constant power

42. More about Narrow band Channel

43. Wide band Channel

44. Inter-symbol Interference (ISI)
Time domain: dispersion (delay spread Tm)
Frequency domain: non-flat response in the band of interest
One-tap filter: flat frequency response
Multi-tap filter: frequency selective response
When symbol time T >> Tm, no ISI (narrowband or low rate)
For higher rate, T comparable to Tm , we need to deal with ISI
Equalization, OFDM, CDMA with RAKE