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The Wireless Channel

The Wireless Channel. Lecture 3. Area 1. Area 2. Short- term fading. Log-normal shadowing. Transmitter. Large and Small Scale Propagation Models. Wireless Mulipath Channel. Channel varies at two spatial scales: large scale fading small scale fading. Large-scale fading.

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The Wireless Channel

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  1. The Wireless Channel Lecture 3

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

  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. Time variations property t2 t(t2) t1 t(t1) Time spreading property t0 t(t0) Impulse Rresponse Ccharacterization • 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 Bcis 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 • Spectral chara. of transmitted • signal not preserved • Multipath components resolved Channel Channel Signal Signal BC BS freq. freq. BS BC

  21. Channel Classification Based on Time-Variations • Fast Fading • High Doppler Spread • 1/Bd@ TC < Ts • Slow Fading • Low Doppler Spread • 1/Bd@ TC> Ts Signal Signal Doppler Doppler BD BS freq. freq. BS BD

  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

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