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The Wireless Channel

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The Wireless Channel

Lecture 3

Area 1

Area 2

Short-term

fading

Log-normal

shadowing

Transmitter

Channel varies at two spatial scales:

large scale fading

small 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.

- 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.

- 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.

- 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:

Time variations property

t2

t(t2)

t1

t(t1)

Time spreading property

t0

t(t0)

- Impulse response: Time-spreading : multipath
- and time-variations: time-varying environment

- Communication takes place at [fc-W/2, fc+ W/2].
- Processing takes place at baseband [-W/2,W/2].

- The frequency response of the system
- Each path is associated with a delay and a complex gain.

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

• 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:

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:

- 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

- 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

Based on Time-Spreading

- Flat Fading
- BS < BCTm < 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

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

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

- The discrete-time baseband-equivalent model

- Rayleigh flat fading model: many small scattered paths
Complex circular symmetric Gaussian .

- Rayleigh PDF:

- 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.

- More practical model

Rayleigh fading

Rician fading

No fading, Constant power

- 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