EELE 5414 Wireless

CommunicationsCommunications

Chapter 5-Part2: Mobile Radio

Propagation: Small-Scale Fading and

Multipath

Outline

• Types of small- scale fading.

– Flat fading.

– Frequency selective Fading.

– Slow fading.– Slow fading.

– Fast fading

• Rayleigh and Ricean Fading distribution.

• Level Crossing and Fading Statistics.

Types of Small-Scale Fading

• The fading experienced by a signal propagatingthrough channel depends on the nature oftransmitted signal (B.W and symbol period,…)w.r.t the characteristics of the channel (rms delayand Doppler spread).and Doppler spread).

• Multipath delay spread � time dispersion andfrequency selective fading.

• Doppler spread � frequency dispersion and timeselective fading.

• The two mechanisms are independent of oneanother.

Flat Fading

• The signal will undergo flat fading if

1. The B.W of the channel is greater than the B.W of the

transmitted signal.

2. The channel has constant gain and linear phase

response over that B.W.response over that B.W.

• The most common type of fading.

• The spectral characteristics of the transmitted signal is reserved at the receiver.

• The strength of the received signal changes with time.

Flat Fading (2)

Flat Fading (3)

• Known also as amplitude varying channels.

• Referred to also as narrowband channels �

the signal B.W is narrow as compared to the

channel flat fading B.W.channel flat fading B.W.

• Summary: a signal undergoes flat fading if

• Bs (signal B.W) << Bc (channel coherence B.W)

and

• Ts (symbol period) >> σ (rms delay spread)

Frequency Selective Fading

• The channel has constant gain and linear phase

over B.W smaller than the transmitted signal B.W.

• The received signal includes multiples versions of

the transmitted waveform which are attenuated the transmitted waveform which are attenuated

(faded) and delayed in time.

• The channel induces inter-symbol interference

(ISI).

• Certain components in the frequency domain

have greater gains than others.

Frequency Selective Fading (2)

Frequency Selective Fading (3)

Fast Fading

• Depends on the Doppler spread � velocity.

• Affected by how rapidly the transmitted

baseband signal changes as compared to the

rate of the channel.rate of the channel.

• Occurs when the channel impulse response

changes rapidly within the symbol period.

• Causes a frequency dispersion due to Doppler

spreading � signal distortion.

Fast Fading (2)

• Summary

• A signal undergoes fast fading if

• Ts (symbol period) > Tc (time coherence of the

channel).channel).

and

• Bs (signal B.W) < Doppler B.W.

• Generally, fast fading only occurs for very low

data rates.

Slow Fading

• The channel impulse response changes at a rate

slower than the transmitted baseband signal.

• The channel can be assumed static.

• Summary• Summary

• Ts (symbol period) << Tc (time coherence of the

channel).

and

• Bs (signal B.W) >> Doppler B.W.

Fading Effects

• Do not mix FLAT/Frequency selective fading

with Fast/Slow Fading � They are

independent.

• Example: there is Flat fading/Fast fading • Example: there is Flat fading/Fast fading

channels in which the amplitude of the delta

function varies faster than the rate of change

of the transmitted signal.

• Also, there is Flat fading/Slow fading channels.

Rayleigh Fading Distribution

• Used to describe the statistical time varying

nature of the received envelope of a flat

fading signal or the envelope of the individual

multipath components.multipath components.

• The Rayleigh distribution has probability

density function (PDF)

Rayleigh Fading Distribution (2)

• The probability that the received signal des

not exceed a specified value R is

• The mean

• The variance

Ricean Fading Distribution

• Used when there is a dominant stationary

(nonfading) signal component present (LOS).

• When the dominant component fades away

� Ricean distribution degenerates a Rayleigh � Ricean distribution degenerates a Rayleigh

distribution.

• The pdf is given by

Modified Bessel function of the first kind

and zero order

Peak amplitude of the

dominant signal

Ricean Fading Distribution

• Often described by the parameter K, the ratio

between the signal power and the variance of

the multipath

Problem 5.7

P5.7, IF a baseband binary message with bit rate Rb=100 kbps is modulated by an RF carrier using BPSK, answer the following:

a- Find the range of values required for the rms delay spread of the channel such that the received signal is a flat fading signal.flat fading signal.

b- If the modulation carrier frequency is 5.8 GHz, what is the coherence time of the channel, assuming a vehicle speed o 30 miles per hour.

c- For the answer in b, is the channel “fast” or “slow”.

d- For the answer in b, how many bits are sent while the channel appears “static”?

Solution

Level Crossing and Fading Statistics

Level Crossing and Fading Statistics

Ex.5.7

Average Fade Duration

• Is the average period of time for which the

received signal is below a specified level R.

• Help in determining the most likely number of

signaling bits that ay be lost during a fade.

Ex. 5.9

Next lecture

• Multiple Access Techniques for wireless

Communications