computer engineering electronics and communications systems basics … · 2019-10-28 · computer...

Basics of Wireless Propagation

Marco Luise, Giacomo [email protected]

Dip. Ingegneria dell’Informazione, Univ. Pisa, Pisa, Italy

Computer Engineering Electronics and Communications Systems

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G. Bacci, M. LuiseBasics of Wireless Propagation

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Dip. Ingegneria dell’Informazione

University of Pisa, Pisa, Italy

Basics of wireless

propagation

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The wireless propagation channel

Basics of wireless propagation

Received contributions at the receiver (uplink):

(e.g., due to

electromagnetic

radiations, electronics

impairments, etc.)

The wireless channel between the transmitter and the receiver fluctuates randomly

for a number of causes

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Free-space propagation


If we consider the air as a perfectly uniform medium, the received power

can be expressed as

free-space path loss

where

gain of the transmit antenna

gain of the receive antenna

tx-rx distance

carrier wavelength

However, this model is not accurate to describe the wireless channel experienced

by cellular-communication signals

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Large- and small-scale models (1/2)


A better suited propagation model is composed by:

o large-scale models, that predict the average energy

received in a wireless system as a function of the

distance between the transmitter and the receiver

o small-scale models, that account for the

instantaneous variations in the propagation

conditions

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Large- and small-scale models (2/2)


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Large-scale fading models (1/3)


Average received power as a function of the MS-BTS distance d

Using the Hata and Okumura models,

reference distance

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Average received power as a function of the MS-BTS distance d

urban scenarios

rural areas

free space

urban scenarios

indoor

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Average received power as a function of a constant distance d

where

dependent on the

propagation

scenario

given by the Hata-

Okumura model:

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Small-scale fading


The propagation laws can be computed using the Maxwell

equations. However, this approach is not useful, due to:

o a large computational complexity, but also

o the need for a valid modelf or different

propagation conditions, also considering

the time variability

We need to identify a practical method to account for

the macroscopic phenomena of wireless propagation

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Wavelengths and frequencies in wireless systems (1/2)


Wireless radio spectrum:

Carrier wavelengths:

speed of light,

3108 m/s

carrier

frequency

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Wavelengths and frequencies in wireless systems (2/2)


Why are such frequencies particularly attractive?

o larger f0’s yield larger path losses:

o smaller f0’s call for larger antennas (with size comparable with )

o smaller f0’s show favorable conditions for over-the-horizon (OTH)

propagation, thus reducing the potential for frequency reuse

o such f0’s can accommodate large enough channel spacing and

provide room for large user multiplexing

o such f0’s have good indoor propagation

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Multipath propagation


In this frequency spectrum, the wireless signal experiences a

multipath propagation: the received signal is a linear combination

of multiple paths

In addition to the direct path (a.k.a.

line of sight (LoS) path), the wireless

signal can propagate due to:

o reflection:

o shadowing:

o scattering:

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Reflection


Due to the different propagation lengths, for each path the reflection introduces:

o amplitude attenuation

o group delay

o phase delay

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Shadowing


Shadowing introduces additional paths when the transmitter and the

receiver are not in visibility, thus affecting the statistics of the channel

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Scattering


Similarly, scattering introduced a disordered reflection of the electro-

magnetic waves, thus impacting on attenuations and phase delays

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Multipath propagation model


To sum up, the received signal is a linear combination of a number of

different propagation paths, each having its own attenuation, phase

rotation, and time delay:

: number of propagation paths

: attenuation of the i-th

path

: phase delay of the i-thpath

: time delay of the i-thpath

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(Preliminary) classification of the wireless channel


Time domain:

o static (time-invariant): its statistics change very slowly wrt

signaling time

o time-varying: its statistics are a function of time

Frequency domain:

o frequency-flat: its behavior is similar across the frequency

components of the signal

o frequency-selective: each frequency component of the

signal is distorted in a different way by the wireless channel

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Static frequency-selective channels (1/4)


For the sake of simplicity, let’s consider the two-ray channel, i.e., N=2:

direct (LoS) path reflected path

A static channel means: the random processes , , , and

are not functions of time

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To simplify the notation, let’s take:

received signal:

Fourier transform:

The frequency response of the channel is

where is the notch frequency of the channel

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The amplitude response of the two-ray channel is

period:

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When extending the calculations to the N-ray channel, we get

Bc is called the coherence bandwidth of the channel

1

1 1 1 1 1 1

10 100 10 100c

N

B

= =

−

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The concept of frequency selectivity (1/2)


We know that the bandwidth of a signal is

the channel is

frequency-flatthe channel is

frequency-selective

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The concept of frequency selectivity (2/2)


The frequency selectivity depends on the statistics

of the channel and of the input signal

There is a practical way to assess the frequency selectivity of a channel:

o : frequency-flat channel

o : frequency-selective channel

Example:

o urban scenarios:

o 3G and 4G signals:

Some form of equalization is needed to combat the frequency selectivity

cB B

cB B

1 ms , Bc 1 MHz/100=10 kHz

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Time-varying frequency-flat channels (1/5)


Due to the relative motion between the transmitter and the receiver, the

communication medium (the wireless channel) evolves through time:

For simplicity, assume a frequency-flat channel:

And so

fading process

100c s sB B T T

s iT i

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To study time and frequency characteristics of A(t), let’s use the kinematic

model for the MS:

Due to the Doppler effect, each frequency component is shifted at the

receiver side by its Doppler shift :

( )x t

( ) ( )exp( 2 )= y t x t j ft

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In reality, when we have rich multipath, the incident wave comes from a

variety of different angles, and the Doppler shift has not just one single

value:

The values of the Doppler effect, are spread around a certain interval of

Doppler frequencies, according to the different ai’s. The receievd signal is

1f

2f

3f

31 2

1 1 2 2 3 3( ) exp( 2 ) exp( 2 ) exp( 2 ) ... ( ) ( ) ( ) = + + + = jj j

y t e j f t e j f t e j f t x t A t x t

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When the «scatterers» (i.e., the objects) in the scenario are very many, the

Doppler shifts are distributed with continuity in the interval [-f0v/c; f0v/c]

1f

2f

3f

The decomposition of A(t) into many Doppler components becomes a

continuos Doppler spectrum, confined within the interval [-f0v/c; f0v/c]

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The behavior of A(t) is given by the impact of the Doppler effect over the

received signal

A key parameter is the maximum Doppler shift at the carrier frequency f0,

called the Doppler spread fD:

Using the Clarke’s model, we can

compute the power spectral density

(PSD) of the random process A(t):

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Example of Flat Fading

Signal amplitude

|A(t)| received at f0=1

GHz by a mobile

terminal

travelling at v=20km/h

in an urban area

~ 30 msec

t~ 300 bits @ 9.6 kb/sec

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The concept of time selectivity 1/2


The time selectivity depends on the statistics of the

channel and of the input signal

Selectivity is quantified through the Coherence Time Tc:

1 1

10 100c

D

Tf

=

: static channel (also means )

: time-selective channel

S cT T

S cT T

Df B

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The concept of time selectivity 2/2


Example (GSM on Frecciarossa): v=324 km/h= 90 m/s, f0=1.8 GHz

BUT the burst time is TB=546.5 ms

1 1

10 100c

D

Tf

=

Rs=270.833 kbaud Ts=3.7 ms

fD=540 Hz TC=18.5 ms

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Bibliography

[01] T.S. Rappaport, Wireless Communications: Principles and Practice, 2nd ed. Upper

Saddle River, NJ: Prentice-Hall, 2002.

[02] A.F. Molisch, Wireless Communications. West Sussex, UK: J. Wiley & Sons, 2005.

[03] A. Mehrotra, GSM System Engineering. Boston, MA – London, UK: Artech House,

1996.

[04] J.D. Parsons, The Mobile Radio Propagation Channel. Chichester, UK: J. Wiley &

Sons, 2000.

[05] M. Pätzold, Mobile Fading Channels. Chichester, UK: J. Wiley & Sons, 2002.

[06] B. Sklar, “Rayleigh fading channels in mobile digital communication systems,

Part I: Characterization,” IEEE Commun. Mag., vol. 35, no. 7, pp. 90–100, July

1997.

[07] B. Sklar, “Rayleigh fading channels in mobile digital communication systems,

Part II: Mitigation,” IEEE Commun. Mag., vol. 35, no. 7, pp. 102–109, July 1997.

[08] M. Hata, “Empirical formula for propagation loss in land mobile radio services,”

IEEE Trans. Veh. Technol., vol. 29, no. 3, pp. 317–325, Aug. 1980.

[09] R.H. Clarke, “A statistical theory of mobile-radio reception,” Bell Systems

Technical Journal, vol. 47, no. 6, pp. 957–1000, July-Aug. 1968.

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