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Mobile Communication Systems 1

Prof. Carlo RegazzoniProf. Fabio Lavagetto

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Basics of radio propagation

Introduction: characteristics of radio propagation;Attenuation;Antenna;Fading effects: Multipath fading Doppler effect Frequency selective and non-selective fading

Conclusion.

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Basics of radio propagation

The free space attenuation

It is the attenuation, only due to the path length and in presence of a free space propagation conditions (no obstacles between the transmitter and the receiver);

The free space introduce the following attenuation term:

The following expression is defined as available loss for the radio link :

Where the two last terms represent the antenna’s gain.

MHzKmFS fRL 1010 log20log2045.32

dBRdBTMHzpkmdBd GGfLA 1010 log20log204.32

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Basics of radio propagationAntennas

There are two main types of antennas:1. Isotropic antenna;2. Directional antenna.

The first one irradiates its energy in all spatial directions in the same manner.

The second one irradiates the signal in a particular direction. The antenna gain is defined as the ratio between the power

radiated by a directional antenna and the one radiated by an isotropic antenna.

In general:

effAG 24 pfc AAeff

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Introduction

Propagation effects:

There are four phenomena (reflection, refraction, diffraction, scattering) associated with the propagation of wireless signals which give rise to

• Multipath;• Fading;• Delay spread;• Doppler shift.

The wireless channel is considered to be gaussian, additive, and band-limited (AWGN). Whereas in real world the channel exhibits non gaussian characteristic (not AWGN).

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The radio channel: multipath propagation

Usually studied channels are characterized by a time-invariant impulse response;

Instead multipath channel is characterised by a time-variant impulse response;

On the transmission of a single impulse (ideally a dirac delta), the response would be typically a time variant impulse train of impulses dispersed in time (defined as time spread, t) with different attenuations.

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Multi-path propagation: the channel impulse response

tfjl

cetsts 2)(Re)( n

nn ttsttx )()()(

tfj

nnl

tfjn

cnc ettsettx 2)(2 )()(Re)(

nnl

tfjnl ttsettr nc )()()( )(2

nn

tfjn tettc nc )()();( )(2

cfjettc 2);();(

c(t) represents the channel response by choosing time t as the reference time where represents the delay with respect to the origin of time axis.

Let the transmitted signal be represented by s(t) and received signal as x(t).

The received signal can be represented as:

Where l means the equivalent low pass response.

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Multi-path effects

• If the propagating channel is slowly time variant, the value of n(t) oscillates with time and its variability has small effects;

• However, n(t) can vary up to 2 in a time interval if n(t) varies along a factor 1/fc, which is a very small value. This can be true for bandpass signals modulated around fc

• n(t) is a very sensitive parameter that characterizes the time-variant channel even if it has small oscillation;

• Moreover, the propagation delay related to each path can be often assumed to change in a complete random uncorrelated way (thus it is considered as a random process )

• This means that the received signal cannot be modelled as Gaussian random process.

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The received signal: envelope modelling

The received signal is dispersed in time with varying attenuation and phase. The signal is amplified (if constructive interference occurs) and attenuated (if destructive interference occurs). When the channel impulse response can be modeled as a Gaussian random process the envelope of the received signal can be modeled as:

Rician: if the Gaussian process has non-zero mean. Practically, the channel can be modeled with a Line on Sight (LoS) path and other non-line of sight paths.

Rayleigh: if the Gaussian process has zero mean. Practically, the channel can be modeled with non-line of sight paths;

Nakagami: it is a general case which can be expressed for both Rician and Rayleigh fading with unequal fading amplitudes.

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Channel correlation functions

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tc ;Time-variant correlation function

of the channel

tfC ;

FT

Time-variant correlation function of the channel

FT

;fSC Doppler power spectrum

;SScattering function

IFT

IFT

The relation between various considered fourier function

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The delay spreadDelay spreadIn general, the delayed paths are longer than the LoS path;As consequence the delayed paths arrive at the receiving antenna with different delays and in different time instants;The delay spread can be computed according the following relation:

c

SSTm

minmax •Smax = distance covered by the longest path;.

•Smin = distance covered by the shortest path.•The major effect due to the delay spread is the presence of Intersymbol Interference (ISI)

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Narrowband and wideband channel and coherence bandwidth

A channel is defined as narrowband if

Where T is the symbol time duration;

A channel is defined as wideband if

The coherence bandwidth is defined according to the following relations:

T > Tm

T < Tm

CC f m

c TB

1

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Channel frequency selectivity and temporal fading

If

the channel is frequency selective otherwise is not frequency selective.

mc T

BT

B11

mTT

Channel frequency selectivity

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Channel frequency selectivity and temporal fading

Temporal fadingThe temporal fluctuations of the amplitude of the received paths are combined at the receiver antenna;This combination can be destructive or constructive

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Channel frequency selectivity and temporal fading

Channel frequency selectivity and fadingThe frequency selectivity and the temporal fading are two different types of distortion that are usually present on the same channel;On a wideband channel both the effects of frequency selectivity and temporal fading are present;On a narrowband channel the temporal fading is present

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Time variance of the channelTemporal variation speed of fading depends on the spreading of frequencies due to the time varying nature of the environment;Phase time varying of replicas provides a spectral increase in a transmitted carrier;This phenomena is characterized by doppler spectrum defined previously;The doppler spread depends on: the relative velocity of the receiver with respect to the

transmitter; the movements of the objects between the transmitter and

the receiver.

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Time variance of the channel

In both cases the doppler spread can be computed as:

c

vfB cd

Path 1 Path 2

ccd fc

vv

c

vfB 21

The coherence time is defined as:

dc Bt 1

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Slow and Fast FadingTtc

If

If

The channel is defined as slowly fading channel and in this case:

Slow fading

Ttc Fast fading

Underspread channel

Overspread channel

cBB ctT

1dmBT

1dmBT

1dmBT

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Conclusion: transmission scheme over fading channels

Transmission technique

Type of channel

Narrowband digital modulation

underspread

Diversity techniques:CDMA;OFDM;MC CDMA

overspread