Tài liệu Theory of the radio channels pptx

Motivation The channel determines: * System resources total bandwidth, carrier frequency, transmitted power, etc... Wireless Channel Overview * Multi-path propagation * Doppler effect

Theory of the-radio channels

Theory of the radio channels

Dr.-Eng Van Duc Nguyen

Back ground of stastistical theory

Definition of autocorrelation function of a

Motivation

The channel determines:

* System resources (total bandwidth, carrier

frequency, transmitted power, etc.)

Wireless Channel Overview

* Multi-path propagation

* Doppler effect

* Channel models

+ Mathematical description of radio channel model

* Data transmission in the presence of additive noise

Multi-Path Propagation

Dr.-Eng Van Duc Nguyen

+ Multi-path phenomenon: Transmitted signals reach

receiver via different paths

+ The received signal from each path is attenuated by

a different factor

Dr.-Eng Van Duc Nguyen

Effect:of Multi-Path:Propagation:

a: frequency /; b: frequency /;

Signo path Senet an pant

Toslrozeved spa Tela reed sgn

Transmitted Channel Received

signal model signal

h(): Channel Impulse Response (CIR)

H( j@): Channel Transfer Function (CTF)

Time-Invariant Channel Transfer- Function Ỷ i

Time delay: 7 Frequency: @

* Time-Invariant channel transfer function (CFT) is the

Fourier transform of CIR:

€oherence:Bandwidth:of:the Channel:

* Coherence bandwidth (A/),= ye

is a measure of the frequency selectivity of a channel

(A/)

* Non-frequency selective channel: (Sf), >> B

+ Frequency selective channel: (Af), << B

Dr.-Eng Van Duc Nguyen 13

* Maximum Doppler frequency for ¢, = 0 :

J2 =6

c

Doppler:Spectrum:

> The Doppler effect leads to:

+ Constant frequency shift

Time-Variant Channel: Impulse:-Rasponse Ễ |

A(z, t)

+ Doppler effect causes time variations of the channel

+ Time-variant channel impulse response is:

N, #

k=l

Goherence:Time:of:the Channel:

is a measure of the time variation of a channel

Pun (At)

* Time-invariant channel: (At), >> T,

* Time-varying channel: (Al), << T,

* There is no line of sight transmission between

transmitter and receiver, i.e there is no dominant path

* The mobile antenna receives a large number of

reflected and scattered waves

* The real and the imaginary part of the channel

coefficients, Re{a ;}, Im{a,} are two zero-mean statistically independent Gaussian random variables,

each having a variance o, The initial phase 6, is

evenly distributed in [0, 27]

Lari

* The probability density function (PDF) of the received

signal amplitude in case of flat fading is a Rayleigh

+ Very low signal amplitudes cause problems

- at the receiver (error bursts)

a

+ Useful channel model for many LOS transmission with a

dominant time-invariant component in addition to time-variant component

* The probability density function (PDF) of the received signal

amplitude in case of flat fading is Rice distribution function

> A detailed mathematical description can be found

in Proakis [1]

Pry (T).7y3At) = El’ (z,,t)h(z,,¢ + At)]

+ WSS and Uncorrelated Scattering channel model

(WSSUS):

9, (fị,7;, AI) = Ø,(rị,AP)ð( —7;)

* WSSUS model is commonly used

Power Delay Profile of the-Channel

>» Definition of power delay profile of the channel:

>» The power delay profile of the channel can be

obtained from the autocorrelation function by setting

+ WSSUS channel model:

Py (@.@ 3A) = J [ø„(r;AðŒ, =p ere aril

= | Joutesane" de, = (AeA)

CTF= channel transfer function

Dr.-Eng Van Duc Nguyen

28

‘Spaced-Frequency, Correlation Function

+ The spaced-frequency correlation function can be obtained from the autocorrelation function by setting At=0, it follows:

'Spaced-Time Correlation Function,

for at

Invorse Fourier Tràmmlm

Relations:between:ACF and Scattering.Eunction i j

Delay power spectral Scattering function Doppler power spectral

Data Transmission in: the: Presence of Additive: Noise

> For realistic models noise must be taken into account

+ Weather condition

nữ) + Man made noise

+ Thermal noise, etc

x(t) yữ)

Transmitted Channel Received

signal model signal

y(t) = x()* h(z) + n(t)

> Question: How to describe mathematically the

statistical characteristics of additive noise term n(¢) ?

+ In general case the additive noise ”(t) can be statistically

described by a random variable x with Gaussian

(normal) distribution, This random variable has the

variance a” and zero-mean, that is:

„=Elx

rng Wn Du Neen

Power Spectrum-of:and:Limited Gaussian:Noise-(1) Ỹ |

System bandwidth B = 2@, leads to band limitation of

TRE Additive noise (9 can be described by

Block:Diagram:of:a:Communication:System:

Discrete channel

Information |_| Source | Channel ‡ Moa:

source coding coding

* Channel capacity C is the maximum data rate which can

be transmitted error-free over the channel

+ With a suitable channel coding and decoding, the bit error

ratio of received signal can be reduced to any level, as long as the data rate 2 is still smaller than the channel capacity C

1948] Fs

c= Blo 4) = Blog(1+SNR)

”

* Shannon's theory:

“By sufficiently involved encoding systems, the

transmitted binary digits at the rate 8og(P, + P,)/P, bits per second, can be obtained with arbitrarily small number of errors.”

Channel Capacity of Some: Practical Systems:

lim channel 3.1 kHz 40 dB 40 kbit/s

Radio medium 6 kHz 50 dB 100 kbit/s wave

| Radio short wave | 15 kHz 70 dB 350 kbit/s

Me channel 5 MHz 45 dB 75 Mbit/s

IEEE 802.114 20 MHz 30dB 200 Mbit/s (HiperLAN/2)

Dr.-Eng Van Duc Nguyen 45

€hannel:modelling by Rice: method (Monte-Carlo:

Channel:modelling.by,Rice method (Monte Carlo

Slowly time-variant channel:

Fast time-variant channel Ỹ

Autocorrelation of the channel