Fundamentals of Radio

communications• Radio waves as a transmission medium

• Time dependent electromagnetic fields produce waves that radiate

from the source to the environment.

• The radio wave based radio communication system is vulnerable to the

environmental factors: mountains, hills reflectors, … .

• The radio signal depends on the distance from the base station, the

wavelength and the communication environment.

• Main problems of radio communication are:

– Multipath propagation phenomena

– Fading phenomena

– Radio resource scarcity

Multipath propagation

• Advantage: connection in case of Non-line-

of-Sight.

• Fluctuation in the received signal’s

characteristics.

The factors affecting radio propagation:

• Reflection: collision of the electromagnetic

waves with an obstruction whose

dimensions are very large in comparison

with the wavelength of the radio wave.

Reflected radio waves.

• Diffraction, shadowing: collision of the

electromagnetic waves with an obstruction

which is impossible to penetrate.

• Scattering: collision of the radio wave with

obstructions whose dimensions are almost

equal to or less than the wavelength of

radio wave.

Baseband Equivalent Model 1

• Communication occurs in passband

• Most of the processing occurs in the baseband

• Complex baseband equivalent

• The baseband equivalent channel is limited to W/2

• Bandlimited waveform can be expanded in terms of

orthogonal basis

( )( )2 0

0 0

c c

b

c

S f f f fS f

f f

+ + >=

+ <

( ) [ ] ( )n

sincbx t x n Wt n= −∑

( ){ }sincn

Wt n−

,2 2

c c

W Wf f

− +

Baseband Equivalent model

• The received signal is described as convolution of the baseband equivalent model and channel taps

• The sample output can be thought as projection of the waveform onto waveform

W sinc(Wτ-m)

• due to the Doppler spread the bandwidth of the channel output is slightly larger than the bandwidth of the input signal.

Baseband Equivalent Model 2

• Baseband model

• hl(m) l - th channel filter tap at time m.

• l - s value is a function of channel gains a (t)– paths whos delay τ (t) are close to l/W.

– l - th tap can be interpreted as sample l/W of the low

pass filter baseband channel response convolved with sinc(Wτ)

( )

( ) ( ) sinc

( ) ( ) sinc

sinc

b

i i

i n

b

i i

n i

b

l i i

i

m my m a x n m n W

W W

m my m x n a m n W

W W

m mh m a m n W

W W

τ

τ

τ

= ⋅ − −

= ⋅ − −

= − −

∑ ∑

∑ ∑

∑

Degrees of freedom 1Transmitted signal

• x(m) is the m - th sample of the signal

• W samples per second

– each sample represents one complex degree of freedom

• Continuous signal x(t) can be approximated by W discrete symbols per second

• Band limited discrete signal has W degrees of

freedom per second

• Continuous time bandlimited complex signal with duration T has dimension approximately WT

Degrees of freedom 2Received signal

• The received singnal is also bandlimited– Bandwidth is approximately W

– Actual bandwidth is wider since the channel

modulates the transmitted signal

• Degrees of freedom of the channel is defined as

the dimension of the received signal space

• A good communication scheme exploits all the

available degrees of freedom in the channel

Channel Bandwidth

Impact of wide

bandwidth• The number of taps increases.

• New tap amplitude statistics

are needed.

Signal amplitude in the channel

Yhteysvälin vaimennus (Path Loss)

-130

-120

-110

-100

-90

-80

-70

-60

0 20 40 60 80 100 120 140 160 180 200

matka (m)

amplitudi (dB)

impulssivaste

-140

-130

-120

-110

-100

-90

-80

-70

400

440

480

520

560

600

640

680

720

760

800

840

880

920

960

1000

1040

1080

1120

1160

1200

1240

1280

1320

1360

1400

1440

1480

1520

1560

1600

viive (ns)

dB

Wideband Channel Modelling

• The channel can be represented

as a sum of flat fading Rayleigh-

or Rician components.

– Each component has its own

doppler spectrum

– Equivalent model is tapped delay

line

• Geographical area from where

multipath components arrive to the

receiver can be divided into

elliptical zones.

• The with of the zone gives enough

small delay variation of the zone.

• The transmission function for a

zone is mostly constant.

tx rx

A1

A

A

noise

source

noise

source

Σ

90

fast fading generator

fastfadinggenerator

fastfadinggenerator

2

N

a1s

a2s

aNs

( )1

2

0

( , ) kM j t

k kk

h t h eπν

λ δ λ τ−

=

= −∑

Examples of channel models used in

GSM developmentBad urban

i 1 2 3 4 5 6

τi/µs 0 0.3 1.0 1.6 5.0 6.6

Pim/dB −2.5 0 −3.0 −5.0 −2.0 −4.0

class class class class class class

Typical urban

i 1 2 3 4 5 6

τi/µs 0 0.2 0.5 1.6 2.3 5.0

Pim/dB −3.0 0 −2.0 −6.0 −8.0 −10.0

class class class class class class

Rural area

i 1 2 3 4 5 6

τi/µs 0 0.1 0.2 0.3 0.4 0.5

Pim/dB 0 −4.0 −8.0 −12.0 −16.0 −20.0

Rice class class class class class

t

f

0 1 2 3 4 5 6 µs

tap coefficient

distributions

UMTS user environments

suburban,

rural macrocells

Satellite cells

urban,

microcellsindoor,

picocells

Radio Channel description

• Link budget: to determine the expected signal level at a a given

distance from transmitter.

– Covering area, Battery life

• Time dispersion: estimation of the different propagation delays related

to the replicas of the transmitted signal which reaches the receiver.

Fading Channel

Large-scale Fading Small-scale Fading

(Rayleigh, Rician)

Oscillation around

signal meanPath loss

Frequency selective

FadingFlat Fading Slow Fading

Fast Fading

(Short term/multipath)

• Large scale fading– Occurs due to the large obstacles in the environment

– Typically frequency independent

– More relevant for network planning

• Small scale fading – Is described as variation of the signal strength over

distance of the order of the carrier wavelength

– Mainly due to the constructive and destructive sum of the multipath signals

– More relevant for designing reliable communication system

Large scale fading

• Ray tracing model

• Model with few parameters– power decay

– simple model• density of obstacles

– shadowing depends on the environment

– the duration of shadow fades lasts from seconds to minutes (more slower time than multipath fading)

• how much energy each obstacle absorbs

– scattering• very large number of individual paths

• received waveform modeled as integral over paths (not sum)

rα−

Doppler spread and coherence time

• Coherence time describes scale of the

variation of the channel– How fast the taps amplitude h[m] vary as a function

of time

• Significant change of the path amplitude occur

over periods of seconds

• Significant change in the phase of the i-th path

occurs in where Di is the Doppler

shift

1

4i

i

TD

=

• If different paths contributing to the l -th path have

different Doppler shifts, the tap magnitude changes significantly

• The change of user speed is inversely proportional to the largest difference between the Doppler shifts

• Coherence time – time interval over which the channel amplitude changes significantly as function of time. (in an order of magnitude sense)

– Typical values are in tens of hundreds of milliseconds

1

4c

s

TD

=

( ),

maxs i ji j

D D D= −

Delay spread and coherence

bandwidth• delay spread – difference in the propagation time

between the shortest and longest paths. (contains only paths with significant energy)

• Typical values are in microseconds

• UWB 3.1 – 10.6 GHz – few hundred taps.

• Frequency coherence shows us how quickly the channel changes as function of the frequency

• Time coherence shows us how quickly channel changes as function of time

( ) ( )( ),

maxi jd i j

T t tτ τ= −

Coherence bandwidth

• Coherence bandwidth Wc=1/(2Td)

• Coherence bandwidth is reciprocal to multipathspread

• Flat fading – the used bandwidth of is less than Wc (delay spread is less than symbol time)

• Frequency selective fading – signal bandwidth is larger than Wc

• Note the frequency selectivity depends not only on the channel but also on the used signal bandwidth.

Delay spread and coherence bandwidth

• Doppler spread Ds <-> Coherence time Tc~1/Ds

– Doppler spread is proportional to the velocity and the

angular spread of the arriving paths.

• Delay spreadTd <-> Coherence bandwidth Wc~1/Td

– Delay spread is proportional to the difference between

the lengths of the shortest and the longest paths

• Under spread /overspread channel

– Delay spread is much less than Coherence time

Td << TcUnderspread

W >> WcFrequency-selective

fading

W << WcFlat fading

Tc >> delay requirementSlow fading

Tc << delay requirementFast fading

Defining characteristicTypes of channel

Example of parameters for the channel

100 HzDoppler spread of paths

corresponding to a tap

50 HzDoppler shift for a path

64 km/hVelocity of the mobile

1 kmDistance between the

transmitter and receiver

1 MHzCommunication bandwidth

1 GHzCarrier frequency

Representative valuesKey channel parameters

Representative valuesKey channel parameters

500 kHzCoherence bandwidth

1 µsDelay spread

2.5 msCoherence time

20 sTime to move over a tap

5 msPath phase change

1 minutePath amplitude change

Error probability in fading channels

• The detection error probability decays

– exponentially in SNR in the AWGN channel

– inversely with the SNR in the fading channel

• Error probability behaves like

• typical error event in the fading channel due to

the channel being in the deep fade

( )

( )

1/

2

0

2

1

1 1

SNR

xP h SNR e dx

event h P deep fadeSNR SNR

−

< =

< ⇒ ≈

∫

-5 0 5 10 15 20 2510

-6

10-5

10-4

10-3

10-2

10-1

100

SNR [dB]

BER

0

0.5

1.0

BPSK in AWGN

BPSK in Ray leigh fading

Turbo code 1/3 rate

Performance of different schemes

in Rayleigh fading channel

21/SNRDifferential QPSK

1 1/(2SNR)Differential BPSK

1 / 21/(2SNR)Noncoherent ort.mod.

45/(2SNR)Coherent 16-QAM

25/(4SNR)Coherent 4-PAM

21/(2SNR)Coherent QPSK

11/(4SNR)Coherent BPSK

Data rate

(Bits/s/Hz)

BER

high SNR

Scheme

Diversity

• A good communication scheme exploits all the available degrees of freedom

• The outage in fading channel is determined by the amplitude of a single signal path– The performance can be improved by passing the information

trough multiple signal paths

• Full diversity is achieved if the symbol is repeated over all possible channel branches.

• With L Rayleigh fading branches of diversity

– at high SNR

( )1

LP error c

SNR≈

Diversity schemes

• Time – interleaving the code symbols over time periods

• Space – use multiple transmit receive antennas, use multiple propagation paths

• Frequency – use wider bandwidth than the coherence bandwidth of the channel

• Polarization – use the fact that signals with different polarization attenuate independently

Examples of repetition schemes

• Repeat the symbol over different coherent

periods

• Repeat the same symbol over different

transmit antennas one at a time

• Repeat the symbol over frequency sub

carriers in different coherence bands

• Transmit a symbol once every delay

spread in a frequency selective channel.

Repetition schemes

• repetition over different coherence periods

• repeating over different transmit antennas

• repeating over different frequency bands

(OFDM)

• transmitting the symbol over every delay

spread in a frequency-selective channel

Time diversity in GSM

• FDD system with 25 MHz bands for uplink

and downlink

• Bands are divided into 200 kHz sub-

channels

• Each channel is shared by eight users by using 577 µs timeslots

– Eight slots form 4.615 ms frames

• Voice is coded into speech 20 ms frames

– The frames are coded with convolutional codes

• 8 time slots are shared between to 20 ms voice

frames

– Maximum possible time diversity 8

• With mobile speed v

Ds= 2 fcv/c

fc is carrier frequency c is speed of light

• Coherence time is Tc=1/(4Ds)=c/(8fc v)

The channel can be assumed to independent if the coherence time is less than 5 ms at 900 MHz this corresponds to the speed 30

km/h

• For walking speed 3 km/h

– Too little time diversity

– Frequency hopping

• Typical delay spread 1 µs

– Coherence bandwidth 500 kHz

– By hopping to a channel that is 500 kHz apart

we can assume that the channels fade

independently – frequency diversity

Antenna diversity

• In the antennas are placed far apart the channel between antennas fade independently

• The channels independence depends on the environment and the distance between the antennas –spatial diversity

• Receive diversity – multiple antennas at the receiver

• Transmit diversity – multiple antennas at the receiver

• Maximum diversity depends on all the paths between the transmitter and receiver

• In order to benefit from the diversity the transmitter should distribute the copies of the information among the tx antennaes

Frequency diversity

• The diversity is achieved by resolving multipath at the receiver

• Single carrier system– Using equalization at the receiver the ISI can be compensated (to some

extend)

– Optimum receiver Maximum Likelihood Sequence Detector (MLSD)

• DS spread spectrum– The ISI is low since the symbols are spread with random code

– By using RAKE receiver the energy from different paths can be combined in phase • Complexity much lower than MLSD

• Multi carrier system– The transmit coding changes ISI channel into noninterfering sub carriers

• Each sub carrier has narrowband flat fading

– In order to benefit from diversity the information should be coded over independently fading frequencies

Impact of the channel estimation

• In RAKE receiver the power of individual channel taps becomes very small and difficult to be estimated

• Similar problem in time diversity

• In Antenna diversity – the received energy per receive antenna is kept

constant the channel measurement is not impacted when number of receive antennas is increased

– In transmit diversity the same power is distributed among different antennas, that reduces the received signal power from different paths