properties of the mobile radio propagation channel jean-paul m.g. linnartz nat.lab., philips...

Properties of the Mobile Radio Propagation Channel

Jean-Paul M.G. LinnartzNat.Lab., Philips Research

99-09-21 Multipath fading 2

Mobile Radio Propagation Channel

Statistical Description of Multipath Fading

The basic Rayleigh / Ricean model gives the PDF of envelope But: how fast does the signal fade? How wide in bandwidth are fades?

Typical system engineering questions: What is an appropriate packet duration, to avoid fades? How much ISI will occur? For frequency diversity, how far should one separate carriers? How far should one separate antennas for diversity? What is good a interleaving depth? What bit rates work well? Why can't I connect an ordinary modem to a cellular phone?

The models discussed in the following sheets

will provide insight in these issues



The Mobile Radio Propagation ChannelA wireless channel exhibits severe fluctuations for small displacements of the antenna or small carrier frequency offsets.

Channel Amplitude in dB versus location (= time*velocity) and frequency

TimeFrequency

Amplitude



Some buzz words about Time Dispersion and Frequency Dispersion

Time Domain Channel variations Delay spreadInterpretation Fast Fading InterSymbol Interference

Correlation Distance Channel equalization

Frequency Doppler spectrum Frequency selective fadingDomain Intercarrier Interference Coherence bandwidthInterpretation

Time Dispersion Frequency Dispersion



Fading is characterised by two distinct mechanisms

• 1. Time dispersion Time variations of the channel are caused by motion of the antenna Channel changes every half a wavelength Moving antenna gives Doppler spread Fast fading requires short packet durations, thus high bit rates Time dispersion poses requirements on synchronization and rate of

convergence of channel estimation Interleaving may help to avoid burst errors

• 2. Frequency dispersion Delayed reflections cause intersymbol interference Channel Equalization may be needed. Frequency selective fading Multipath delay spreads require long symbol times Frequency diversity or spread spectrum may help



Time dispersion of narrowband signal (single frequency)

Transmit: cos(2 fc t)

Receive: I(t) cos(2 fc t) + Q(t) sin(2 fc t)= R(t) cos(2 fc t + )

I-Q phase trajectory

• As a function of time, I(t) and Q(t) follow a random trajectory through the complex plane

• Intuitive conclusion: Deep amplitude fades coincide with large phase rotations

99-09-21 Doppler 7


Doppler shift

• All reflected waves arrive from a different angle• All waves have a different Doppler shift

The Doppler shift of a particular wave is cos f c cv

= f 0

Maximum Doppler shift: fD = fc v / c

Joint Signal Model

• Infinite number of waves• Uniform distribution of angle of arrival : f() = 1/2

• First find distribution of angle of arrival the compute distribution of Doppler shifts• Line spectrum goes into continuous spectrum

99-09-21 Doppler 8


Doppler Spectrum

If one transmits a sinusoid, …what are the frequency components in the received signal?

Power density spectrum versus received frequency

Probability density of Doppler shift versus received

frequency

The Doppler spectrum has a characteristic U-shape.

Note the similarity with sampling a randomly-phased

sinusoid

No components fall outside interval [fc- fD, fc+ fD]

Components of + fD or -fD appear relatively often

Fades are not entirely “memory-less”

99-09-21 Autocorrelation 9


Autocorrelation of the signal

We now know the Doppler spectrum.

But how fast does the channel change?

Wiener-Kinchine Theorem: Power density spectrum of a random signal is the Fourier Transform of

its autocorrelation Inverse Fourier Transform of Doppler spectrum gives autocorrelation of

I(t) and Q(t)

99-09-21 Autocorrelation 10


Autocovariance of amplitude

C J 2 f D 02

J 0 i s z e r o - o r d e r B e s s e l f u n c t i o n o f f i r s t k i n d .

N o t e t h a t t h e c o r r e l a t i o n i s a f u n c t i o n o f

d i s t a n c e o r t i m e o f f s e t :

D cf = fv

c =

d

w h e r e

d i s t h e a n t e n n a d i s p l a c e m e n t d u r i n g , w i t h d = v

i s t h e c a r r i e r w a v e l e n g t h ( 3 0 c m a t 1 G H z )



How to handle fast multipath fading?

Analog User must speak slowly

GSM Blocks of data shorter than average non-fade

period Error correction and interleaving to avoid

burst errors Error detection and speech decoding Fade margins in cell planning

DECT Diversity reception at base station

IS95 Wideband transmission averages channel

behaviour This avoids burst errors and deep fades



Frequency Dispersion

• Frequency dispersion is caused by the delay spread of the channel

• Frequency dispersion has no relation to the velocity of the antenna



Frequency Dispersion: Delay Profile

Typical sample of impulse response h(t)

If we transmit a pulse (t) we receive h(t)

Delay profile: PDF of received power: "average h2(t)"

Local-mean power in delay bin is p f()



Typical Delay SpreadsMacrocells TRMS < 8 sec

• GSM (256 kbit/s) uses an equalizer

• IS-54 (48 kbit/s): no equalizer

• In mountanous regions delays of 8 sec and more

occur

GSM has some problems in Switzerland

Microcells TRMS < 2 sec

• Low antennas (below tops of buildings)

Picocells TRMS < 50 nsec - 300 nsec

• Indoor: often 50 nsec is assumed

• DECT (1 Mbit/s) works well up to 90 nsec

Outdoors, DECT has problem if range > 200 .. 500 m



Channel Parameters at 1800 MHz

Environment Delay Spread Angle spread Max. Doppler shift

Macrocellular: Rural flat 0.5 ms 1 degree 200 Hz

Macrocellular: Urban 5 ms 20 degrees 120 Hz

Macrocellular: Hilly 20 ms 30 degrees 200 Hz

Microcellular: Factory, Mall 0.3 ms 120 degrees 10 Hz

Microcellular: Indoors, Office 0.1 ms 360 degrees 2..6 Hz



Typical Delay Profiles

1) Exponential

2) Uniform Delay Profile

Experienced on some indoorchannels

Often approximated by N-RayChannel

3) Bad Urban



How do systems handle delay spreads?

Analog Narrowband transmission

GSM Adaptive channel equalization Channel estimation training sequence

DECT Use the handset only in small cells with small delay spreads Diversity and channel selection can help a little bit

“pick a channel where late reflections are in a fade”

IS95 Rake receiver separately recovers signals over paths with excessive delays

Digital Audio Broacasting OFDM multi-carrier modulationThe radio channel is split into many narrowband (ISI-free) subchannels



Frequency and Time Dispersion

M o d e l : E a c h w a v e h a s i t s o w n a n g l e a n d e x c e s s d e l a y

A n t e n n a m o t i o n c h a n g e s p h a s e

c h a n g i n g c a r r i e r f r e q u e n c y c h a n g e s p h a s e

T h e s c a t t e r i n g e n v i r o n m e n t i s d e f i n e d b y

a n g l e s o f a r r i v a l

e x c e s s d e l a y s i n e a c h p a t h

p o w e r o f e a c h p a t h



Scatter Function of a Multipath Mobile Channel

Gives power as function of

Doppler Shift (derived from angle )

Excess Delay

Example of a scatter plot

Horizontal axes: x-axis: Excess delay time y-axis:Doppler shiftVertical axis z-axis: received power



Scatter Function of a Multipath Mobile Channel

Doppler Shift derived from angle

Excess DelayExample of a scatter plot



Correlation of Fading vs. Frequency Separation

W h e n d o w e e x p e r i e n c e f r e q u e n c y - s e l e c t i v e f a d i n g ?

H o w t o c h o o s e a g o o d b i t r a t e ?

W h e r e i s f r e q u e n c y d i v e r s i t y e f f e c t i v e ?



C o n s i d e r t w o ( r a n d o m ) s i n u s o i d a l s i g n a l s

S a m p l e 1 a t f r e q u e n c y f 1 a t t i m e t 1

S a m p l e 2 a t f r e q u e n c y f 2 a t t i m e t 2

C o v a r i a n c e o f a m p l i t u d e s

1 2R , R2

02

21 2

2 2R M S

C = J ( 2

v)

1 + 4 ( f - f ) T

S p e c i a l c a s e s

Z e r o d i s p l a c e m e n t / m o t i o n : = 0

Z e r o f r e q u e n c y s e p a r a t i o n : f = 0



Coherence BandwidthDefinition: Coherence. Bandwidth is the frequency separation for which the

correlation coefficient is down from 1 to 0.5 Thus 1 = 2(f1 - f2) TRMS

so Coherence Bandwidth BW = 1 (2 TRMS)

We derived this for an exponential delay profile

Another rule of thumb:

ISI affects BER if Tb > 0.1TRMS

Conclusion: Either keep transmission bandwidth much smaller than the coherence

bandwidth of the channel, or use signal processing to overcome ISI, e.g.

Equalization DS-CDMA with rake OFDM

Effects of fading on modulated radio signals

99-09-21 Multipath fading


Effects of Multipath (I)

Frequency

Tim

e

Narrowband

Frequency

Tim

e

OFDM

Frequency

Tim

e

Wideband

99-09-21 Multipath fading


Effects of Multipath (II)

Frequency

Tim

e

+-+--+-+

DS-CDMA

Frequency

Tim

e +

-

-

FrequencyHopping

Tim

e

Frequency

+ - + -

+ - +-

+ - +-

MC-CDMA

Time Dispersion Revisited

The duration of fades and the optimum packet length



Time Dispersion Revisited: Duration of Fades

In the next slides we study the temporal behavior of fades.

Outline:

# of level crossings per second

Model for level crossings

Average non-fade duration

Effective throughput and optimum packet length

Average fade-duration



Two-State ModelVery simple mode: channel has two-states Good state: Signal above “threshold”, BER is virtually zero Poor state: “Signal outage”, BER is 1/2, receiver falls out of sync, etc

Markov model approach: Exponential distribution of sojourn time Prob(T >T0) = exp(-T0/Tave) Memory-less transitions

This model may be sufficiently realistic for many investigations

99-09-21 Fade duration 30


Average Fade / Nonfade Duration

F a d e d u r a t i o n s a r e r e l e v a n t t o c h o o s e p a c k e t d u r a t i o n

D u r a t i o n d e p e n d o n

F a d e m a r g i n = 2 p / R 02

D o p p l e r s p r e a d

A v e r a g e f a d e d u r a t i o n T F N T = ( R R )F 0P r

A v e r a g e n o n f a d e d u r a t i o n T N F+

N F 0N T = ( R R )P r



Average nonfade duration

N FD

T = = 2 f

1 P r ( o u t a g e )

L e v e l C r o s s R a t e

A v e r a g e n o n f a d e d u r a t i o n i s i n v e r s e l y p r o p o r t i o n a l t o D o p p l e r s p r e a d

A v e r a g e n o n f a d e d u r a t i o n i s p r o p o r t i o n a l t o f a d e m a r g i n



How to handle long fades when the user is stationary?

Analog Disconnect user

GSM Slow frequency hopping Handover, if appropriate Power control

DECT Diversity at base station Best channel selection by handset

IS95 Wide band transmission avoids most deep fades (at least in macro-cells) Power control

Wireless LANs Frequency Hopping, Antenna Diversity



Optimal Packet length

We want to optimize

#User bitsEffective throughput = ---------------- Prob(success)

#Packet bits

This requires a trade off between

Short packets: much overhead (headers, sync. words etc).

Long packets:may experience fade before end of packet.



Optimal Packet length

At 1200 bit/s, throughput is virtually zero:Almost all packets run into a fade. Packets are too long

At high bit rates, many packets can be exchanged during non-fadeperiods. Intuition:

Packet duration < < Av. nonfade duration

fc = 900 MHz72 km/h (v=20 m/s)fade margin 10 dB



Derivation of Optimal Packet length A s s u m e e x p o n e n t i a l , m e m o r y l e s s n o n f a d e d u r a t i o n s( T h i s i s a n a p p r o x i m a t i o n : I n r e a l i t y m a n y n o n f a d e p e r i o d s h a v e

d u r a t i o n o f / 2 , d u e t o U - s h a p e d D o p p l e r s p e c t r u m )

S u c c e s s f u l r e c e p t i o n i f1 ) A b o v e t h r e s h o l d a t s t a r t o f p a c k e t2 ) N o f a d e s t a r t s b e f o r e p a c k e t e n d s

F o r m u l a :

P s u c c e x p e x p( ) = -1

- T

T = -

1-

2 f TL

N F

D L

w i t h T L p a c k e t d u r a t i o n



Average fade duration

1

η

1exp

π

η-

f 2 = T

D

F

A F D i s i n v e r s e l y p r o p o r t i o n a l t o D o p p l e r s p r e a d

F a d e d u r a t i o n s r a p i d l y r e d u c e w i t h i n c r e a s i n g m a r g i n , b u t t i m e b e t w e e n f a d e s

i n c r e a s e s m u c h s l o w e r

E x p e r i m e n t s : F o r l a r g e f a d e m a r g i n s : e x p o n e n t i a l l y d i s t r i b u t e d f a d e d u r a t i o n s

R e l e v a n t t o f i n d l e n g t h o f e r r o r b u r s t s a n d d e s i g n o f i n t e r l e a v i n g



Conclusion

• The multipath channel is characterized by two effects:

Time and Frequency Dispersion

• Time Dispersion effects are proportional to speed and carrier frequency

• System designer needs to anticipate for channel anomalies

properties of the mobile radio propagation channel jean-paul m.g. linnartz nat.lab., philips...

Documents

frequency components

fc fd components of

interval fc fd

doppler spreadfast

maximum doppler shift

cos2p fc t qt sin2p

cos2p fc treceive

received signal