Mobile Radio PropagationChannel Models

Dr. Chih-Peng Li (李志鵬)

2

Table of ContentsIntroductionPropagation Path Loss Model

Friis Free Space ModelHata Model

Large Scale Propagation Model – Long Term FadingLognormal Distribution

Small scale Propagation Model – Short Term FadingMultipath

Delay Spread vs. Coherent BandwidthFlat Fading vs. Frequency Selective FadingNarrowband vs. Wideband

3

Table of ContentsDoppler’s Effect

Doppler’s Shift vs. Coherent TimeFast Fading vs. Slow Fading.

Rayleigh DistributionLevel Crossing Rate

Ricean DistributionComputer Simulation of Multipath InterferenceChannel Models in WCDMAFading Counteraction – Diversity Schemes

Introduction

5

Main Components of Radio Propagation

Propagation Path Loss. ( ~ 1/r2 in free space)Large Scale: Propagation models that predict the strength for an arbitrary separation distance.Small Scale: Propagation models that characterize the rapid fluctuation of the received signal strength over very short travel distance (~λ ) or short time duration (~s).

6

Large-Scale Propagation ModelsPropagation models that predict the mean signal strength for an arbitrary transmitter-receiver (T-R) separation distance are useful in estimating the radio coverage area of a transmitter.

They characterize signal strength over large T-R (transmitter – receiver) separation distances (several hundreds or thousands of meters).

7

Small-Scale Propagation ModelsSmall-scale fading is used to describe the rapid fluctuation of the amplitude of a radio signal over a short period of time or travel distance.Fading is caused by interference between two or more versions of the transmitted signal which arrive at the receiver at slightly different time.These waves, called multi-path waves, combine at the receiver antenna to give a resultant signal which can vary widely in amplitude and phase.

8

Small-Scale Propagation Models

The received signal power may vary by as much as three or four orders of magnitude (30 or 40 dB) when the receiver is moved by only a fraction of a wavelength.Typically, the local average received power is computed by averaging signal measurements over a measurement track of 5λ to 40 λ.

Hint : with f = 1 GHz ~ 2 GHz,

cmcmfc 15~30==λ

9

Small-Scale vs. Large-Scale Fading

Propagation Path Loss Model

11

Free Space Propagation Model

The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight (LOS)path between them.

e.g. satellite, microwave ling-of-sight radio link.

As with most large-scale radio wave propagation models, the free space model predicts that received power decays as a function of the T-R separation distance raised to some power.

12

Friis Free Space Equation

meters.in h wavelengt the:n.propagatio torelatednot factor loss system the:

meters.in distance separation R-T the:gain. antennareceiver the:

gain. antennaer transmitt the:.separation R-T

theoffunction a ish power whic received :)(power. ed transmitt:

)4()( 22

2

λ

πλ

LdGG

dPP

LdGGPdP

r

t

r

t

rttr =

13

The gain of an antenna is related to its effective aperture, Ae, by:

The effective aperture Ae is related to the physical size of the antenna.The miscellaneous losses L (L≥1) are usually due to transmission line attenuation , filter losses, and antenna losses in the communication system.L=1 indicates no loss in the system hardware.

Friis Free Space Equation

2

4λπ eAG =

14

Log-distance Path Loss Model

( )0

ndPL dd

⎛ ⎞∝ ⎜ ⎟⎝ ⎠

( ) ( )00

dB 10 log dPL PL d nd

⎛ ⎞= + ⎜ ⎟

⎝ ⎠

15

Hata Model

An empirical formulation of the graphical path loss data provided by OkumuraValid from 150M to 1500Mhz.hte : 30m ~ 200m (base station antenna height)hre : 1m~10m (mobile antenna height)d : T-R separation distance (in km)a (hre) : correction factor for effective mobile antenna height.

dhhahfdburbanL

terete

c

log)log55.69.44()(log82.13log16.2655.69))((50

−+−−+=

16

Hata Model

For small to medium sized city:

For large city:

For suburban area:

For open rural areas:

dBfhfha crecre )8.0log56.1()7.0log1.1()( −−−=

2

2

( ) 8.29(log1.54 ) 1.1 for 300

( ) 3.2(log11.75 ) 4.97 for 300re re c

re re c

a h h dB f MHz

a h h dB f MHz

= − ≤

= − ≥

4.5)]28/[log(2)()( 25050 −−= cfurbanLdbL

98.40log33.18)(log78.4)()( 25050 −−−= cc ffurbanLdbL

17

Hata Model in PCS BandExtension of Hata model to 2 GHz.

Mtere

tec

CdhhahfdburbanL

+−+−−+=

10

50

log)log55.69.44()(log82.13log9.333.46))((

centersan metropolitfor 3dB areassuburban andcity sized mediumfor 0dB

==MC

kmkmdmmh

mmhMHzMHzf

re

te

20~1:10~1:

200~30:2000~1500:

Large Scale Propagation ModelLong-Term Fading

19

Shadow Fading – Lognormal DistributionWhen reaching the mobile station, the radio wave will have traveled through different obstructions such as buildings, tunnels, hills, trees, etc. This is called the shadowing effect.The received signal R, when measured in decibels, has a normal density function. Thus R is described by lognormal distribution.

The PDF of R is:

Xσ: a zero-mean Gaussian distributed random variable (dB) with standard deviation 4 - 10 dB.

( ) ( ) ( ) σσ XddndPLXdPLdPL +⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⋅+=+=

00 log10

( )( ) ( )

( )

2 2ln / 21 02

0 0

r me rp r r

r

σ

πσ− −⎧ ≥⎪= ⎨

⎪

20

Correlation of Path Loss

Shadow Fading:

Correlation of Path Loss: (from Viterbi, Principles of Spread Spectrum Communications)

1010ζ∝nattenuatio

2 2

2

1,

( ) ( ) ( ) 0,

( ) ( ) ( ) .

mobile base station

mobile base station

mobile base station

a b

a b

E E E

Var Var Var

ζ ξ ξ

ζ ξ ξ

ζ ξ ξ σ

−

−

−

= ⋅ + ⋅

+ =

= = =

= = =

Small Scale Propagation ModelShort-Term Fading

22

Small Scale Fading -- 1Problem 1: multi-path induces inter-symbol interference(ISI) and delay spread.

23

Impulse Response Model of a MultipathChannel

A mobile radio channel may be modeled as a linear filter with a time varying impulse response, where the time variation is due to receiver motion in space.The filtering nature of the channel is caused by the summation of amplitudes and delays of the multiple arriving waves at any instant of time.

24

Channel Impulse ResponseDue to the different multipath waves which have propagation delays which vary over different spatial locations of the receiver, the impulse response of the linear time invariant channel shouldbe a function of the position of the receiver.

( , ) ( ) ( , ) ( ) ( , )

where ( , ) is the channel impulse resonse. ( ) is the transmitted signal. ( , ) is the received signal at position .

y d t x t h d t x h d t d

h d tx ty d t d

τ τ τ∞

−∞

= ⊗ = −∫

25

Multipath Radio Channel

26

Multipath Propagation Effect

27

Measured Multipath Power Delay Profiles

From a 900 MHz cellular system in San Fancisco.

28

Measured Multipath Power Delay Profiles

Inside a grocery store at 4 GHz.

29

Delay SpreadDelay spread and coherence bandwidth are used to describe the time dispersive nature of the channel.Received Signal:

Delay Spread corresponds to standard deviation of Ti .

Excess delay is the relative delay of the i-th multipathcomponent as compared to the first arriving component.

)()(1

∑=

−=n

iii Ttath δ

τσ

30

Time Dispersion Parameters

Mean Excess Delay: the first moment of the power delay profile.

RMS (room mean square) Delay Spread: the square root of the second central moment of the power delay profile.

∑∑

∑∑

==

kk

kkk

kk

kkk

P

P

a

a

)(

)(

2

2

τ

ττττ

22 )(ττσ τ −=

∑∑

∑∑

==

kk

kkk

kk

kkk

P

P

a

a

)(

)( 2

2

22

2

τ

ττττ

31

Time Dispersion Parameters

These delays are measured relative to the first detectable signal arriving at the receiver at τ0=0.The equations in the previous page do not rely on the absolute power level of P(τ), but only the relative amplitudes of the multipath components within P(τ).Typical values of rms delay spread are on the order of microseconds in outdoor mobile radio channels and on the order of nanoseconcds in indoor radio channels.

32

Typical Measured Values of RMS Delay Spread

33

Maximum Excess DelayMaximum Excess Delay (ΧdB) = the time delay during which multipath energy falls to ΧdB below maximum.Maximum Excess Delay (ΧdB) can also be defined as τx-τ0, where τ0 is the first arriving signal; τx is the maximum delay at which a multipath component is within X dB of the strongest arriving multipath signal.The value of τx is sometimes called the excess delay spread of a power delay profile.

34

Example of An Indoor Power Delay Profile

35

Coherence BandwidthTime domain focus on excess delay.Frequency domain focus on coherence bandwidth Bc.Bc is defined related to rms delay spread ∝ 1/(Bc)Bc (Coherence Bandwidth)

A statistical measure of the range of frequencies over which the channel can be considered flat (i.e. a channel which passes all spectral components with approximately equal gain and linear phase.).The range of frequencies over which two frequency components have a strong potential for amplitude correlation.Two sinusoids with frequency separation greater than Bc are affected quite differently by the channel.

36

Coherence BandwidthVersion 1: the bandwidth over which the frequency correlation is above 0.9

Version 2: the bandwidth over which the frequency correlation is above 0.5

150c

Bτσ

=

15c

Bτσ

=

37

Types of Small-Scale Fading

Based on multi-path time delay spread

Flat Fading (narrowband system)BW of signal < BW of channelDelay spread < Symbol period

Frequency Selective Fading (wideband system)BW of signal > BW of channelDelay spread > Symbol period

38

Wideband v.s. Narrowband

f f

t1

t2 Signal Bandwidth

wideband narrow band

Signal Bandwidth

39

Flat Fading

Signal undergoes flat fading if CS BB >STTs : reciprocal BW (e.g. symbol period)Bs : BW of the TX modulationστ : rms delay spread Bc : Coherence BW

40

Flat Fading

The mobile radio channel has a constant gain and linear phase response over a bandwidth which is greater than the bandwidth of the transmitted signal.The multipath structure of the channel is such that the spectral characteristics of the transmitted signal are preserved at the receiver.The strength of the received signal changes with time, due to fluctuations in the gain of the channel caused by multipath.

41

Flat Fading

Typical flat fading channels cause deep fades, and thus may require 20 or 30 dB more transmitter power to achieve low bit error rates during times of deep fades as compared to systems operating over non-fading channels.Also known as amplitude varying channel.Also referred to as narrowband channels since the bandwidth of the applied signal is narrow as compared to the channel flat fading bandwidth.The most common amplitude distribution of flat fading channel is the Rayleigh distribution.

42

Frequency Selective Fading

Signal undergoes frequency selective fading if CS BB > and τσ

43

Frequency Selective FadingThe channel possesses a constant-gain and linear phase response over a bandwidth that is smaller than the bandwidth of transmitted signal.The received signal includes multiple versions of the transmitted waveform which are attenuated and delayed in time.The channel induces inter-symbol interference.Certain frequency components in the received signal spectrum have greater gains than others.Also known as wideband channels.M-ray Rayleigh fading model is usually used for analyzing frequency selective small-scale fading.

44

Small Scale Fading -- 2Problem 2: moving receiver induces fading effects (Doppler shift) for each ray path.

45

Doppler Effect

Doppler is a frequency shift, cause by movement of the mobile antenna relative to the base station-Δf = V/λ (at 250 km/h and 900 MHz, Δf = 208 Hz)

V

f

f + ∆ff - ∆f

46

Doppler Shift / Spread

θθ coscos tvdl ∆==∆

θλπ

λπφ cos22 :Change Phase tvl ∆=∆=∆

θλ

φπ

cos21 :ShiftDoppler v

tfd =∆

∆⋅=

47

Doppler Spread and Coherence Time

Delay spread and coherence bandwidth do not offer information about the time varying nature of the channel caused by either relative motion between the mobile and base station, of by movement of objects in the channel.Doppler spread and coherence time are parameters which describe the time varying nature of the channel in a small-scale.Doppler spread BD is a measure of the spectral broadening caused by the time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero.When a pure sinusoidal tone of frequency fc is transmitted, the received signal spectrum, called the Doppler spectrum, will be in the range fc-fd to fc+fd , where fd is Doppler shift.

48

Coherence Time

Coherence time Tc is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersiveness of the channel in the time domain.Coherence time is a statistical measure of the time duration over which the channel impulse response is essentially invariant.Coherence time is the time duration over which two received signals have a strong potential for amplitude correlation.

49

Coherence TimeVersion 1:ƒm : the maximum Doppler shift, ƒm = ν/λ

Version 2: the time over which the time correlation > 0.5

Version 3: Geometric mean of version 1 and version 2.

mc fT 1≈

mc fT π169≈

mmc ff

T 423.016

92 == π

50

Doppler Power Spectrum

51

Types of Small-Scale FadingBased on Doppler Spread

Fast FadingHigh Doppler spread.Coherence time < Symbol Period.Channel variations faster than base-band signal variations

Slow FadingLow Doppler spread.Coherence time > Symbol period.Channel variations slower than base-band signal variations

52

Fast FadingTS>TC and BS

53

Slow Fading

TSBDChannel impulse response changes at a rate much slower than the transmitted baseband signal s(t).The channel may be assumed to be static over one or several reciprocal bandwidth intervals.The Doppler spread of the channel is much less than the bandwidth of the baseband signal.The velocity of the mobile and the basebandsignaling determines whether a signal undergoes fast fading or slow fading.

54

Type of Small-Scale Fading

55

Type of Small-Scale Fading

Rayleigh Distribution

57

Rayleigh Distribution

Rayleigh distributions are commonly used to describe the statistical time varying nature of the received envelope of a flat fading signal, or the envelope of an individual multipath component.

Envelope of the sum of two quadrature Gaussian noise signals obeys a Rayleigh distribution.

58

Typical Rayleigh Fading Envelope

59

Rayleigh DistributionConsider a carrier signal s at a frequency ω0 and with an amplitude a:

The received signal sr is the sum of n waves:

)exp( 0tjas ω⋅=

[ ] [ ]

θθ

θθ

θθθ

θθ

θωθω

sin cos :where

sin and cos :have We

sincos)exp( :Define

)exp()exp( where

)(exp)(exp

22211

11

1

01

0

ryrxyxr

ayax

jyxajajr

jajr

tjrtjas

n

iii

n

iii

n

iii

n

iii

n

iii

n

iiir

==+=

≡≡

+≡+=

=

+≡+=

∑∑

∑∑

∑

∑

==

==

=

=

60

Rayleigh DistributionBecause (1) n is usually very large, (2) the individual amplitudes ai are random, and (3) the phases θi have a uniform distribution, it can be assumed that (from the central limit theorem) x and yare both Gaussian variables with means equal to zero and variance

Because x and y are independent random variables, the joint distribution p(x,y) is

The distribution p(r,θ) can be written as a function of p(x,y) :

222 σσσ ≡= yx

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−== 2

22

2 2exp

21)()(),(

σπσyxypxpyxp

),(),( yxpJrp =θ

61

Rayleigh Distribution

The probability that the envelope of the received signal does not exceed a specified value R is given by the corresponding cumulative distribution function (CDF)

2

2

22

2 2

0

/ / cos sin; ( , ) exp

/ / sin cos 2 2Thus, the Rayleigh distribution has a pdf:

exp 0 ( ) ( , ) 2

0 ot

x r x r r rJ r p ry r y r

r r rp r p r d

π

θ θ θθ

θ θ θ πσ σ

θ θ σ σ

∂ ∂ ∂ ∂ − ⎛ ⎞≡ = = = −⎜ ⎟∂ ∂ ∂ ∂ ⎝ ⎠

⎛ ⎞− ≥⎜ ⎟= = ⎝ ⎠∫

herwise

⎧⎪⎨⎪⎩

⎟⎟⎠

⎞⎜⎜⎝

⎛−−==≤= ∫ 2

2

0 2exp1)()Pr()(

σRdrrpRrRP

R

62

Rayleigh DistributionMean:

Variance:

Median value of r is found by solving:

Mean squared value:

Most likely value = max { p(r) } = σ

σπσ 2533.12

)(][0

==== ∫∞

drrrprErmean

22

2

0

2222

4292.02

2

2)(][][

σπσ

πσσ

=⎟⎠⎞

⎜⎝⎛ −=

−=−= ∫∞

drrprrErEr

∫=medianr

drrp0

)(21

σ177.1=medianr

∫∞

==0

222 2)(][ σdrrprrE

63

Rayleigh Probability Density Function

64

Level Crossing and Fading Statistics

The level crossing rate (LCR) is defined as the expected rate at which the Rayleigh fading envelope, normalized to the local rms signal level, crosses a specified level in a positive-going direction.

Useful for designing error control codes and diversity.Relate the time rate of change of the received signal to the signal level and velocity of the mobile.

65

Level Crossing Rate (LCR)

The number of level crossings per second is given by:2

0

( , ) 2

is the tim e derivative of ( ) (i.e. the slope)

( , ) is the joint density function of and at is the m axim um D oppler frequency

/ is the value of the sp

R m

m

rm s

N r p R r d r f e

r r t

p R r r r r Rf

R R

ρπ ρ

ρ

∞ • • •−

•

• •

= =

=

=

∫

ecified level , norm alized to the local rm s am plitude of the fading envelope.

R

Clarke, R. H., “A Statistical Theory of Mobile-Radio Reception,”Bell Systems Technical Journal, Vol. 47, pp. 957-1000, 1968.

66

Average Fade DurationAverage fade duration is defined as the average period of time for which the received signal is below a specified level R. For a Rayleigh fading signal, this is given by:

where Pr[r≤R] is the probability that the received signal r is less than R and is given by

where τi is the duration of the fade and T is the observation interval of the fading signal.

[ ]1 PrR

r RN

τ = ≤

[ ] 1Pr ii

r RT

τ≤ = ∑

67

Average Fade DurationThe probability that the received signal r is less than the threshold R is found fro the Rayleigh distribution as:

where p(r) is the pdf of a Rayleigh distribution.The average fade duration as a function of ρ and fm can be expressed as

)exp(1)(]Pr[ 20

ρ−−==≤ ∫R

drrpRr2

22

2σρ R=

2

12m

ef

ρ

τρ π

−=

68

Average Fade DurationThe average duration of a signal fade helps determine the most likely number of signaling bits that may be lost during a fade.

Average fade duration primarily depends upon the speed of the mobile, and decreases as the maximum Doppler frequency fm becomes large.

Ricean Distribution

70

Ricean Fading Distribution

When there is a dominant stationary (non-fading) signal component present, such as a line-of-sight propagation path, the small-scale fading envelope distribution is Ricean.

θθ

θωωωθω

sincos

)(

)](exp[)exp(])[( )exp()](exp['

22200

esdirect wav

0

wavesscattered

0

ryrAx

yAxr

tjrtjjyAxtjAtjrsr

==+

++=

+≡++≡++=

71

Ricean Fading DistributionBy following similar steps described in Rayleigh distribution, we obtain:

( )

∑

∫

∞

=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎪⎩

⎪⎨⎧

<

≥≥⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=

00

2

0220

202

22

2

2!

function. Besselorder -zeroth modified theis

cosexp21

where0for 0

0r0,Afor 2

exp)(

ii

i

rr

rrr

ix(x)I

dArArI

)(r

ArIArrrp

θσ

θπσ

σσσ

π

72

Ricean Fading DistributionThe Ricean distribution is often described in terms of a parameter K which is defined as the ratio between the deterministic signal power and the variance of the multipath. It is given by K=A2/(2σ2) or in terms of dB:

The parameter K is known as the Ricean factor and completely specifies the Ricean distribution.As A 0, K -∞ dB, and as the dominant path decreases in amplitude, the Ricean distribution degenerates to a Rayleighdistribution.

2

2( ) 10 log [dB]2AK dBσ

= ⋅

73

Ricean Fading Distribution

Computer Simulation of Multi-path Interference

Reference: “Microwave Mobile Communications”,by W.C. Jakes, pp. 60-71.

75

Frequency Selective Fading ChannelRayleigh fading is usually adopted for flat fading channel model.Frequency selective fading channel model is usually modeled as the sum of several flat fading channels with different delays.

t0

t1

tn-1

Rayleigh

Rayleigh

Rayleigh

∑

76

Spatial Correlations at the Base Station

Scattering model for spatial correlations at the base station –generation of Rayleigh distribution.

77

Computer Simulation of Rayleigh Fading

Simulator that duplicates mobile radio spectrumProducing random phase modulation, a Rayleigh fading envelope, and a time-averaged, discrete approximation to the desired power spectrum.Simulation inputs:

Carrier frequency.Mobile velocity.Sampling rate.

The number of frequency components (N0) needed is at least 8 (N is at least 34 where N0 =0.5*(N/2-1) and N/2 is an odd integer).

78

Computer Simulation of Rayleigh FadingSimulator that duplicates mobile radio spectrum

Channel Models in WCDMA

80

(I) Static Propagation ConditionThe propagation for the static performance measurement is an Additive White Gaussian Noise (AWGN) environment. No fading or multi-paths exist for this propagation model.

81

(II) Multi-Path Fading Propagation Conditions

Table B.1 shows propagation conditions that are used for the performance measurements in multi-path fading environment. All taps have classical Doppler spectrum, defined as: ( )

( )21 [ , ]

1D D

D

S f f f ff f

∝ ∈ −−

Table B.1: Propagation Conditions for Multi path Fading Environments

-9781-9781

-6521-6521020000

-3260-32600976-10976

00000000

Average Power [dB]

Relative Delay [ns]

Average Power [dB]

Relative Delay [ns]

Average Power [dB]

Relative Delay [ns]

Average Power [dB]

Relative Delay [ns]

Case 4, 250 km/hCase 3, 120 km/hCase 2, speed 3 km/hCase 1, speed 3km/h

82

(III) Moving Propagation Conditions

The dynamic propagation conditions for the test of the base band performance are non-fading channel models with two taps. The moving propagation condition has two tap, one static, Path0, and one moving, Path1. The time difference between the two paths is according Equation (B.1). The parameters for the equation are shown in Table B.2. The taps have equal strengths and equal phases.

Table B.2: Parameters for moving propagation

40⋅10-3 s-1Δω

1 µsB

5 µsA

Figure B.1: The moving propagation conditions

( ))sin(12

tAB ⋅∆++=∆ ωτ (B.1)

t 1

P 1

∆τ

P 0

t 0

83

(IV) Birth-Death Propagation Conditions

The dynamic propagation conditions for the test of the basebandperformance is a non-fading propagation channel with two taps. The moving propagation conditions has two taps, Path1 and Path2 which alternate between 'birth' and 'death'. The positions the paths appear are randomly selected with an equal probability rate and are shown in Figure B.2.

0 1 2 3 4 5-1-2-3-4-5 0 1 2 3 4 5-1-2-3-4-5 0 1 2 3 4 5-1-2-3-4-5

P1 P2 P1 P1 P2 P1P2 P2

Figure B.2: Birth death propagation sequence

84

Birth-Death Propagation Conditions

1. Two paths, Path1 and Path2 are randomly selected from the group [-5, -4, -3, -2, -1, 0 ,1, 2, 3, 4, 5] µs. The paths have equal magnitudes and equal phases.

2. After 191 ms, Path1 vanishes and reappears immediately at a new location randomly selected from the group [-5, -4, -3, -2, -1, 0 ,1, 2, 3, 4, 5] µs but excludes the point Path2. The magnitudes and the phases of the tap coefficients of Path 1 and Path 2 shall remain unaltered.

3. After an additional 191 ms, Path2 vanishes and reappears immediately at a new location randomly selected from the group [-5, -4, -3, -2, -1, 0 ,1, 2, 3, 4, 5] µs but excludes the point Path1. The magnitudes and the phases of the tap coefficients of Path 1 and Path 2 shall remain unaltered.

4. The sequence in 2) and 3) is repeated.

Fading Counteraction(Diversity Schemes)

86

Fading CounteractionsLong-Term (large scale) Fading Counteraction: Macroscopic diversity (Space diversity)

S-diversityS+I-diversityS/I-diversity

87

Fading CounteractionShort-Term (small scale) Fading Counteraction: Microscopic diversity.

Space diversity - spacing is between receiving antennas.Polarization: orthogonality of the polarized wave components.Angle: directional antenna.Frequency: two or more different carriers.Time: time separation.Hopping: frequency hopping and time hopping.

88

Combining SchemesSwitched Combining

Pure Selection: the received signals are continuously monitored so that the best signal can be selected.Threshold Selection: the received signals are scanned in a sequential order, and the first signal with a power level above a certain threshold is selected.

Gain CombiningMaximal Ratio Combining (MRC): each one of the M signals has a gain proportional to its own signal-to-noise ratio.Equal Gain Combining: all of the signals have a gain equal to one.