Institute(of(Digital(Communications(Li3Fi(R&D(Centre(

The(University(of(Edinburgh,(UK(

Outline(! (Introduction(to(Free3Space(Optical((FSO)(Communication((

! (FSO(Channel(Model(

! (Spatial(Diversity(for(MIMO(FSO((

! (Aperture(Averaging,(Correlation(and(Near3Field(Effects(

! (Distributed(MIMO/Relaying(

! (Conclusions(

2

"  The(“Last(Mile”(Bottleneck(Problem(

"  Only(about(5%(of(commercial(buildings(are(connected(to(fiber("  FSO(Links(provide(a(virtual(extension(of(backbone(fiber(network(at(

a(comparatively(low(cost!(3

Why(Free(Space(Optical(Communication?((

Very%Fast%(>%2.5%Gbps)%Fiber%links%between%

major%cities%

Local%Area%Networks%in%buildings%are%also%

fast%(>100Mbps)%

Typically%~1%Mbps%

FSO(Applications(

"  >1(Gbps(over(134km,(10%Gbps%up(to(350m("  HD(video(transport(in(FIFA(World(Cup(2010(((BBC(&(MRV)(

4

Airborne(Communications(

"  Air3to3air(and(air3to3ground(acquisition(("  Pointing(and(tracking(algorithms(

5

Satellite(Communications(

"  ESA(Artemis(experiment("  LEO(to(GEO(communication((link(range(approx(45,000(km)(

6

Quantum(Communication(

7

! (Look(at(the(positive(side(of(a(negative(quantum(rule:("  One(cannot(take(a(measurement(without(perturbing(the(system.(

8

Free3Space(Optical(Channel(

Sunlight

Building Motion

Window Attenuation

Fog

Scintillation

Range

Low Clouds

Alignment

((((((((((((((((((((((((((((((((((

Free3Space(Optical(Channel(

ξ (r) = !ξ ( !r )R∫ h(r, !r )dr

hi (r, !r ) =e jkL+ jk r− !r 2/2L

jλLe−aL/2 eχ (r, !r )+ jφ (r, !r )

Green’s%function%for%vacuum%propagation%(Diffraction)%%

Absorption%and%scattering%loss%

%%%Atmospheric%Turbulence%

(

+"

Background%%Noise%

Transmitter% Receiver%

×"

Atmospheric%%Effect%

!ξ ( !r ) ξ (r)

9

Atmospheric(Turbulence(

1r1′r

2′r

2r

! (Turbulence:(Homogenous(and(Isotropic((

! (Weak(Turbulence:((((((((((((((((((((((((are(Gaussian(random(processes(based(on(Rytov(theory((

χ (r, !r ),φ (r, !r )

! (2nd(Order(Statistics:(Space(invariant(but(length3dependent(

! (Impairments:(Intensity(fluctuation((fading),(phase(distortion( 10

Numerical(Modeling(! (Random(Wave(Vectors(! (Random(Phase(screens("  Simulate(log3amplitude(and(phase(simultaneously(

(

0

00

Phase (D = 10 cm)

Phase (D = 20 cm)

2π

2πMax

Amplitude (D = 20 cm)

Amplitude (D = 10 cm)

0

Max

Fig. 5. The amplitude and phase of a distorted optical field after propagation

through the atmosphere over receive apertures with diameters D = 10 cm and

D = 20 cm.

18

0

00

Phase (D = 10 cm)

Phase (D = 20 cm)

2π

2πMax

Amplitude (D = 20 cm)

Amplitude (D = 10 cm)

0

Max

Fig. 5. The amplitude and phase of a distorted optical field after propagation

through the atmosphere over receive apertures with diameters D = 10 cm and

D = 20 cm.

18

0

00

Phase (D = 10 cm)

Phase (D = 20 cm)

2π

2πMax

Amplitude (D = 20 cm)

Amplitude (D = 10 cm)

0

Max

Fig. 5. The amplitude and phase of a distorted optical field after propagation

through the atmosphere over receive apertures with diameters D = 10 cm and

D = 20 cm.

18

0

00

Phase (D = 10 cm)

Phase (D = 20 cm)

2π

2πMax

Amplitude (D = 20 cm)

Amplitude (D = 10 cm)

0

Max

Fig. 5. The amplitude and phase of a distorted optical field after propagation

through the atmosphere over receive apertures with diameters D = 10 cm and

D = 20 cm.

18

11 !  Simulation(of(Atmospheric(Turbulence(for(Optical(Systems(with(Extended(Sources,(AO,(2012(

Near3Field(vs(Far3Field(Near3Field( Far3Field(

Near3Field(

Far3Field(γ = h1 !ξ1

2+ h2 !ξ2

2 !h = aDiff e

−aL/2 eχ+ jφ

hi (r, !r ) =e jkL+ jk r− "r 2/2L

jλLe−aL/2 eχ (r, !r )+ jφ (r, !r )

ξi (r) = !ξi ( !r )R∫ h(r, !r )drγ = ξ1(r)+ξ2(r)2

Aperture∫ dr

12

Point sources Ωfv

Lens

Detector

Airy patterns

Misalignment(&(Pointing(Errors(

13

t=0 Δt T [s] N=T/Δt # of Trials

emitted not emitted p = mΔt, q =1-p

Noise(in(Optical(Communication((

14

! (The(Poisson(Limit((

! (Gaussian(Limit(

�  (N(is(very(large(and(λ= E{K} = Np is(finite.((

P(K = k) = Nk

!

"##

$

%&& p

kqN−k"  Binomial(distribution:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((E{K} = Np

P(K = k) = (λ)k

k!e−λ

! Photoelectric(Effect(

! (Rate3Adaptive(techniques("  Raptor(code("  Punctured(LDPC(code((

! (Hybrid(RF/FSO(System("  Adapts(to(weather(variations((

! (Spatial(diversity(" MIMO(" Distributed(MIMO(or(Relay3assisted(communication(

Reliable(FSO(communication(

15

MIMO(FSO(Systems(

16

! (Noise(Model:((! Background3noise(limited((! Thermal3noise(limited(! Shot3noise(limited(((

Receive(Spatial(Diversity((

17

h1*$

h2*$

hN*$

! (Maximum(Ratio(Combining((MRC)((

! (Equal3Gain(Combining((EGC)((

! (Selection(Combining((SC):(((((((((((((((((((((((r = max(ri)((

BER Performance of Free-Space Optical Transmission with Spatial Diversity. IEEE Trans. Wireless Commun. 6:2813-2819

18

Transmit(Diversity(in(RF(systems(((#  Repetition Coding: No diversity. Signals with random phases are

added together which may be constructive or destructive.

#  Space-Time Coding: An emerging coding technique which has

been developed to make diversity by having redundancy in both time and space since 1998.

Alamouti Code

MIMO(FSO(Diversity(Systems(

Point sources Ωfv

Lens

Detector

Airy patterns

! Initial(studies(proposed(Modified(space(time(block(codes(for(MIMO(FSO.(

(

19 !  Do(We(Really(Need(OSTBCs(for(FSO(with(Direct(Detection?,(IEEE(Trans.(Wireless(Commun.,(%

!  Do(we(really(need(space3time(block(codes(for(IM/DD(FSO?(

(

MIMO(FSO(Diversity(Systems(! Modified(space3time(block(codes(proposed(for(MIMO(FSO†(((

(

† M. K. Simon and V. Vilnrotter, IEEE Trans. on Wireless Comm., Jan. 2005

~x : “bitwise not” of x x* : complex conjugate of x

! Repetition(coding(vs(STBC(((

(

20

Performance(of(FSO(MIMO((

21

Diversity(Gain(Analysis(

!  We(defined(the(so3called(“Relative%Diversity%Gain”$(to(quantify(the(diversity(gain(of(FSO(systems:%

!  The(conventional(definition(of(diversity(order(is(not(useful(for(FSO(diversity(systems:(

!  For(MIMO(FSO,(it(yields%

22

Diversity(Gain(Analysis(

!  In(the(presence(of(misalignment(and(pointing(errors(

!  Weak(Turbulence((Lognormal):(((

!  Strong(Turbulence((Exponential):(

!  Diversity(gain(of(Gamma3Gamma(model:(

(((((((((((((((((((((((((((((((((((((((((((((((((((Or(more(appropriately(((((((((

23

MIMO(FSO:(near3field(

Diffraction%Effect%

Near3Field(

Far3Field(

Near3Field( Far3Field(

Turbulence%Correlation%

Near3Field(

Far3Field(

24 !  Diversity(and(Multiplexing(for(Near3field(Atmospheric(Optical(Communications,(TCOM,(2013(

Near3Field(Effects(

25

Safari M, Hranilovic S (2013) Diversity and Multiplexing for Near-Field Atmospheric Optical Communication. IEEE Trans. Commun 61:1988-1997

Diversity(Gain(Analysis(

!  Overall(system:(Amount(of(Fading((

Variance(of(received(power(normalized(by(squared(mean(power(

!  Transmitter(Side:(Beam(Averaging(Factor((

Amount(of(fading(of(multi3beam(system(normalized(by(that(of(

single3beam(system(

26

Results:(Transmit(Diversity(Gain(

d D=20 cm r0

L

27

Far3field(vs(Near3Field(! The(BER(performance(of(the(single(and(dual3beam(FSO(systems(versus(the(optical(SNR(defined(as(SNR(=(RP/σn.(

d D r0

L

29

Relay3Assisted(FSO(Systems(! ((Serial(Relaying:(Source(and(destination(are(connected(through(K(amplify3and3forward((AF)(or(decode3and3forward((DF)(relays.((

! ((Parallel(Relaying:(The(source(has(multiple(transmit(apertures(each(of(which(is(pointed(in(the(direction(of(one(of(the(K(relays.((

LK,K+1 L2,3 L1,2 L0,1 R1 R2 R3 RK / ( 1)tP P K= +

RK LK,K+1

L3,K+1 L2,K+1

L1,K+1

L0,K L0,3

L2,0 L0,1

R1

R2

R3 / (2 )tP P K=

! (Direct(Transmission:(Considered(as(benchmark(scheme.(

L0,K+1 = L tP P=

30

System(Model(! ((Signal(Model:((

" (Binary(PPM(Modulation((IM/DD):(

! ((Relaying(Strategy:(" (Decoded3and3Forward((DF)(Relaying:(the(signal(is(decoded(and(retransmitted(if(SNR(is(above(a(given(threshold.(((

" %Amplify3and3Forward((AF)(Relaying:(the(signal(is(scaled(after(a(debiasing$operation(which(improves(power(efficiency.(((

31

!  Relay3Assisted(Free3Space(Optical(Communication,(TWCOM,(2008,(%!  Multi3Hop(Relaying(over(Turbulent(Atmospheric(Poisson(Channel,(TCOM,(2012(!  Optimal(Relay(Placement(and(Diversity(Analysis(of(Relay3Assisted(FSO(systems,(JOCN,(2013(

Performance(of(DF(FSO(Relaying(! (We(observe(an(impressive(performance(gain(of(18.5(dB(by(adding(only(one(relay(at(the(target(Pout(=(1036(.(! (The(serial(relaying(scheme(takes(advantage(of(distance3dependency(of(fading(to(a(greater(extent.((

((Serial(Relaying((

0 10 20 30 40 5010

-15

10-10

10-5

100

PM [dB]

Out

age

Prob

abilit

y

AnalyticalNumerical

DirectTransmission

K=1

K=2

K=3

0 10 20 30 40 5010

-15

10-10

10-5

100

PM [dB]

Out

age

Prob

abilit

y

AnalyticalNumerical

DirectTransmission

K=1

K=2K=3

((Parallel(Relaying((32

Relay3Assisted(FSO(Systems(

LK,K+1 L0,1 R1 RK

RK LK,K+1

L3,K+1 L2,K+1

L1,K+1

L0,K

L0,3

L2,0 L0,1

R1

R2

R3

33

! (Which(relaying(strategy(wins?(Serial(or(Parallel?(

! (Diversity(Gain:(

! (Optimal(Power(Control(Laws(for(Multi3Hop(Poisson(Channel.(

Number(of(hops(( Number(of(diversity(paths(

Conclusion(! The(problem(of(reliable(optical(communication(over(

turbulent(atmosphere(was(introduced.(

! Different(solution(using(spatial(diversity(including(MIMO(and(relay3assisted(schemes(were(considered.((

! The(Diversity(FSO(systems(have(been(analyzed(through(different(analytical(models(including(near3field/far3field(and(Gaussian/Poisson(models.(

! Although(the(technology(called(“optical(wireless”,(there(are(some(fundamental(differences(with(“RF(wireless”((which(need(to(be(carefully(considered(in(the(system(design.(

34