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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(
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" 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)(
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Airborne(Communications(
" Air3to3air(and(air3to3ground(acquisition((" Pointing(and(tracking(algorithms(
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Satellite(Communications(
" ESA(Artemis(experiment(" LEO(to(GEO(communication((link(range(approx(45,000(km)(
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Quantum(Communication(
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! (Look(at(the(positive(side(of(a(negative(quantum(rule:(" One(cannot(take(a(measurement(without(perturbing(the(system.(
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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)
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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.
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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.
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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
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Point sources Ωfv
Lens
Detector
Airy patterns
Misalignment(&(Pointing(Errors(
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t=0 Δt T [s] N=T/Δt # of Trials
emitted not emitted p = mΔt, q =1-p
Noise(in(Optical(Communication((
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! (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(
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MIMO(FSO(Systems(
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! (Noise(Model:((! Background3noise(limited((! Thermal3noise(limited(! Shot3noise(limited(((
Receive(Spatial(Diversity((
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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
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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(((
(
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Performance(of(FSO(MIMO((
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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%
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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(((((((((
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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(
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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(
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Results:(Transmit(Diversity(Gain(
d D=20 cm r0
L
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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
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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=
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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.(((
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! 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
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! (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.(
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