Abstract

A new modulation scheme with a sensitivity of 2.3 photons per bit at a bit-error ratio (BER) of 103 is discussed theoretically and demonstrated experimentally. We achieve a limiting sensitivity of 2.3 photons per bit (3.7 dB photons per bit) by stacking the modulation formats 64PPM, 4FSK and polarization-switched (PS) QPSK. This modulation stack encodes 11 bit per symbol (PPM: 6 bit, FSK: 2 bit, PS-PQSK: 3 bit). We also replaced 4FSK by 2ODFM (2-channel multiplex) for comparison. With 64PPM-2OFDM-PS-QPSK a total of 12 bit are encoded (PPM: 6 bit, 2 OFDM channels with PS-QPSK: 2 × 3 bit). Both modulation stacks show a similar limiting sensitivity and are probably the highest sensitivities so far reported for a BER of 103, Our theoretical considerations are supported by simulations and experiments.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2011 (3)

2010 (2)

2009 (2)

2008 (2)

Agrell, E.

Bao, H.

Boroson, D. M.

Burrows, E. C.

Caplan, D. O.

Chandrasekhar, S.

Chraplyvy, A. R.

Essiambre, R. J.

Foschini, G.

Goebel, B.

Kachelmyer, A. L.

Karlsson, M.

Kikuchi, K.

Kramer, G.

Liu, X.

Marshall, T.

Nebendahl, B.

Osaki, M.

Robinson, B. S.

Shieh, W.

Stevens, M. L.

Szafraniec, B.

Tang, Y.

Tkach, R. W.

Winzer, P.

Winzer, P. J.

Wood, T. H.

J. Lightwave Technol. (2)

Opt. Express (6)

Opt. Lett. (1)

Other (17)

D. O. Caplan, “Laser communication transmitter and receiver design,” in Free-Space Laser Communications: Principles and Advances, J. C. R. Arun K. Majumdar, ed. (Springer, 2005), pp. 109–246.

M. Pfennigbauer, W. R. Leeb, M. Aspelmeyer, T. Jennewein, and A. Zeilinger, “Free-Space Optical Quantum Key Distribution Using Intersatellite Links,” in Intersatellite Link Workshop, (Proccedings of the CNES, 2003)

P. J. Winzer, “Modulation and multiplexing in optical communications,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, Technical Digest (CD) (Optical Society of America, 2009), paper CTuL3.
[Crossref]

D. O. Caplan, “High-Performance Free-Space Laser Communications and Future Trends,” in Optical Amplifiers and Their Applications, Technical Digest (CD) (Optical Society of America, 2005), paper TuB1.

D. O. Caplan, J. J. Carney, and S. Constantine, “Parallel direct modulation laser transmitters for high-speed high-sensitivity laser communications,” in CLEO:2011- Laser Applications to Photonic Applications, Technical Digest (CD) (Optical Society of America, 2011), Postdeadline Paper PDPB12.

B. S. Robinson, “Semiconductor-Based All-Optical Switching for Optical Time-Division Multiplexed Networks,” (Massachusetts Institute of Technology, PhD Thesis, 2003).

A. Ludwig, M.-L. Schulz, P. Schindler, R. Schmogrow, A. Mustafa, B. Moos, S. Brunsch, T. Dippon, D. Malsam, D. Hillerkuss, F. Roos, W. Freude, C. G. Koos, and J. Leuthold, “Stacking PS-QPSK and 64PPM for Long-Range Free-Space Transmission,” in Advanced Photonics 2013, OSA Technical Digest (Optical Society of America, 2013), paper NW2C.2.

T. A. Eriksson, P. Johannisson, M. Sjodin, E. Agrell, P. A. Andrekson, and M. Karlsson, “Frequency and polarization switched QPSK,” in European Conference on Optical Communication (ECOC), Technical Digest (CD) (Optical Society of America, 2013), paper Th2D4.

D. J. Geisler, T. M. Yarnall, W. E. Keicher, M. L. Stevens, A. M. Fletcher, R. R. Parenti, D. O. Caplan, and S. A. Hamilton, “Demonstration of 2.1 Photon-Per-Bit Sensitivity for BPSK at 9.94-Gb/s with Rate-1/2 FEC,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (Optical Society of America, 2013), paper OM2C.6.
[Crossref]

I. T. U. Telecommunication Standardization Sector, “Forward Error Correction for High Bit Rate DWDM Submarine Systems, G. 975.1,” ( www.itu.int/rec/T-REC-G.975.1-200402-I/en , Feb. 2004).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE-The international Society for Optical Engineering, 2005).

R. H. Barker, “Group synchonizing of binary digital systems,” in Communication Theory, W. Jackson, ed. (1953), pp. 273–287.

J. G. Proakis and M. Salehi, Digital Communications, 5th ed. (McGraw-Hill, 2008).

K. P. Ho, Phase-Modulated Optical Communication Systems (Springer Science + Business Media, Inc., 2005).

G. Jacobsen, Noise in Digital Optical Transmission Systems (Artech House, Inc., 1994).

C. Walck, Hand-book on Statistical Distributions for Experimentalists, Internal Report (Universitet Stockholms, 1996).

M. K. Simon, S. M. Hinedi, and W. C. Lindsey, Digital Communication Techniques, Signal Design and Detection (Prentice-Hall, 1994).

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Figures (6)

Fig. 1
Fig. 1 Setup with transmitter and pre-amplified coherent receiver. The signal is modulated by a dual-polarization (DP) IQ-modulator driven by an arbitrary waveform generator (AWG). The free-space optical channel is emulated by a variable optical attenuator (VOA), followed by a coupler that taps the optical input and monitors the power entering the pre-amplified receiver with a power meter (PM). An optical spectrum analyzer (OSA) is used to monitor the OSNR and the polarization controlled (PC) signal is detected by a coherent polarization-diversity receiver. Two real-time oscilloscopes store the signals for offline processing. The laser acts both as a continuous-wave source for the transmitter and as a local oscillator (LO) for the receiver.
Fig. 2
Fig. 2 Schematic display of stacking PPM with FSK and PS-QPSK symbols represented in time domain (top row), in constellation space (middle row), and in frequency domain (bottom row). The columns show typical (a) PPM, (b) FSK and (c) PS-QPSK symbols. The PS-QPSK symbols are depicted as a subset of the PM-QPSK symbols. The right-most column (d) displays the PPM-FSK-PS-QPSK stack. Each PPM pulse comprises optical sine and cosine-shaped optical fields that contain the information on the frequencies, phases and polarization.
Fig. 3
Fig. 3 Calculated bit error ratios (BER) for different modulation/multiplexing stacks. (a) BER as a function of the number of photons per bit (b) BER as a function of the number of photons per symbol.
Fig. 4
Fig. 4 Measured 64PPM-4FSK-PS-QPSK receiver signal. (a) In-phase (blue) and quadrature (red) components of a baseband signal as a function of time. The plots show the x-polarization components of 4 random symbols with symbol duration T sym . (b) Zoom into the non-zero slot of the 4th symbol. (c) Optical spectrum. Four peaks at ±750 MHz and ±1.5 GHz are to be seen. The carrier fc in the center of the spectrum is (not perfectly) suppressed.
Fig. 5
Fig. 5 Bit error ratio (BER) as a function of the number of photons per bit for different modulation formats. PSQ abbreviates the format PS-QPSK. (a) Individual modulation formats 4FSK, PS-PQSK, and 64PPM with sensitivities per bit of 9 dB, 7 dB, and 5 dB, respectively, at a target BER= 10 3 . (b) Stacked modulation formats 4FSK-PS-QPSK, 64PPM-4FSK-PS-QPSK, and 64PPM-2OFDM-PS-QPSK. The limiting number of photons per bit reduces when stacking more modulation formats. The stacked format 64PPM-4FSK-PS-QPSK shows a limiting photon number per bit of 3.7 dB, slightly better than 64PPM-2OFDM-PSQ. Theoretically calculated BER for various modulation format stacks comprising 64PPM, 4FSK, PS-QPSK and including 2OFDM are shown for comparison.
Fig. 6
Fig. 6 Comparison of the results derived from the power meter (PM) and the optical spectrum analyzer (OSA) for 64PPM-4FSK-PS-QPSK.

Equations (21)

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BER total (FSK) = SER PPM ( M 2( M1 ) log 2 ( M )+ 1 2 log 2 ( N )+ 1 2 ×3 ) log 2 ( M )+ log 2 ( N )+3 +( 1 SER PPM ) SER FSK ( N 2( N1 ) log 2 ( N )+ 1 2 ×3 ) log 2 ( M )+ log 2 ( N )+3 +( 1 SER PPM )( 1 SER FSK ) BER PSQ ×3 log 2 ( M )+ log 2 ( N )+3 .
BER total (OFDM) = SER PPM ( M 2( M1 ) log 2 ( M )+ 1 2 ×2×3 ) log 2 ( M )+2×3 +( 1 SER PPM ) BER PSQ ×2×3 log 2 ( M )+2×3
N Pbit = P Sig h f c R bit = P Sig h f c R sym n bits/sym
SNR bit  =  2 B O R sym n bits/sym OSNR
ρ(t)=s(t)+n(t),s=( s x s y )=( I x +j Q x I y +j Q y ),n=( n x n y )=( n I,x +j n Q,x n I,y +j n Q,y )
r FSK =| r x |+| r y |, r x,y = s x,y + n x,y = I x,y + n I,x,y +j( Q x,y + n Q,x,y ).
| s x |=| s y | A FSK ,where  A FSK 2 { 0, slot / T slot }.
p r ( r,A )={ r σ 2 e r 2 + A 2 2 σ 2 I 0 ( Ar σ 2 ) for r>0 0 for r0.
p FSK ( r FSK , A FSK )= p r ( | r x |, A FSK )* p r ( | r y |, A FSK )=( p r * p r )( r FSK , A FSK )
s α =[ s xα s yα ]=[ I xα +j Q xα I yα +j Q yα ] , s β =[ s xβ s yβ ]=[ I xβ +j Q xβ I yβ +j Q yβ ]
r OFDM = r FSKα + r FSKβ =| r xα |+| r yα |+| r xβ |+| r yβ | =| I xα + n I,xα +j( Q xα + n Q,xα ) |+| I yα + n I,yα +j( Q yα + n Q,yα ) | +| I xβ + n I,xβ +j( Q xβ + n Q,xβ ) |+| I yβ + n I,yβ +j( Q yβ + n Q,yβ ) |
| s xα |=| s xβ |=| s yα |=| s yβ | A OFDM  and2 A OFDM 2 { 0, slot / T slot }
p OFDM ( r OFDM , A OFDM )= p FSK ( r FSKα , A OFDM ) p FSK ( r FSKβ , A OFDM ) =( p FSK p FSK )( r OFDM , A OFDM )
SER PPM =1 P c
P c = [ r 1 p 0 ( r 0 )d r 0 ] M1 p 1 ( r 1 )d r 1 = [ 1 r 1 p 0 ( r 0 ) d r 0 ] M1 p 1 ( r 1 )d r 1
BER PPM = 2 k1 2 k 1 SER PPM = M 2 1 M1 SER PPM
SNR x = 1 2 A FSK 2 σ x 2 = 1 2 s N ASE = 1 2 G N Psym h f c n sp ( G1 )h f c 1 2 N Psym , N Pbit = N Psym n bit/sym
s n ( t )=Acos( 2πn×Δft )+jAsin( 2πn×Δft )=Aexp( j2πn×Δft )
ρ ( f )= + [ s(t)+n(t) ] e j2πft dt , r x ( f )= + [ I x (t)+ n I,x (t)+j( Q x (t)+ n Q,x (t) ) ] e j2πft dt , r y ( f )= + [ I y (t)+ n I,y (t)+j( Q y (t)+ n Q,y (t) ) ] e j2πft dt .
r F ( f n )=| r x ( f n ) |+| r y ( f n ) |, r x,y ( f n )= f n 1 2 Δf f n + 1 2 Δf r x,y ( f )df
BER PSQ = 1 2 π + ( 33erfc(r)+ erfc 2 (r) )erfc( r )exp[ ( r s N 0 ) 2 ]dr

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