Abstract

We introduce broadcast MIMO communication systems over multimode optical fibers or waveguides. Based on BeamForming (BF) at the transmitter, decoupled virtual subchannels are provided to multiple uncoordinated conventional direct detection receivers. This optical technique, extending Zero-Forcing BF wireless MIMO techniques to quadratic detection, is applicable to photonic interconnects, e.g. short-reach point-to-(multi)point transmission over MMF, up to rates of 100 Gb/s for distances up to 100 m.

© 2007 Optical Society of America

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References

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  1. H.R. Stuart, "Dispersive Multiplexing in Multimode Optical Fiber," Science 289, 281-283 (2000).
    [CrossRef] [PubMed]
  2. D. Lenz, B. Rankov, D. Erni, W. Bachtold, A. Wittneben, "MIMO Channel for Modal Multiplexing in Highly Overmoded Optical Waveguides," Int. Zurich Seminar on Communications 196-199 (2004).
  3. <other>. C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, "Mode group diversity multiplexing transceiver design for graded-index multimode fibres," in ECOC '05 Paper We4.P.113 2005.</other>
  4. Y. Yadin, M. Orenstein, "Parallel optical interconnects over multimode waveguide," J.Lightwave Technol. 24,380-386 (2006).
    [CrossRef]
  5. M. Greenberg, M. Nazarathy, and M. Orenstein, "Data Parallelization by Optical MIMO Transmission over Multi-Mode Fiber with Inter-Modal Coupling," in LEOS '06 Montreal Canada Paper WX 5, (2006).
  6. K. Balemarthy and S. E. Ralph, "MIMO Processing of Multi-mode Fiber Links," in LEOS '06 paper WX4 (2006).
  7. R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
    [CrossRef]
  8. Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
    [CrossRef]
  9. Y. Taesang and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, " IEEE J. Sel. Areas Commun. 24, 528-541 (2006).Q3
    [CrossRef]
  10. J. Kahn, "Compensating Multimode Fiber Dispersion Using Adaptive Optics, " in OFC '07 Anaheim, Paper OTuL1 (2007).
  11. Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.
  12. P. Pepeljukovski et al, "Data Center and High Performance Computing Interconnects for 100 Gb/s and Beyond," in OFC '07 paper OMR4, (2007).
  13. B. Noble and J.W. Daniel, Applied Linear Algebra (Prentice-Hall, 1988).

2006 (4)

Y. Yadin, M. Orenstein, "Parallel optical interconnects over multimode waveguide," J.Lightwave Technol. 24,380-386 (2006).
[CrossRef]

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Y. Taesang and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, " IEEE J. Sel. Areas Commun. 24, 528-541 (2006).Q3
[CrossRef]

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

2004 (1)

Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
[CrossRef]

2000 (1)

H.R. Stuart, "Dispersive Multiplexing in Multimode Optical Fiber," Science 289, 281-283 (2000).
[CrossRef] [PubMed]

Goldsmith, A.

Y. Taesang and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, " IEEE J. Sel. Areas Commun. 24, 528-541 (2006).Q3
[CrossRef]

Haardt, M.

Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
[CrossRef]

Hsu, R. C. J.

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Jalali, B.

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Lipson, M.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Manipatruni, S.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Orenstein, M.

Y. Yadin, M. Orenstein, "Parallel optical interconnects over multimode waveguide," J.Lightwave Technol. 24,380-386 (2006).
[CrossRef]

Sayed, A. H.

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Schmidt, B.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Shah, A.

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Shakya, J.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Spencer, Q. H.

Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
[CrossRef]

Stuart, H.R.

H.R. Stuart, "Dispersive Multiplexing in Multimode Optical Fiber," Science 289, 281-283 (2000).
[CrossRef] [PubMed]

Swindlehurst, A. L.

Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
[CrossRef]

Taesang, Y.

Y. Taesang and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, " IEEE J. Sel. Areas Commun. 24, 528-541 (2006).Q3
[CrossRef]

Tarighat, A.

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

Xu, Q.

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Yadin, Y.

Y. Yadin, M. Orenstein, "Parallel optical interconnects over multimode waveguide," J.Lightwave Technol. 24,380-386 (2006).
[CrossRef]

IEEE Comm. Lett. (1)

R. C. J. Hsu, A. Tarighat, A. Shah, A. H. Sayed, and B. Jalali, "Capacity enhancement in coherent optical MIMO (COMIMO) multimode fiber links," IEEE Comm. Lett. 10, 195-197 (2006).Q1
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

Y. Taesang and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming, " IEEE J. Sel. Areas Commun. 24, 528-541 (2006).Q3
[CrossRef]

IEEE Trans. Sig. Proc. (1)

Q. H. Spencer, A. L. Swindlehurst, M. Haardt, "Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels, "IEEE Trans. Sig. Proc. 52, 461-471 (2004).Q2
[CrossRef]

J.Lightwave Technol. (1)

Y. Yadin, M. Orenstein, "Parallel optical interconnects over multimode waveguide," J.Lightwave Technol. 24,380-386 (2006).
[CrossRef]

Opt.Express (1)

Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, "12.5 Gbit/s carrier-injection-based silicon micro-ring silicon modulator, " Opt.Express 14, 9430-9435 (2006). http://www.opticsexpress.org/abstract.cfm?id=125469.

Science (1)

H.R. Stuart, "Dispersive Multiplexing in Multimode Optical Fiber," Science 289, 281-283 (2000).
[CrossRef] [PubMed]

Other (7)

D. Lenz, B. Rankov, D. Erni, W. Bachtold, A. Wittneben, "MIMO Channel for Modal Multiplexing in Highly Overmoded Optical Waveguides," Int. Zurich Seminar on Communications 196-199 (2004).

<other>. C. P. Tsekrekos, A. Martinez, F. M. Huijskens, and A. M. J. Koonen, "Mode group diversity multiplexing transceiver design for graded-index multimode fibres," in ECOC '05 Paper We4.P.113 2005.</other>

M. Greenberg, M. Nazarathy, and M. Orenstein, "Data Parallelization by Optical MIMO Transmission over Multi-Mode Fiber with Inter-Modal Coupling," in LEOS '06 Montreal Canada Paper WX 5, (2006).

K. Balemarthy and S. E. Ralph, "MIMO Processing of Multi-mode Fiber Links," in LEOS '06 paper WX4 (2006).

J. Kahn, "Compensating Multimode Fiber Dispersion Using Adaptive Optics, " in OFC '07 Anaheim, Paper OTuL1 (2007).

P. Pepeljukovski et al, "Data Center and High Performance Computing Interconnects for 100 Gb/s and Beyond," in OFC '07 paper OMR4, (2007).

B. Noble and J.W. Daniel, Applied Linear Algebra (Prentice-Hall, 1988).

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Figures (3)

Fig. 1.
Fig. 1.

(Color online) ZFBF concept: Each PM (r) , r = 1,2,…,nU is focusing light onto the r-th detector.

Fig. 2.
Fig. 2.

Massively parallel transmission of 112 Gb/s over a single MMF Point-to-Multipoint ZFBF MIMO broadcast system. At the input, 32 × 3.5 Gb/s data streams are mapped into 64 optical input ports by means of the proposed ZFBF MIMO precoder. 32 active photodetectors (out of 64) are spread along the output facets of various branches. The r-th photodiode receives its own 3.5 Gb/s data stream from the r-th input, with no cross-talk from the other tributaries. The 32 uncoordinated, decoupled, conventional OOK receivers then detect an aggregate >100 Gb/s. A point-to-point >100 Gb/s link may be similarly constructed, with all 32 detectors co-located at the fiber output facet. All E-O modulators of the Multi-Port E-O Modulator or SLM are fed from a single laser.

Fig. 3.
Fig. 3.

(Color online) Performance of the ZFBF MIMO system described in Fig. 2. (a,b):BER vs. optical SNR per bit (10 log γU ) for MIMO, MISO, SISO over MMF with η =10 dB loss, for the ZMSW and Ortho. Ch. (a): ZFBF MISO outperforms SISO by ~6 dB, both providing 1 b/sym (b): ZFBF MIMO: nU = 2, 4, 8,16, 32 . The curves for nU = 4, 8 almost coincide. Doubling the number of bits per symbol to 16, and then to 32 requires modest power increases in two steps of ~1 dB. (c): Spectral efficiency vs. SNR performance comparison of the novel ZFBF MIMO/MISO vs. multi-level SISO, for a fixed BER of 10-4.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

I r d = m = 1 D 0 E ̃ m d ( r ) 2 = E ̃ d ( r ) 2 = H ( r ) E ̃ s 2 = E ̃ s H ( r ) H ( r ) E ̃ s = E ̃ s G ( r ) E ̃ s
ρ r { E ̃ s } I r d ( E ̃ s ) E ̃ s 2 = E ̃ s G ( r ) E ̃ s E ̃ s | E ̃ s
I r d ( A ̃ ( r ) ) = A ̃ ( r ) G ̃ ( r ) A ̃ ( r ) = δ r r ; r , r { 1,2 , n U } , n U n R
E ̃ S = ( E 0 n U ) As = ( E 0 n U ) r = 1 n U A ̃ ( r ) S r
I r d ( E ̃ s ) = ( E 0 2 n U ) I r d ( A ̃ ( r ) ) S r 2 = ( E 0 2 n U ) S r 2
P T E ̃ s 2 = E 0 2 r = 1 n U A ̃ ( r ) 2 n U = E 0 2 ρ eff 1 ; ρ eff n U ( r = 1 n U ρ r 1 ) 1 = ρ r H
γ r = ( E 0 2 n U ) S r 2 σ I = P T ρ eff ( n u σ I ) = γ U ρ eff
H ¯ ( r ) A ̃ ( r ) = 0
ρ r I r d ( A ̃ ( r ) ) A ̃ ( r ) 2 = 1 A ̃ ( r ) 2 = a ̃ ( r ) g ( r ) a ̃ ( r ) a ̃ ( r ) | a ̃ ( r )
BER = Q [ γ U ρ eff ]

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