Abstract

This paper analyzes the capacity of the free space coherent optical MIMO transmission system. Two scenarios are considered (i.e., with and without the adaptive optics compensation). It is generally accepted that the adaptive optics compensation can significantly improve the system performance, which is rigorously true when the MIMO algorithm is not implemented. However, it might not be the case in the coherent MIMO systems. When the turbulence strength is weak or moderate, this work demonstrates that the phase-only wave-front corrector will increase the mean eigen value of the coherent system capacity matrix HHH and make the eigen value distribution more even, i.e. it will decrease the maximal eigen value while increasing the average eigen value. Hence, the capacity of the system with adaptive optics increases when the channel information is not available, because the sub-channels are placed with equal powers. When the channel information is perfectly available and the water filling algorithm is used to optimize the power allocation, the system with adaptive optics could have a deteriorated performance as the capacity is more related to the large eigen values especially in the low signal to noise ratio (SNR) regime. When the turbulence strength is strong, it is found that adaptive optics will decrease both the mean and maximal eigen values for the capacity matrix HHH, and therefore the system capacity degrades, whether the channel information is available or not.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2016 (2)

J.-Y. Wang, J. Dai, R. Guan, L. Jia, Y. Wang, and M. Chen, “Channel capacity and receiver deployment optimization for multi-input multi-output visible light communications,” Opt. Express 24(12), 13060–13074 (2016).
[Crossref] [PubMed]

J. Zhou, J. Zong, and D. Liu, “The Higher Order Statistics of OAM Modal Amplitudes Under Atmosphere Turbulence,” IEEE Photonics Technol. Lett. 28(23), 2653–2656 (2016).
[Crossref]

2015 (3)

2014 (5)

2013 (1)

2012 (2)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

S. Moser, “Capacity results of an optical intensity channel with input-dependent Gaussian noise,” IEEE Trans. Inf. Theory 58(1), 207–223 (2012).
[Crossref]

2009 (1)

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55(10), 4449–4461 (2009).
[Crossref]

2008 (2)

2007 (1)

2000 (1)

Ahmed, N.

Anguita, J. A.

Bao, C.

Belmonte, A.

Bock, R.

Boyd, R. W.

Chandrasekaran, N.

Chen, M.

Cheng, M.

Cvijetic, M.

Dai, J.

Dan, W.

Dolinar, S.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Fazal, I. M.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Gao, J.

Guan, R.

Hu, Q.

Hu, Q.-S.

Hu, Z.

Huang, H.

Jia, L.

Kahn, J. M.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity Limits of Spatially Multiplexed Free-Space Communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Lapidoth, A.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55(10), 4449–4461 (2009).
[Crossref]

Lavery, M. P. J.

Li, G.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity Limits of Spatially Multiplexed Free-Space Communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Li, L.

Li, M.

Li, X.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity Limits of Spatially Multiplexed Free-Space Communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

K. Zhu, G. Zhou, X. Li, X. Zheng, and H. Tang, “Propagation of Bessel-Gaussian beams with optical vortices in turbulent atmosphere,” Opt. Express 16(26), 21315–21320 (2008).
[Crossref] [PubMed]

Liu, D.

J. Zhou, J. Zong, and D. Liu, “The Higher Order Statistics of OAM Modal Amplitudes Under Atmosphere Turbulence,” IEEE Photonics Technol. Lett. 28(23), 2653–2656 (2016).
[Crossref]

J. Zhou, J. Zong, and D. Liu, “Coupled mode theory for orbital angular momentum modes transmission in the presence of atmosphere turbulence,” Opt. Express 23(25), 31964–31976 (2015).
[Crossref] [PubMed]

Moser, S.

S. Moser, “Capacity results of an optical intensity channel with input-dependent Gaussian noise,” IEEE Trans. Inf. Theory 58(1), 207–223 (2012).
[Crossref]

Moser, S. M.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55(10), 4449–4461 (2009).
[Crossref]

Neifeld, M. A.

Ren, Y.

Shapiro, J. H.

Takashima, Y.

Tang, H.

Tur, M.

Vasic, B. V.

Wang, J.

J.-B. Wang, Q.-S. Hu, J. Wang, M. Chen, and J.-Y. Wang, “Tight bounds on channel capacity for dimmable visible light communications,” J. Lightwave Technol. 31(23), 3771–3779 (2013).
[Crossref]

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Wang, J.-B.

Wang, J.-Y.

Wang, L.

Wang, Y.

Wigger, M. A.

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55(10), 4449–4461 (2009).
[Crossref]

Willner, A. E.

Wu, J.

Xie, G.

Yan, Y.

Yang, J.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yu, Z.

Yue, Y.

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zhang, Y.

Zhao, F.

Zhao, N.

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity Limits of Spatially Multiplexed Free-Space Communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Zheng, X.

Zhou, G.

Zhou, J.

Zhu, K.

Zhu, Y.

Zong, J.

Appl. Opt. (3)

IEEE Photonics Technol. Lett. (1)

J. Zhou, J. Zong, and D. Liu, “The Higher Order Statistics of OAM Modal Amplitudes Under Atmosphere Turbulence,” IEEE Photonics Technol. Lett. 28(23), 2653–2656 (2016).
[Crossref]

IEEE Trans. Inf. Theory (2)

A. Lapidoth, S. M. Moser, and M. A. Wigger, “On the capacity of free-space optical intensity channels,” IEEE Trans. Inf. Theory 55(10), 4449–4461 (2009).
[Crossref]

S. Moser, “Capacity results of an optical intensity channel with input-dependent Gaussian noise,” IEEE Trans. Inf. Theory 58(1), 207–223 (2012).
[Crossref]

J. Lightwave Technol. (4)

Nat. Photonics (2)

J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

N. Zhao, X. Li, G. Li, and J. M. Kahn, “Capacity Limits of Spatially Multiplexed Free-Space Communication,” Nat. Photonics 9(12), 822–826 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Optica (1)

Other (1)

D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press (2005).

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Figures (7)

Fig. 1
Fig. 1 The schematic to evaluate the capacity during the simulation
Fig. 2
Fig. 2 The capacity of the 76 modes transmission system (Cn2 = 10−14 m-2/3) (a) Without the channel information and equal power is assumed for each sub-channel (b) With the channel information and the watering filling algorithm is implemented to optimize the power allocation.
Fig. 3
Fig. 3 The eigen value distribution of the capacity matrix HHH (Cn2 = 10−14 m-2/3).
Fig. 4
Fig. 4 The capacity of the 76 modes transmission system (Cn2 = 5 × 10−15 m-2/3) (a) Without the channel information and equal power is assumed for each sub-channel (b) With the channel information and the watering filling algorithm is implemented to optimize the power allocation.
Fig. 5
Fig. 5 The eigen value distribution of the capacity matrix HHH (Cn2 = 5 × 10−15 m-2/3).
Fig. 6
Fig. 6 The capacity of the 76 modes transmission system (Cn2 = 10−13 m-2/3) (a) Without the channel information and equal power is assumed for each sub-channel (b) With the channel information and the watering filling algorithm is implemented to optimize the power allocation.
Fig. 7
Fig. 7 The eigen value distribution of the capacity matrix HHH (Cn2 = 10−13 m-2/3).

Equations (15)

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K( k x , k y , k z )=FT( R( x,y,z ) )= ( 2π ) 3 0.033 C n 2 ( k 2 + 1 L 0 2 ) 11/6 f( k, k l ) f( k, k l )=exp( k 2 k l 2 )( 1+1.802( k k l )0.254 ( k k l ) 7 6 ) k 2 = k x 2 + k y 2 + k z 2 k l =3.3/ l 0
r=Hx+n
C= q=1 Q log 2 ( 1+ λ q P q σ 2 )
P q = P tot Q
P q = ( μ σ 2 λ q ) + P tot = q P q ( x ) + ={ 0( x<0 ) x( x>0 )
| H ii ad | 2 > | H ii non | 2
i=1 Q λ i =Tr( H H H )= i=1 Q j=1 Q | H ij | 2
j=1 | H ij ad | 2 = j=1 | H ij non | 2 =1
j=1 Q | H ij ad | 2 j=1 Q | H ij non | 2 1
j=1 Q | H ij ad | 2 > j=1 Q | H ij non | 2
i=1 Q j=1 Q | H ij ad | 2 > i=1 Q j=1 Q | H ij non | 2 i=1 Q λ i ad Q > i=1 Q λ i non Q
u m p ( r,ϕ,z )= 2p! π( p+| m | )! 1 w( z ) ( r 2 w( z ) ) | m | exp( r 2 w 2 ( z ) ) L p | m | ( 2 r 2 w 2 ( z ) ) exp( j k 0 r 2 z 2( z 2 + z R 2 ) )exp( j( 2p+| m |+1 ) tan 1 ( z z R ) )exp( jmϕ )
w( z )= w 0 1+ ( z/ z R ) 2 z R = π w 0 2 λ 0
2 φ+ k 0 2 ( 1+2Δn )φ=0
R( xx',yy',zz' )= Δn( x,y,z )Δn( x',y',z' )

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