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Ultimate Limits on Photon and Spectral Efficient Communication through Atmospheric Turbulence

Jeffrey H. Shapiro, Nivedita Chandrasekaran, Ligong Wang

Published Oct 1, 2013• 0 citations
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Abstract

Abstract: Bounds on the ergodic classical and private capacities for optical communication through turbulence are presented, showing that high photon and spectral efficiencies can be achieved simultaneously in the near-field power transfer regime. © 2013 Optical Society of America OCIS codes: (060.2605) Free-space optical communication; (010.1330) Atmospheric turbulence.

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Abstract: Bounds on the ergodic classical and private capacities for optical communication through turbulence are presented, showing that high photon and spectral efficiencies can be achieved simultaneously in the near-field power transfer regime. © 2013 Optical Society of America OCIS codes: (060.2605) Free-space optical communication; (010.1330) Atmospheric turbulence.
Vacuum-propagation optical communication with high photon efficiency (many bits/photon) and high spectral efficiency (many bits/s ·Hz) requires operation in the near-field power transfer regime with a large number of spatial modes. For terrestrial propagation paths, however, the effects of atmospheric turbulence must be factored into the photon and spectral efficiency assessments. In Part I of this study [N. Chandrasekaran and J. H. Shapiro, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part I: Channel Model and Propagation Statistics,” J. Lightw. Technol., vol. 32, no. 6, pp. 1075-1087, Mar. 2014], modal-transmissivity statistics were derived for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function, and these bounds were evaluated for ~ 200 spatial-mode systems whose transmitters used either focused-beam (FB), Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either did or did not employ adaptive optics. This Part II paper derives upper and lower bounds for the ergodic Holevo capacities of classical and private information transmission over the multiple spatial-mode turbulent channel that can be evaluated from Part I's transmissivity statistics. Also included are bounds on the ergodic capacity for on-off keying encoding and direct detection. It is shown that: 1) adaptive optics are not necessary to realize high photon information efficiency and high spectral efficiency simultaneously; 2) an FB-mode system with perfect adaptive optics outperforms its HG-mode and LG-mode counterparts; and 3) the converse is true when adaptive optics are not employed.
Optical communication with high photon-efficiency (many bits/photon) and high spectral efficiency (SE) (many bits/s-Hz) cannot be achieved unless multiple spatial modes are employed. For vacuum propagation, it is known that achieving 10 bits/photon and 5 bits/s-Hz requires 189 low-loss spatial modes at the ultimate Holevo limit and 4500 such modes at the Shannon limit for on-off keying with direct detection. For terrestrial propagation paths, however, atmospheric turbulence corrupts multiple spatial-mode operation. This paper derives power-transmissivity bounds and average intermodal crosstalks for the turbulent channel that depend solely on the mutual coherence function of the atmospheric Green's function. These statistics are then evaluated for ~ 200 spatial-mode systems whose transmitters use either focused-beam, Hermite-Gaussian (HG), or Laguerre-Gaussian (LG) modes and whose receivers either do or do not employ adaptive optics. It is shown that: (1) adaptive optics are not necessary for achieving both high photon information efficiency (PIE) and high SE; (2) systems employing HG or LG modes achieve the same capacities through turbulence; and (3) the orbital angular momentum carried by LG modes does not provide turbulence immunity. In the companion paper [N. Chandrasekaran, J. H. Shapiro, and L. Wang, “Photon Information Efficient Communication Through Atmospheric Turbulence-Part II: Bounds on Ergodic Classical and Private Capacities,” J. Lightw. Technol., vol. 32, no. 6, pp. 1088-1097, Mar. 2014], the transmissivity bounds are used to quantify the turbulence-induced loss in PIE versus SE performance for these mode sets.
Free-space optical communication systems potentially gain many dBs over RF systems. There is no upper limit on the theoretically achievable photon efficiency when the system is quantum-noise-limited: a) Intensity modulations plus photon counting can achieve arbitrarily high photon efficiency, but with sub-optimal spectral efficiency. b) Quantum-ideal number states can achieve the ultimate capacity in the limit of perfect transmissivity. Appropriate error correction codes are needed to communicate reliably near the capacity limits. Poisson-modeled noises, detector losses, and atmospheric effects must all be accounted for: a) Theoretical models are used to analyze performance degradations. b) Mitigation strategies derived from this analysis are applied to minimize these degradations.
The capacity of the bosonic channel with additive Gaussian noise is unknown, but there is a known lower bound that is conjectured to be the capacity. We have quantified the gap that exists between this known achievable rate and rates achievable by the known methods of detection including direct, heterodyne, and homodyne detection. We have also quantified these capacities in the case of multiple independent spatial modes in terms of spectral and photon efficiency. Furthermore, we have considered the ergodic and outage capacities of fad-ing channel models for far-field and near-field propagation through atmospheric turbulence. For the far field, good models for the transmissivity statistics are known. For the near field we establish bounds on these capacities, and we show that these bounds are reasonably tight. Finally, we extend the results for ergodic capacity to the case of multiple spatial modes where a turbulent atmosphere results in crosstalk between different spatial modes.
Free-Space Optical (FSO) communication technology can cater to various types of connectivity requirements within optical networks, including core, edge, and access networks. However, the performance of FSO communication links can be adversely affected by severe atmospheric conditions, such as turbulence and weather-related factors. In this study, we have investigated the benefits of photon entangled 16-QAM- FSO link in improving the performance of FSO communication under diverse weather and atmospheric turbulence conditions. The efficient implementation of a practical secure quantum communication network may revolutionize the terrestrial and non-terrestrial communication both form speed and security point of view.