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On the estimation and detection for optical turbulent channels.

Robert O. Harger, K. Kurimoto

Published Jan 1, 1972• 0 citations
OpenAlex

Abstract

Consideration of the problem of filtering and detecting signals received through a turbulent channel at optical frequencies. Adopting the semiclassical method of quantum mechanics, application is made to the direct detection of a single-path optical communication channel where the received field is assumed to be the coherent signal field degraded by the atmospheric turbulence with a signal-independent, additive, zero-mean Gaussian background radiation.

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•Jan 1, 2011•1 citation
Consideration of the problem of filtering and detecting signals received through a turbulent channel at optical frequencies. Adopting the semiclassical method of quantum mechanics, application is made to the direct detection of a single-path optical communication channel where the received field is assumed to be the coherent signal field degraded by the atmospheric turbulence with a signal-independent, additive, zero-mean Gaussian background radiation.
In this letter, we analyze the average probability of error of quantum modulation schemes in weakly turbulent quantum communication channels utilizing coherent states. Atmospheric turbulence-induced fading is a significant challenge that degrades the performance of free-space quantum communication systems. We derive and present closed-form expressions for the average probability of error for various detection methods: classical (shot-noise limited) single-photon detection, coherent detection, and the optimal quantum hypothesis-testing (Helstrom) detection for binary quantum modulation schemes. Our analysis focuses on the transmission of classical data modulated by quantum coherent states over a log-normal turbulent channel. Additionally, we discuss the lower bounds of the average capacities for Helstrom detection, providing comprehensive insights into the achievable information rates in realistic atmospheric conditions. The derived expressions show excellent agreement with numerical Monte Carlo simulations across a broad range of average transmitted photon numbers, offering valuable guidelines for the design and optimization of quantum communication systems.
Quantum light propagation through turbulent atmosphere has become a subject of intensive research, spanning both theoretical and experimental studies. This interest is driven by its important applications in free-space quantum communication, remote quantum sensing, and environmental monitoring. At the same time, this phenomenon itself poses an intriguing fundamental problem. A consistent theoretical description typically makes explicit assumptions about the measurement scheme at the receiver station and/or the method of quantum-information encoding. A common and straightforward approach encodes the information in quantum states of a quasi-monochromatic mode, representing a pulsed Gaussian beam. Atmospheric turbulence induces random distortions of the pulse shape and, consequently, random fluctuations of the transmittance through the receiver aperture. These fluctuations, characterized by the probability distribution of transmittance (PDT), directly affect the quantum state of the received light. In this paper we examine various analytical models of the PDT, validate them through numerical simulations, and assess their range of applicability. Furthermore, we extend the analysis beyond the standard ensemble-averaging approach, recognizing that realistic experiments typically involve time averaging. This requires a detailed examination of the underlying random process, including the study of temporal correlations and their impact on nonclassical properties of electromagnetic radiation.
Communication theory problems incorporating quantum effects for optical-frequency applications are discussed. Under suitable conditions, a unique quantum channel model corresponding to a given classical space-time varying linear random channel is established. A procedure is described by which a proper density-operator representation applicable to any receiver configuration can be constructed directly from the channel output field. Some examples illustrating the application of our methods to the development of optical quantum channel representations are given. Optimizations of communication system performance under different criteria are considered. In particular, certain necessary and sufficient conditions on the optimal detector in M-ary quantum signal detection are derived. Some examples are presented. Parameter estimation and channel capacity are discussed briefly.
Many fundamental and applied experiments in quantum optics require transferring nonclassical states of light through large distances. In this context the free-space channels are a very promising alternative to optical fibers as they are mobile and enable to establish communications with moving objects, using satellites for global quantum links. For such channels the atmospheric turbulence is the main disturbing factor. The statistical properties of the fluctuating transmittance through the turbulent atmosphere are given by the probability distribution of transmittance (PDT). We derive the consistent PDTs for the atmospheric quantum channels by step-by-step inclusion of various atmospheric effects such as beam wandering, beam broadening and deformation of the beam into elliptic form, beam deformations into arbitrary forms. We discuss the applicability of PDT models for different propagation distances and optical turbulence strengths in the case when the receiver module has an annular aperture. We analyze the optimal detection and correction strategies which can improve the channel transmission characteristics. The obtained results are important for the design of optical experiments including postselection and adaptive strategies and for the security analysis of quantum communication protocols in freespace.
In this paper we consider the detection of noisy binary quantum optical coherent states transmitted over a turbulent medium, such as terrestrial links or satellite optical connections across the atmosphere. The propagation effect is accounted for by a random attenuation factor, which is characterized in terms of its statistical distribution. Depending on the knowledge of the propagation coefficient, error performance can vary significantly and different receiver structures show different behaviors and robustness to the channel mismatch. The performance of the quantum optimal receiver and the square root measurement (SRM) are compared, and their sensitivity to the variability of the propagation coefficient is considered. It results that the phase variability of the propagation coefficient plays a fundamental role. The optimal receiver, in the absence of instantaneous channel knowledge, performs worse than the SRM, denoting a greater sensitivity to channel estimation accuracy.
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.