Continuous variable-quantum key distribution (CV-QKD) protocols attract increasing attentions in recent years because they enjoy high secret key rate (SKR) and good compatibility with existing optical communication infrastructure. Classical coherent receivers are widely employed in coherent states based CV-QKD protocols, whose detection performance is bounded by the standard quantum limit (SQL). Recently, quantum receivers based on displacement operators are experimentally demonstrated with detection performance outperforming the SQL in various practical conditions. However, potential applications of quantum receivers in CV-QKD protocols under turbulent channels are still not well explored, while practical CV-QKD protocols must survive from the atmospheric turbulence in satellite-to-ground optical communication links. In this paper, we consider the possibility of using a quantum receiver called multi-stage CD-Kennedy receiver to enhance the SKR performance of a quadrature phase shift keying (QPSK) modulated CV-QKD protocol in turbulent channels. We first derive the error probability of the multi-stage CD-Kennedy receiver for detecting QPSK signals in turbulent channels and further propose three types of multi-stage CD-Kennedy receiver with different displacement choices, i.e., the Type-I, Type-II, and Type-III receivers. Then we derive the SKR of a QPSK modulated CV-QKD protocol using the multi-stage CD-Kennedy receiver and post-selection strategy in turbulent channels. Numerical results show that the multi-stage CD-Kennedy receiver can outperform the classical coherent receiver in turbulent channels in terms of both error probability and SKR performance and the Type-II receiver can tolerate worse channel conditions compared with Type-I and Type-III receivers in terms of error probability performance.

Channel modeling for the satellite-to-underwater laser communication (StULC) link remains challenging due to long distances and the diversity of the channel constituents. The StULC channel is typically segmented into three isolated channels: the atmospheric channel, the air-water interface channel, and the underwater channel. Previous studies involving StULC channel modeling either focused on separated channels or neglected the combined effects of particles and turbulence on laser propagation. In this paper, we established a comprehensive StULC channel model by an analytical-Monte Carlo hybrid approach, taking into account the effects of particles, bubbles, and turbulence. We first obtained the intensity distribution of the transmitted laser beam after passing through the turbulent atmosphere based on the extended Huygens-Fresnel principle. Then we derived a closed-form probability density function of angular fluctuations of the beam refracted by the random sea surface. These analytical results are then mapped to initialize photon states for the Monte Carlo simulation of the underwater channel. Based on the proposed StULC channel model, we analyzed the bit error rate and the outage probability under different environmental conditions and system parameters. Numerical results demonstrated that the influence of underwater particle concentration on the communication performance is more pronounced than that of both the atmospheric turbulence and the underwater turbulence. In addition, enlarging the receiver aperture provides a more effective performance improvement than increasing the receiver field-of-view angle.

Modeling of multiple-scattering channels in atmospheric turbulence is essential for the performance analysis of long-distance non-line-of-sight (NLOS) ultraviolet (UV) communications. Existing works on the turbulent channel modeling for NLOS UV communications either focused on single-scattering cases or estimate the turbulent fluctuation effect in an unreliable way based on Monte-Carlo simulation (MCS) approach. In this paper, we establish a comprehensive turbulent multiple-scattering channel model by using a more efficient Monte-Carlo integration (MCI) approach for NLOS UV communications, where both the scattering, absorption, and turbulence effects are considered. Compared with the MCS approach, the MCI approach is more interpretable for estimating the turbulent fluctuation. To achieve this, we first introduce the scattering, absorption, and turbulence effects for NLOS UV communications in turbulent channels. Then we propose the estimation methods based on MCI approach for estimating both the turbulent fluctuation and the distribution of turbulent fading coefficient. Numerical results demonstrate that the turbulence-induced scattering effect can always be ignored for typical UV communication scenarios. Besides, the turbulent fluctuation will increase as either the communication distance increases or the zenith angle decreases, which is compatible with existing experimental results and also with our experimental results. Moreover, we demonstrate numerically that the distribution of the turbulent fading coefficient for UV multiple-scattering channels under all turbulent conditions can be approximated as log-normal distribution; and we also demonstrate both numerically and experimentally that the turbulent fading can be approximated as a Gaussian distribution under weak turbulence.

Security analysis of continuous variable quantum key distribution (CV-QKD) remains a topic of extensive academic investigation. In this work, we propose a coherent-state CV-QKD protocol integrating a displacement-based quantum receiver and post-selection strategies. We establish a framework of the protocol under both individual and collective attacks, incorporating practical constraints such as noises and device imperfections. To enhance performance of the protocol, the postselection strategy and the transmitted signal power are optimized for different channel attenuation levels. Numerical results offer insights into the strategy of employing displacement receivers in CV-QKD protocols, revealing that larger transmitted signal power is required under low channel attenuation or severe receiver-side imperfections and noises to achieve higher the secret key rate.

Ultraviolet (UV) communication research has prioritized channel modeling for its critical role in system optimization. Current non-line-of-sight (NLoS) UV modeling mainly addresses obstacle-free scenarios and single-obstacle situations: the former manifests constrained applicability at small transceiver elevation angles with obstacle susceptibility, while the latter suffers from high modeling complexity and can only handle one-obstacle scenarios, which pose critical challenges for Internet of Things applications. To overcome these limitations, we propose a single-collision model for short-range NLoS UV channels incorporating both scattering and reflection effects. Initially, the impact of air scattering on the received pulse energy is presented for diverse obstacle situations, where an obstacle-boundary approximation method (OBAM) is developed to reduce the modeling complexity. Besides, the dimensions, coordinates, shapes, orientation angles, and number of obstacles are considered to emulate practical environments. Subsequently, the impact of obstacle reflection on the received pulse energy is investigated for single, double, and multiple obstacle situations. On this basis, we account for certain scenarios where obstacle surfaces comprise multiple sub-regions, each characterized by distinct reflection coefficients attributed to their varying material compositions. Moreover, we verify the proposed model by comparing it with the Monte-Carlo photon-tracing (MCPT) model and the obstacle-free integral model via simulations. These results demonstrate that the path loss curves obtained by the proposed model exhibit close alignment with those simulated by the MCPT model, while its calculation time is less than 10% that of the MCPT model. Additionally, when obstacle reflection is prominent, the assessment error of the proposed OBAM can be ignored in estimating the path loss of NLoS UV channels containing obstacles.

As data transmission demand grows rapidly, terahertz (THz) frequency has been regarded as the most promising candidate in future sixth-generation (6G) communication systems. Facing severe path loss, THz communications have to use massive MIMO technology to promote the directional transmission gain in narrow beams. However, narrow beams and wide bandwidth signal in THz communications together result in the time-frequency-space non-stationary channel. To track this non-stationary channel, we first combine THz massive MIMO communication system with orthogonal time frequency space (OTFS) modulation to get the union sparse channel on delay-Doppler-angle (DDA) domain. Then this non-stationary channel is modeled through our proposed DDA-2D-Markov models (DDA-2D-MM) considering the unique channel characteristics on delay, Doppler and angle dimension respectively. Besides, we design a unique DDA-structured approximate message passing (DDA-STAMP) algorithm to track the dynamic channel with the prior information in consecutive time slots to improve the algorithm convergence speed and accuracy performance. Simulation results show that the proposed DDA-STAMP algorithm enhances both of the time consumption and accuracy performance in THz massive MIMO-OTFS communication channel tracking.

Ultraviolet (UV) communication is a promising technology for civilian and military secure communication systems due to nonline-of-sight transmission, low background noise, and high local security. The full-duplex relay-assisted UV communications can achieve longer communication distances and higher efficiency of time–frequency utilization compared with direct UV communications. However, due to the strong scattering effect, serious interrelay-interference (IRI) is inevitably introduced in multihop full-duplex relay links. To mitigate the impacts of IRI, this article proposes an alternate iterative-Newton method (AINM) to optimize jointly the relay placement and transmit powers of each relay. We further propose a space-division coupled full-duplex relay configuration to reduce the influence of IRI. Numerical results show that the proposed AINM can significantly decrease the bit-error rate (BER); and the proposed space-division scheme can further decrease the BER but sacrifices about half achievable information rate. Besides, we demonstrate that, when the communication links are strong, the distance between adjacent relays should gradually decrease and the transmit power increase from the source node to the destination node. However, when the communication links are weak, each relay should adopt its maximum transmit power to achieve the minimum BER.

Traditional optical positioning techniques employing visible light signals or infrared light signals require line-of-sight links between transmitters and receivers. The wireless positioning techniques using ultraviolet (UV) signals can enjoy both non-line-of-sight (NLOS) positioning ability and immunity to electromagnetic jamming. In this work, we focus on NLOS UV positioning techniques using linearly-arrayed photon-counting receivers. We first derive the geometrical and physical constrains for the NLOS UV positioning using linearly-arrayed receivers. We then derive the analytical relation between location parameters and pointing parameters of unknown transmitter and propose a NLOS UV positioning method with acceptable computational complexity. We further derive the Cramér-Rao bounds for the positioning method when the separate distance between adjacent receivers equals zero. Numerical results demonstrate that the proposed NLOS UV positioning methods using photon-counting receivers can achieve a distance error less than 2 m when the transmitting elevation angle is greater than 30 degrees and the separate distance is greater than 2 m. Besides, we demonstrate that at least three receivers are required to avoid multiple solution problem; and three receivers are enough for achieving an acceptable positioning error for NLOS UV positioning using photon-counting receivers.

Continuous variable quantum key distribution (CV-QKD) protocol has drawn much attention due to its compatibility with existing optical communication systems. In this paper, we propose a quaternary modulated CV-QKD protocol using displacement receivers and adopt the post-selection scheme to overcome the ‘3dB limit’. We first establish the model of displacement receiver for discriminating quaternary modulated coherent signals in a realistic situation. The performance of non-adaptive displacement receiver and multi-stage feedforward receiver are both investigated under different noises and device imperfections. To improve the receiver performance, we numerically optimize the displacement operation and check the quantum advantage of the displacement receivers over the classical homodyne detection. Then we analyze the security of the proposed CV-QKD protocol. The secret key rate is derived for both types of displacement receivers under the collective beam splitting attack. We also optimize the transmitted signal photons for different channel transmission efficiencies under practical system constraints. Numerical results shed light on the practical application of displacement receivers in CV-QKD protocols. This includes evaluating the necessity of optimizing the displacement and incorporating the feedforward structure in a displacement receiver according to different practical system limitations. Moreover, under higher channel transmission efficiency and increased receiver noise level, a larger coherent amplitude is required for transmitting signals to attain the maximum secret key rate.

The strong scattering effects of ultraviolet (UV) signals in the atmosphere enables the non-line-of-sight (NLOS) ability of UV communications, but introduces large time dispersion of the channel impulse response (CIR), which inevitably results in serious inter-symbol interferences (ISIs). Because a larger transmitting rate can introduce a larger ISI, it is meaningful to study the impact of CIR on the ISI and further quantify the achievable information rate (AIR) of NLOS UV communications. In this paper, we analyzed the influence of both coplanar and non-coplanar geometries on the CIR for multiple scattering effects and proposed a modified Gamma function (MGF) to precisely characterize the CIR. Based on the MGF model, we quantified the ISIs and derived the bit-error rate (BER) and the AIR under thermal noise for both on-off keying (OOK) modulation and 2-pulse-position modulation (2-PPM) using photon-counting receivers. The simulation results showed that the proposed MGF model can achieve higher fitting precision of both CIRs and BERs compared with the existing Gamma function model. Besides, we demonstrated that when the thermal noise photons are less than 10, the OOK and 2-PPM can achieve an AIR of 15 Mbit/s and 13 Mbit/s, respectively, under typical system geometries.

Spatial diversity receptions are usually employed to improve the performance of scattering based optical communication (SOC) systems. Existing works on the diversity receptions for SOC systems ignored the detecting properties of the photomultiplier tube (PMT) receivers. In this paper, we focus on single-input multiple-output (SIMO) SOC systems using PMT receivers. We first present the system model of SIMO SOC system considering the link geometries and prove that the traditional maximum-ratio combining is no longer the optimal combining method for PMT receivers. Then we propose the statical combining method and derive its statistical characteristics and the bit-error rate (BER). We further derive some analytical results of the optimal weights for the statical combining in terms of minimizing the BER or maximizing the average signal-to-noise ratio (SNR). Simulation results show that, in non-turbulent channels, the statical combining for maximizing the average SNR can always outperform the equal-gain combining, especially when the difference between signal strengths on different branches is large. Besides, more weights should be allocated to the branches with either larger signal strength or small turbulent variances. Fortunately, in practical SOC systems, the branch with larger signal strength usually enjoys smaller turbulent variance.

Optical positioning techniques have inherent ad-vantages such as high precision, low power consuming and immunity to the electromagnetic interference. However, it is challenging to estimate the non-line-of-sight (NLOS) targets using current optical positioning methods. In this work, we propose an NLOS ultraviolet positioning method based on a simplified single-scattering channel model, which can obtain both the location and the pointing direction of the transmit-ter. Numerical results demonstrated that the proposed NLOS ultraviolet positioning method can achieve a positioning error less than 2 meters and an azimuth error less than 2 degrees by using two photon-counting receivers under typical transceiver geometries within 100 meters. Besides, we found that the positioning performance can be improved by increasing the gap between two receiving elevation angles.

In this paper, the performance of optimally displaced threshold detection (ODTD) for discriminating ternary coherent signals is theoretically investigated. We first establish the receiver model for ternary phase shift keying optical quantum communication system using Kennedy receiver with ODTD in a realistic situation. Then we analytically study the error probability for ODTD and formulate a joint optimization problem to minimize this error probability of detection, which is a challenging mixed-integer programming (MIP) problem due to the discreteness of the detection threshold. We then propose an efficient algorithm to tackle this MIP problem and design the displacement and the threshold on both detection branches. We also discuss the receiving scheme using ODTD in the case of unequal prior probabilities and optimize the signal power distribution between the two branches. Numerical results show that for the discrimination of ternary coherent signals using Kennedy-type receiver, ODTD can mitigate the influence of thermal noise and dark count noise and is robust to imperfect quantum efficiency. Besides, we find that the error probability performance can be improved by optimizing the decoding order of the ternary signals and the reflectance of the beam splitter.

The full-duplex optical communications can be achieved simply by separating the transmitting link and the receiving link in the space. However, it is challenging to achieve the non-line-of-sight (NLOS) full-duplex ultraviolet (UV) communication due to the serious self-interference caused by the strong multiple scattering effects of UV signals. To explore the capacity of NLOS full-duplex UV communications, in this paper, we first quantify the self-interference using an analytical channel impulse response function. Based on the quantified self-interference, we then derive the error rate and the corresponding achievable information rate (AIR) for on- off keying modulation, 4-digital-pulse-interval modulation and 4-pulse-position modulation. We further propose a self-interference cancelling (SIC) method to mitigate the impacts of self-interferences. Simulation results show that the proposed SIC method can significantly improve the error rate and AIR performances. Besides, we find that the NLOS full-duplex UV communication will gradually lose its advantage over the NLOS half-duplex UV communication as either the communication distance or the elevation angle increases. However, using the proposed SIC method, the NLOS full-duplex UV communication can hold its advantage in a wide range of system geometries.

The generalized Kennedy receiver can be used to improve the secret key rate of continuous variable quantum key distribution protocol and thus attracts much attention recently. In this letter, we analytically study the performance of the post-selection based generalized Kennedy receiver in the presence of thermal noise. To improve the performance of the generalized Kennedy receiver, we optimize the displacement operation for different post-selection parameter and different thermal noises. Numerical results show that the thermal noise can greatly degrade the performance of the post-selection based generalized Kennedy receiver. Besides, the resistance of the generalized Kennedy receiver to the thermal noise can be improved by choosing an appropriate post-selection parameter.

Because of the potential applications in quantum information processing tasks, discrimination of binary coherent states using generalized Kennedy receiver with maximum a posteriori probability (MAP) detection has attracted increasing attentions in recent years. In this paper, we analytically study the performance of the generalized Kennedy receiver having optimally displaced threshold detection (ODTD) in a realistic situation with noises and imperfect devices. We first prove that the MAP detection for a generalized Kennedy receiver is equivalent to a threshold detection in this realistic situation. Then we analyze the properties of the optimum threshold and the optimum displacement for ODTD, and propose a heuristic greedy search algorithm to design these parameters. We prove that the ODTD asymptotically approaches the Kennedy receiver with threshold detection when the signal power is large, and we also clarify the connection between the generalized Kennedy receiver with threshold detection and the one-port homodyne detection. Numerical results show that the proposed heuristic greedy search algorithm can obtain a lower and smoother error probability than the existing methods.

A free-space optical communication system using non-mode-selective photonic lantern (PL) based coherent receiver is studied. Based on the simulation of photon distribution, the power distribution at the single-mode fiber end of the PL is quantitatively described as a truncated Gaussian distribution over a simplex. The signal-to-noise ratios (SNRs), bit-error rate (BER), and outage probability of PL based receiver using selection combining (SC), equal-gain combining (EGC), and maximal-ratio combining (MRC) over Gamma-Gamma turbulence channels are analyzed and compared with the single-mode fiber (SMF) receiver and multimode fiber (MMF) receiver. We demonstrate that EGC is the most suitable combining for PL based receiver because the PL power distribution has limited influence on the BER and outage probability when EGC is used and can greatly affect the BER and outage probability when SC is used. Numerical results show that PL based receiver with EGC requires 6 dB less SNR than the SMF receiver and 5.5 dB less SNR than the MMF receiver at BER of 10−6in moderate turbulence.

An optical quantum communication system with receiver diversity is proposed for free-space communication using the optical combining technique and a generalized Kennedy receiver. The quantum channel model of the proposed system is established using the P -representation in the presence of both turbulence and thermal noise. A conditional dynamics based Kennedy receiver with threshold detection is proposed to mitigate the influence of both turbulence and thermal noise. The error probabilities for different types of generalized Kennedy receiver, i.e., the Kennedy receiver, the Type-II receiver, and the conditional dynamics based Kennedy receiver, are analytically studied and the lower bounds for these error probabilities are obtained. Numerical results show that both the Kennedy receiver and the Type-II receiver fail in the presence of either turbulence or thermal noise. The performance of the proposed conditional dynamics based Kennedy receiver with threshold detection can surpass the standard quantum limit given by the homodyne receiver in either weak turbulence or small thermal noise.

Monte-Carlo models are analyzed for multiple scattering channels in optical wireless communications. It is demonstrated that the system impulse response function can be obtained by Monte-Carlo integration model. The convergence performance for the Monte-Carlo integration model is analyzed and improved by introducing different sampling methods. The simulation results show that the gamma function model for channel impulse response function can only be applied to the cases where the common volume between the transmitted light beam and the receiving field-of-view is open. Numerical simulation suggests that for a three-order scattering case, the computation efficiency of the Monte-Carlo integration model based on partial importance sampling is about 12 times of the original Monte-Carlo integration model based on uniform sampling, and 5.6 times of the widely used Monte-Carlo simulation model. The numerical results also show that the Monte-Carlo integration model based on partial importance sampling has higher computation efficiency than the Monte-Carlo simulation model in a higher-order scattering communication scenario.