Multiple-input Multiple-output Free-space Optical Research Articles

Harnessing the power of ML for robust SISO and MIMO FSO communication systems in fog weather

This study examines Free Space Optical (FSO) communication’s performance in different fog conditions, focusing on Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) setups. In low fog, SISO handles signal degradation well. MIMO improves link robustness in moderate fog. High fog challenges traditional FSO, leading to ML integration to optimize communication parameters. For weather channel classification, a preprocessing scheme reduces features from 12 to 2 given that the 12 features are Bit Error Rate (BER), Quality Factor (Q-factor) and Received Optical Power (ROP) for different 4 users. A Gaussian Process Classifier (GPC) achieves an accuracy greater than 99%, surpassing SVM, Decision Tree, and Random Forest. GPC’s fit and predict functions execute in 0.15 s, outperforming NuSVM (0.2 s). This study highlights FSO, SISO, MIMO, and Machine Learning (ML) practicality in enhancing communication resilience in adverse weather, especially in fog-prone areas.

Tensor-Train Decomposition-Based Hybrid Beamforming for Millimeter-Wave Massive Multiple-Input Multiple-Output/Free-Space Optics in Unmanned Aerial Vehicles with Reconfigurable Intelligent Surface Networks

Unmanned aerial vehicles (UAVs) can support low-cost, highly mobile communications while making it possible to establish dedicated terrestrial networks. To overcome the pointing error (PE) and beam misalignment of millimeter-wave large-scale multiple-input multiple-output/free-space optics (MIMO/FSO) caused by UAV jitter, a millimeter-wave massive MIMO/FSO hybrid beamforming method based on tensor train decomposition is proposed. This approach is used for reconfigurable intelligent surface (RIS) network-assisted UAV millimeter-wave massive MIMO/FSO to improve system spectral efficiency. Firstly, the high-dimensional channel of RIS-assisted millimeter-wave massive MIMO/FSO in UAV is represented as a low-dimensional channel by tensor training decomposition. Secondly, the two-way gated recursive unit attention neural network model can effectively solve the FSO PE caused by UAV jitter, and the fast fading channel and Doppler frequency shift are estimated by the Fast Cyclic Tensor Power Method (FCTPM) based on tensor training decomposition. Finally, the RIS phase shift matrix is optimized by singular value decomposition. The hybrid beamforming and RIS phase-shift matrices were estimated by using the low-complexity phase extraction alternating minimization method to solve the beam misalignment problem. Simulation results show that by using the proposed method, the spectrum utilization rate is improved by 23.6% compared with other methods.

On the performance of a hybrid frequency–phase-keying-based MIMO hybrid RF/FSO communication link

A hybrid technique in optical wireless communications is an effective solution to counter impairments and to improve link availability. In this work, a hybrid frequency phase keying (FPK) modulation scheme, based on frequency shift keying (FSK) and phase shift keying (PSK), for a hybrid radio frequency (RF)/free space optical (FSO) communication system is proposed. The hybrid FPK modulation scheme combines advantageous features of FSK and PSK and has the possibility to provide improved link performance in adverse channel conditions. A transmit aperture selection (TAS) and maximal ratio combining (MRC) diversity-based multiple-input–multiple-output (MIMO) hybrid RF/FSO system is considered to mitigate adverse fading effects. Analytical closed-form expressions are derived for the average symbol error probability to trace the performance of the TAS-MRC-based MIMO hybrid RF/FSO system with FPK modulation over fading and pointing error conditions. A comparative analysis of average symbol error performance is presented. The results clearly indicate that the proposed FPK modulation scheme with the MIMO hybrid RF/FSO communication system link is advantageous, as it exploits the complementary properties of both RF and FSO channel characteristics and PSK and FSK modulation schemes. In addition, the proposed MIMO hybrid RF/FSO system with FPK modulation offers superior performance, compared with MIMO RF, FSO, or hybrid RF/FSO systems applied with FSK and PSK modulation schemes. An optimum beam waist is derived analytically, and it is further verified with a numerical optimization technique. All results are validated using Monte Carlo simulation.

Probabilistically shaped polar-coded MIMO-FSO communication systems with spatially correlated fading.

In this paper, the probabilistically shaped polar-coded multiple-input multiple-output free-space optical (MIMO-FSO) communication system with or without spatially correlated (SC) fading is investigated to improve transmission performance. The designed shaping-polar encoder can flexibly generate three typical shapes of distribution via shaping bits and be decoded in the conventional method. The achievable information rate (AIR) of MIMO-FSO systems with or without SC fading is evaluated to determine the number of shaping bits for the shaping-polar encoder. The non-pairwise distributions are demonstrated to be more suitable for turbulence channels than other distributions. The results show that the AIR of the shaped 4 × 4 systems even exceeds that of the uniform 4 × 5 systems in the low signal-to-noise ratio regions over strong turbulence channels. In terms of bit error rate performance, more than 15 dB shaping gains can be achieved by the shaped 4 × 4 systems compared to the uniform single-input single-output polar-coded systems. In addition, the shaped 4 × 4 systems outperform the uniform ones ranging from 1 dB to 1.9 dB over different atmospheric turbulence channels with or without SC fading, comparable to the uniform MIMO systems with one more physical receiver.

Novel Approximate Distribution of the Sum of Lognormal-Rician Turbulence Channels With Pointing Errors and Applications in MIMO FSO Links

In this paper, an approximate closed-form probability density function expression for the sum of lognormal-Rician turbulence channels with Rayleigh pointing errors is developed. The results of Kolmogorov-Smirnov goodness-of-fit statistical tests show that the proposed approximation is highly accurate across a wide range of channel conditions. Also, the analysis of approximation error is presented in detail, and it indicates that a more efficient approximation can be achieved for larger coherence parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> and smaller variance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma _{z}^{2}$</tex-math></inline-formula> . To reveal the importance of proposed approximation, the closed-form expressions for the ergodic capacity, outage probability, and bit-error rate are derived in terms of Meijer’s G-function. The performance of multiple-input multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) diversity technique are analyzed in detail under different scenarios, including the number of transmit and receive apertures, turbulence channels, and presence of pointing errors. It is observed that MIMO technology can offer a significant improvement in FSO performance when compared with the single-input single-output (SISO) systems. The ergodic capacity and BER performance at high signal-to-noise ratio are also obtained to provide further insights. Numerical results demonstrate the accuracy of the proposed approach.

Performance analysis of MIMO FSO systems with EGC diversity receiver over lognormal-Rician turbulence

Two approximate closed-form probability density function expressions for the sum of lognormal-Rician random variates (RVs) and the sum of square root of lognormal-Rician RVs are obtained. The proposed expressions are shown to provide high accuracy over a wide range of channel conditions according to Kolmogorov–Smirnov goodness-of-fit statistical tests results. Also, the analysis of the approximation error is presented to indicate that a higher approximation accuracy can be achieved for larger r or smaller variance σz2. To reveal the importance of the proposed approximation, new approximate closed-form expressions of the ergodic capacity, average bit error rate for the intensity-modulation direct-detection (IMDD), and coherent multiple-input multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining diversity technique over lognormal-Rician turbulence channels are developed. It is observed that MIMO technology can offer a significant improvement in system performance and the performance of coherent FSO systems outperforms that of IMDD systems. The Monte Carlo simulation results are further utilized to illustrate the accuracy of the proposed approach.

Design of high throughput 2.7 Tbps DWDM System under MIMO-FSO Channel as Back-up Optical Link for 5G Networks

The present article aims to investigate and evaluate the performances of DWDM (or Dense Wavelength Division Multiplexed) system under MIMO-FSO (or multiple input multiple output-free space optical) channel. However, the proposed system is configured and simulated in the worst-case meteorological conditions, and we base here on the variation of the attenuation coefficient. In this article, the proposed system is devoted to 90 users, every user exploits 30 Gbps. So, the total capacity of system is 90x30 Gbps. In addition, the use of MIMO technique in FSO channel ensures us the stability of the proposed system in the worst-case meteorological conditions and especially when the system exploits a high throughput. To assess the acceptable performance levels of the proposed system, it is necessary to use the following criteria: the minimum bit error rate (or BER) performance, the maximum quality factor (or Q-Factor) and the optical signal to noise ratio (or OSNR) performance. Finally, the proposed system in this paper provides a promising solution for 5G networks as back-up optical link.

Composite Fading Model for Aerial MIMO FSO Links in the Presence of Atmospheric Turbulence and Pointing Errors

In this letter, we introduce accurate approximation expressions for composite fading channel model and outage probability of multiple-input multiple-output (MIMO) free space optical (FSO) link between two unmanned aerial vehicles (UAVs) in hovering state. In our derivations, we consider the effects of weather attenuation, random fluctuations in UAVs' positions and orientations, and atmospheric turbulence. Our proposed model is unified with respect to turbulence effect, which means it is valid for different atmospheric turbulence models. We show the accuracy of the proposed model through comparisons with Monte Carlo simulations under different channel conditions.

Novel approximate distribution of the sum of Gamma–Gamma variates with pointing errors and applications in MIMO FSO links

In this work, a novel approximate closed-form probability density function for the sum of Gamma–Gamma random variates with Rayleigh pointing errors is derived by means of the well-known Jensen’s inequality. We employ the Kolmogorov–Smirnov goodness-of-fit statistical tests to verify the accuracy of the proposed approximation. The test results demonstrate that an exact distribution can be efficiently approximated by this derived approximate expression over a wide range of channel conditions. Also, the analysis of the approximation error is presented to indicate that a higher approximation accuracy can be achieved for small pointing errors. The series representation of this approximate expression is also developed, which enables us to avoid dealing with the integration. To reveal the importance of proposed approximation, new approximate closed-form expressions of the average bit error rate (BER) and ergodic capacity are derived. The performance for multiple-input multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) diversity technique are analyzed with different parameters, including the number of transmit and receive apertures, strength of atmospheric turbulence, and presence of pointing errors. It is observed that the pointing errors significantly degrade the performance of MIMO FSO systems. The numerical results and simulation are further utilized to illustrate the accuracy of the proposed approach.

Performance enhancement of hybrid diversity for M-ary modified pulse-position modulation and spatial modulation of MIMO-FSO systems under the atmospheric turbulence effects with geometric spreading

In this paper, we propose a novel model for hybrid spatial diversity of M-ary pulse position modulation (M-ary PPM) and spatial modulation (SM) with a multiple-input multiple-output (MIMO) links (i.e., optical receiver diversity) in a free-space optical (FSO) communication system under the atmospheric turbulence (AT) effects with geometric spreading (GS). In the proposed design, the spatial index modulator (SIM) and modified pulse position modulation (MPPM) schemes are combined to improve the system efficiency of the spatial diversity for the M-ary PPM modulated MIMO–FSO communication. In this work, we investigate and enhance the performance of the MIMO-FSO link using a digital pulse position modulation (DPPM) and on–off keying non-return-to-zero (OOK–NRZ). We propose a MIMO-based FSO link using spatial diversity and M-ary PPM modulation technique to compensate for the performance degradation due to geometric losses and atmospheric attenuation. Here, we have combined the N-SM with L-MPPM (N-SM/L-MPPM) and (M × N MIMO) to improve the system performance and provide high bandwidth and a higher throughput under the impact of the AT and GS. We analyze the GS impact on the performance of MIMO–FSO systems using SM over the Gamma–Gamma (GG) model. The performance is achieved by using the PPM technique, so the AT influences and fading are mitigated hence the ability to combat AT and the FSO link systems are enhanced sufficiently. Also, we improve the performance of the proposed link using a novel hybrid of SM/PPM and DPPM over GG to maximize the range and enhance the receiver sensitivity. Simulation results obtained for the bit-error-rate (BER) and average transmitted optical power for the DPPM and OOK modulation against various AT conditions are compared with the spatial diversity techniques and proved that both of the FSO systems based MIMO–SM/MPPM offers better performance in the receiver sensitivity and channel capacity. The obtained results show that the conjunction of the receiver diversity and SM/M-ary MPPM is a magnificent solution for mitigating the strong turbulence (ST) and GS effects. The proposed design provides an excellent optical signal-to-noise ratio (SNR) and high-sensitivity for the SIM/PPM-MIMO in the ST regime and GS. The numerical results report that the DPPM sensitivity improves about 10–11 dB at a distance of 2.5 km and the BER of 10−12 more than an equivalent OOK–NRZ modulation. The SIM/PPM-MIMO offers about 4 dB, 2 dB optical SNR improvements over without SIM/PPM-MIMO for the no turbulence and ST with GS for the FSO link, respectively. This work could be beneficial to the practical implementation of the hybrid spatial diversity for the SM/M-ary MPPM based MIMO-FSO links under the AT effects with GS.

Performance improvement of MIMO FSO systems against destructive interference

Although multiple-input multiple-output (MIMO) technique is used in free space optical (FSO) systems to reduce the effect of atmospheric turbulence, however, employing this technique without sufficient attention to the interference of laser beams not only does not reduce the effect of atmospheric turbulence, but also it can significantly degrade the performance of the FSO system. This study investigates that the average intensity of laser beams at the receiver aperture of MIMO FSO systems is very sensitive to small variations of path lengths between the transmitter and receiver. Therefore, the destructive interference that degrades the performance of MIMO FSO systems compared to equivalent single-input single-output (SISO) FSO ones is due to the difference in path lengths of laser beams between transmitter and receiver apertures. For this reason and in order to mitigate the interference effect, the authors compensate small changes of path lengths through adjusting the sending times and the initial parameters of laser beams in the transmitter apertures. The authors' analysis supported by numerical results show that the adjustment of laser parameters could increase the chance of peak intensity of MIMO-FSO systems to be higher than the peak intensity of equivalent SISO-FSO ones.

Free space optical links over Málaga turbulence channels with transmit and receive diversity

This paper introduces a multiple-input multiple-output (MIMO) free space optical (FSO) communication system with both transmit and receive diversity employing Alamouti space–time block-coding (STBC) at the transmitter end and switch-and-examine combining (SEC) at the receiver end, and presents analytical expressions for various performance measures of the system such as outage probability, bit-error-rate (BER) and capacity. The effects of the atmospheric turbulence over FSO link is modelled by the newly introduced Málaga distribution which serves as a general statistical model and covers most of the earlier statistical characterizations as special cases. For the computation of the performance metrics we propose a new unified analytical framework which yields closed-form expressions. The framework is also useful in finding switching threshold values that achieve the optimum performance for the proposed MIMO FSO system. The presented graphical plots exhibit that the corresponding Monte-Carlo simulations validate the derived analytical results for each of the considered metrics.

Bit error rate and outage analysis of MIMO-FSO communications over K-distributed atmospheric channels with imperfect feedback

In this paper, we propose a weighting scheme (WS) for an imperfect feedback-based multiple-input multiple-output free-space optical (MIMO-FSO) system over K-distributed fading channels which employs equal gain combining (EGC) at the receiver. More precisely, the optimal beamforming vector is obtained so as to minimize the upper bound of the average bit error rate (BER) of the proposed scheme. For performance comparison, we consider three competitive schemes referred to as error-free feedback (EF), erroneous feedback (FWE) and repetition coding (RC). Moreover, the performance of the proposed method is analyzed in terms of outage probability. To this aim, we first derive the expression of the outage probability for the WS (proposed), FWE, RC and EF schemes and then, the performance of these methods is compared through different numerical simulations. We show that the proposed beamforming scheme outperforms the FWE and RC schemes in terms of BER and outage probability, even under an imperfect feedback link. Moreover, we show that the performance of the proposed scheme approaches that with ideal feedback by decreasing the error probability of the feedback link.

Extended Golden Light Code for FSO-MIMO Communications With Time Diversity

In this paper, we consider a latency tolerant $2 \times n_{r}$ free space optical multiple-input multiple-output (FSO-MIMO) communication with a time diversity order of two. For this configuration, we propose an extended golden light code (E-GLC) construction that encodes data over two independent optical MIMO channel realizations. The main objective of this code construction is to jointly extract the spatial and the temporal diversity while keeping a multiplexing gain of two symbols per channel use. The proposed coding scheme is compliant with the optical intensity modulation and direct detection constraints that restrict the laser outputs to positive magnitude values with peak and average constraints. The error rate performance evaluations show that the E-GLC outperforms the other known replication-based schemes.

Performance of multiple-input multiple-output free space optics using hybrid subcarrier intensity modulation with avalanche photodiode receiver

In order to improve the performance of a free space optical (FSO) communication system, hybrid pulse position modulation-binary phase shift keying-subcarrier intensity modulation (PPM-BPSK-SIM) technique is proposed. The system performance is further improved by using multiple-input multiple-output (MIMO) configuration and avalanche photodiode (APD) receiver. The use of multiple lasers and photo detectors in MIMO FSO system reduces the scintillation effect in the atmosphere. In this study, the impact of different parameters like irradiance, link distance, and turbulence level have been considered for the bit error rate (BER) analysis. The relevant mathematical model is also presented. The simulation results show that the hybrid PPM-BPSK-SIM scheme performs better compared to PPM and BPSK-SIM schemes. Also, APD receiver shows a noticeable BER improvement than p-type intrinsic n-type (PIN) receiver in our proposed scheme.

Performance of multiple-input multiple-output free space optics using hybrid subcarrier intensity modulation with avalanche photodiode receiver

In order to improve the performance of a free space optical (FSO) communication system, hybrid pulse position modulation-binary phase shift keying-subcarrier intensity modulation (PPM-BPSK-SIM) tec...

Performance Enhancement of an Orbital-Angular-Momentum-Multiplexed Free-Space Optical Link Under Atmospheric Turbulence Effects Using Spatial-Mode Multiplexing and Hybrid Diversity Based on Adaptive MIMO Equalization

In this paper, we propose an adaptive multiple-input–multiple-output (MIMO) free-space optical (FSO) links using an orbital-angular-momentum (OAM)-multiplexed based on the spatial-mode multiplexing (SMM) through the turbulent channel. We propose to use the SMM and spatial-mode diversity (SMD) combined with an adaptive MIMO technique to mitigate the atmospheric turbulence effects. In this paper, our objective is to design the adaptive MIMO–FSO links based on OAM–MIMO/SMM multiplexed and analyze its performance in the atmospheric turbulence conditions. The simulation results show four OAM modes-based MIMO/SMM and resulting in four OAM-multiplexed channels. Each OAM mode carries a 100-Gbit/s quadrature phase-shift keying signal (aggregate 400 Gbit/s) on a single wavelength channel ( $\lambda \sim 1550$ nm) and is transmitted for a 2-km link. The calculated received power and inter-channel crosstalk of an OAM–MIMO/SMM signal fluctuate by 4.5 −6 dB, respectively. The power penalties can be reduced by 1–4 dB for all channels after OAM–MIMO/SMM equalization at a bit-error rate (BER) of 10−9. The calculating results show that the system using an OAM-based MIMO/SMM and SMD multiplexing achieves superior BER performance using an adaptive MIMO/SMM equalization. The Numerical results show favorable transmission performance of OAM based on MIMO/SMM and the SMD multiplexing compared to the conventional-MIMO (CMIMO) of FSO transmission link. The Simulation models verified the superior BER performance of OAM–SMD-based MIMO/SMM. The SMM/MIMO–SMD technique performed better in the channel capacity and signal-to-noise ratios over other commonly used CMIMO algorithms. To sufficiently discuss the OAM–MIMO/SMM behavior-based SMD multiplexing, the performance of the novel SMM/MIMO–SMD technique is analyzed using simulations based on the Matlab/simulink program in order to verify the accuracy of the models and simulation results. This paper could be useful for the practical implementation of the SMM and the SMD using an adaptive MIMO equalization in the FSO systems.

Polar-Coded MIMO FSO Communication System Over Gamma-Gamma Turbulence Channel With Spatially Correlated Fading

In this paper, for the first time to the best of our knowledge, a polar-coded multiple-input multiple-output (MIMO) free space optical (FSO) communication system is proposed to combat turbulence-induced fading. Here, the spatially correlated fading, which dominates the MIMO FSO system aggravation, is taken into consideration in this polar-coded MIMO FSO system. To evaluate our scheme, the ergodic capacity of the gamma-gamma modeled MIMO FSO turbulence channel with and without spatially correlated fading is studied. The results of ergodic capacity and Monte Carlo simulation show that the polar-coded multiple photodetector scheme can effectively mitigate the fading induced by turbulence, and the polar-coded multiple optical sources scheme is robust to the spatially correlated turbulence. Further, more than 20 dB net coding gain (NCG) is achieved for the polar-coded MIMO FSO scheme in a strong turbulence condition with spatially correlated fading. Compared with low density parity check codes, polar codes achieve a 0.4–1.6 dB NCG improvement under a strong turbulence condition with and without spatially correlated fading, which verifies that our scheme is a promising candidate for combating turbulence-induced fading.

Adaptive MIMO FSO Communication Systems with Spatial Mode Switching

In this paper, we propose an adaptive multiple-input multiple-output (MIMO) free-space optical (FSO) system with dynamic adaptation between spatial modes of operation. The proposed adaptive system supports three MIMO modes. In the spatial multiplexing mode, the system transmits independent parallel data streams over multiple apertures to increase data rate. In diversity mode, the system transmits coded streams through multiple apertures to extract diversity gains. In hybrid mode, a trade-off between diversity and multiplexing gains is targeted. For each operation mode, we first derive the outage probability for the MIMO FSO system over log-normal turbulence channels. Then, we formulate the design of an adaptive FSO system to select the MIMO mode that yields the highest throughput while satisfying a predefined target outage probability. Extensive numerical results are provided to demonstrate the performance of the proposed adaptive scheme.

Performance analysis of an OAM multiplexing-based MIMO FSO system over atmospheric turbulence using space-time coding with channel estimation.

The average bit error rate (ABER) performance of an orbital angular momentum (OAM) multiplexing-based free-space optical (FSO) system with multiple-input multiple-output (MIMO) architecture has been investigated over atmospheric turbulence considering channel estimation and space-time coding. The impact of different types of space-time coding, modulation orders, turbulence strengths, receive antenna numbers on the transmission performance of this OAM-FSO system is also taken into account. On the basis of the proposed system model, the analytical expressions of the received signals carried by the k-th OAM mode of the n-th receive antenna for the vertical bell labs layered space-time (V-Blast) and space-time block codes (STBC) are derived, respectively. With the help of channel estimator carrying out with least square (LS) algorithm, the zero-forcing criterion with ordered successive interference cancellation criterion (ZF-OSIC) equalizer of V-Blast scheme and Alamouti decoder of STBC scheme are adopted to mitigate the performance degradation induced by the atmospheric turbulence. The results show that the ABERs obtained by channel estimation have excellent agreement with those of turbulence phase screen simulations. The ABERs of this OAM multiplexing-based MIMO system deteriorate with the increase of turbulence strengths. And both V-Blast and STBC schemes can significantly improve the system performance by mitigating the distortions of atmospheric turbulence as well as additive white Gaussian noise (AWGN). In addition, the ABER performances of both space-time coding schemes can be further enhanced by increasing the number of receive antennas for the diversity gain and STBC outperforms V-Blast in this system for data recovery. This work is beneficial to the OAM FSO system design.