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

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.

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.

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.

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.

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.

Performance analysis of MIMO FSO link with Alamouti coding and switch-and-examine combining

Atmospheric turbulence is one of the main causes of degrading the quality of service in free-space optical (FSO) systems. The use of diversity techniques in an FSO system can minimize the fading effect which is caused by atmospheric turbulence. When diversity combining is applied at both the transmitter and the receiver ends, the system can mitigate the degradation more effectively. In this paper, we consider a $$2\times L$$ multiple-input multiple-output FSO system with on–off keying modulation where the link is affected by gamma–gamma fading. Alamouti space–time coding is implemented at the transmitter, while the receiver employs switch-and-examine combining. Analytical expressions for different performance metrics such as outage probability, average bit error rate and average capacity are derived using a moment-generating function-based approach. Numerical results are provided and are compared with Monte Carlo simulations.

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.

Effective capacity of MIMO free-space optical systems over gamma–gamma turbulence channels

In this paper, we provide the capacity limits of multiple-input multiple-output (MIMO) free-space optical communication (FSO) system in the presence of quality of service (QoS) requirements. Closed-form expression for the effective capacity of MIMO FSO system with equal gain combining (EGC) is derived. In order to provide insights into the impact of various system parameters, asymptotic expressions are further analyzed in the high signal-to-noise ratio (SNR) regime. Special cases are provided according to the derived results at the same time. Numerical results are given to validate all the analytical results, and the influences of QoS requirements and MIMO configurations are also illustrated.

Performance analysis of multiple-input multiple-output free-space optical systems with partially coherent Gaussian beams and finite-sized detectors

Multiple-input multiple-output (MIMO) techniques are employed in free-space optical (FSO) links to mitigate the degrading effects of atmospheric turbulence. We consider a MIMO FSO system, which consists of a radial laser array with partially coherent Gaussian beams at the transmitter and a detector array with Gaussian apertures at the receiver. The average power and the power correlation function at the finite-sized receiver apertures are formulated by using the extended Huygens–Fresnel principle in weak atmospheric turbulence. This let us further quantify the performance metrics such as the power scintillation index, the aperture averaging factor, and the average bit error rate (BER) as functions of system parameters. The derived power scintillation equation correctly reduces to the existing coherent and partially coherent Gaussian beam scintillation indices in the limiting cases. Using the performance metrics, we analyze the effect of various practical system parameters on the performance of a MIMO FSO system. Practical system parameters include the transmitter and receiver ring radius, number of beamlets, number of finite-aperture receivers, source size, degree of source coherence, receiver aperture radius, link distance, and the structure constant of atmosphere.

MIMO FSO communication using subcarrier intensity modulation over double generalized gamma fading

Atmospheric turbulence-induced fading is known to have a serious detrimental effect on the performance of free-space optical (FSO) communication. The involvement of multiple lasers and photodetectors in FSO systems offers an effective way to overcome fading. Very recently, a new generic fading model, called double-generalized gamma (double GG), is developed for accurately describing irradiance fading over a wide range of turbulence conditions. Therefore, for a general and exact study of the multiple-input multiple-output (MIMO) FSO system, the double GG fading model is adopted in this paper. We investigate the MIMO FSO systems using subcarrier intensity modulation. Two typical transmit diversity schemes, repetition code (RC) and orthogonal space-time block code (OSTBC), are considered. We first propose a new power series expression for the probability density function of the double GG fading. Then we derive the average error rate expressions for both schemes in terms of double power series. The truncated forms of the derived power series enable the rapid and accurate numerical computation of the error rates. Furthermore, we present the asymptotic error rate analyses at high electrical signal-to-noise ratio (SNR) for both schemes. Closed-form diversity order and coding gain for both schemes are also obtained. Our numerical results, verified by simulation, confirm that RC outperforms OSTBC for MIMO FSO systems with subcarrier intensity modulation in double GG fading. The asymptotic coding gain of the RC scheme over the OSTBC scheme is analytically quantified for varying degrees of the fading strength.

Outage capacity and outage rate performance of MIMO free-space optical system over strong turbulence channel

In this paper, we investigate outage capacity, outage probability, and outage rate performance of multiple-input multiple-output (MIMO) free-space optical system operating over strong turbulence channels. The MIMO optical system employs intensity modulation direct detection with on-off signaling, and equal gain combining technique at the receiver. We derived novel closed-form expressions for three system metrics, namely, outage capacity, outage probability, and outage rate. Expressions derived here are based on the generalized Gamma–Gamma channel model, which is based on scintillation theory that assumes that the irradiance of the received optical wave is modeled as the product of small-scale and large-scale turbulence eddies. The results are evaluated for different values of received signal-to-noise ratios, strong turbulence conditions, and several values of transmit/receive diversity.

Performance Analysis of Space-Diversity Free-Space Optical Links Over Exponentiated Weibull Channels

We propose a simple analytical method for evaluating the average bit-error rate (BER) performance of multiple input multiple output (MIMO) free-space optical (FSO) communication systems over independent exponentiated Weibull (EW) channels. We first present an accurate approximation to the probability density function (PDF) of the sum of independent EW random variables corresponding to the EW-distributed FSO channel fading. Then, a closed-form expression for the BER of MIMO FSO systems using ON–OFF keying is derived based on the obtained PDF. The proposed method is validated through comparing the BER results obtained by the analytical calculation and the Monte Carlo simulation.

On the Ergodic Capacity of MIMO Free-Space Optical Systems Over Turbulence Channels

The free-space optical (FSO) communications can achieve high capacity with huge unlicensed optical spectrum and low operational costs. The corresponding performance analysis of FSO systems over turbulence channels is very limited, especially when using multiple apertures at both transmitter and receiver sides. This paper aim to provide the ergodic capacity characterization of multiple-input multiple-output (MIMO) FSO systems over atmospheric turbulence-induced fading channels. The fluctuations of the irradiance of optical channels distorted by atmospheric conditions is usually described by a gamma-gamma ($\Gamma \Gamma$) distribution, and the distribution of the sum of $\Gamma \Gamma$ random variables (RVs) is required to model the MIMO optical links. We use an $\alpha$-$\mu$ distribution to efficiently approximate the probability density function (PDF) of the sum of independent and identical distributed $\Gamma\Gamma$ RVs through moment-based estimators. Furthermore, the PDF of the sum of independent, but not necessarily identically distributed $\Gamma \Gamma$ RVs can be efficiently approximated by a finite weighted sum of PDFs of $\Gamma \Gamma$ distributions. Based on these reliable approximations, novel and precise analytical expressions for the ergodic capacity of MIMO FSO systems are derived. Additionally, we deduce the asymptotic simple expressions in high signal-to-noise ratio regimes, which provide useful insights into the impact of the system parameters on the ergodic capacity. Finally, our proposed results are validated via Monte-Carlo simulations.

SER Analysis of MPPM-Coded MIMO-FSO System over Uncorrelated and Correlated Gamma-Gamma Atmospheric Turbulence Channels

The performance of multiple-input multiple-output free space optical (MIMO-FSO) communication systems, that adopt multipulse pulse position modulation (MPPM) techniques, is analyzed. Both exact and approximate symbol-error rates (SERs) are derived for both cases of uncorrelated and correlated channels. The effects of background noise, receiver shot-noise, and atmospheric turbulence are taken into consideration in our analysis. The random fluctuations of the received optical irradiance, produced by the atmospheric turbulence, is modeled by the widely used gamma-gamma statistical distribution. Uncorrelated MIMO channels are modeled by the α-μ distribution. A closed-form expression for the probability density function of the optical received irradiance is derived for the case of correlated MIMO channels. Using our analytical expressions, the degradation of the system performance with the increment of the correlation coefficients between MIMO channels is corroborated.

Inter-aperture correlation in MIMO free space optical systems

We present a unified framework for determining the inter-aperture separations in multiple-input–multiple-output (MIMO) free space optical (FSO) systems such that the transmitter–receiver paths are resolvable. The analysis framework is also useful in determining the amount of spatial correlation for a given set of system configuration parameters and aperture separations. It is applicable to both point apertures and also apertures with larger diameters and can be used at both transmit and receive arrays. We show that the results obtained via theoretical derivations are in good agreement with those in the literature obtained via measurements or simulations. The theoretical calculations reveal that even under strong turbulence conditions and very long link distances, aperture separations at the order of a few tens of centimeters are sufficient to have resolvable paths with independent fading gains. Furthermore, the channel correlations increase relatively slowly with decreasing inter-aperture separations which are below these values. We also provide design guidelines to obtain resolvable paths for several commonly used system configurations.

Performance and Design of Coherent and Differential Space-Time Coded FSO Systems

Free-space optical (FSO) communication enables high rate data transmission over the atmospheric channel. However, turbulence-induced fading poses severe challenges for operating these systems. Employing spatial diversity has been proposed as an effective measure to improve system performance. In this paper, we first develop a comprehensive model for multiple-input multiple-output (MIMO) coherent and differential FSO systems with heterodyne detection taking into account all relevant signal and noise terms. For the sake of comparison, a similar model is also developed for direct detection. An asymptotic performance analysis is presented for MIMO FSO systems employing coherent and differential space-time codes (STCs) over Gamma-Gamma fading channels. We consider the practically important case of two transmit and an arbitrary number of receive apertures and provide a simple STC design criterion for coherent and differential FSO systems. Our results reveal that, in contrast to FSO systems with intensity modulation and direct detection (IM/DD), for coherent and differential FSO systems, orthogonal space-time block codes previously introduced in the RF literature, are preferable over repetition STCs, which do not yield full diversity. We quantify the asymptotic performance gain of coherent space-time coded FSO systems compared to IM/DD systems and show that this gain is mainly caused by the superiority of heterodyne detection compared to direct detection rather than the different STC and modulation designs.