Milica I. Petkovic

Partial Relay Selection With Outdated Channel State Estimation in Mixed RF/FSO Systems

We study a dual-hop relaying system, composed of mixed radio frequency (RF)/free-space optical (FSO) links. Partial amplify-and-forward relay selection is assumed, which is based on outdated channel state information (CSI). The RF link is subject to Rayleigh fading, while the FSO link is affected by atmospheric turbulence, modeled by Gamma-Gamma distribution. Novel analytical expressions for the outage probability and average bit error rate (BER) are derived. Numerical results are presented and validated by Monte-Carlo simulations. The outage probability and average BER dependence on turbulence strength, average signalto-noise ratio (SNR) over RF hop, average electrical SNR over FSO hop, number of relays, and rank of selected relay, are also investigated, while the effect of time correlation between current source-relay channel and its outdated CSI, is considered. The results illustrate that the outdated CSI used for the relay selection has a strong effect on the system performance, especially in weak turbulence conditions of the FSO hop. Furthermore, the improvement of the system performance with increase of the number of the relays is highly dependent on the FSO channel state.

Mixed RF/FSO Relaying With Outdated Channel State Information

We investigate the outage probability and the average bit error rate (BER) performance of a dual-hop amplify-and-forward (AF) relaying system, composed of a mixed radio frequency (RF)/free-space optical (FSO) link, when simultaneously outdated channel state information (CSI) is assumed at the relay and there is a misalignment between transmitter and receiver apertures in FSO link. In contrast to the majority of works on CSI-assisted AF relays, in this paper, we assume that the estimated CSI is outdated, when the relay amplifies the transmitted signal. The RF link experiences Rayleigh fading, while the FSO link is under the influence of atmospheric turbulence, modeled by the Gamma-Gamma distribution. Novel analytical expressions for the outage probability and the average BER are derived in a power series form, which in some special cases are simplified to offer engineering insight into the effects of important transceiver and channel parameters on the system performance. Numerical and simulation results show that there is an optimal value of the transmitter beam waist, which minimizes the overall outage probability. This optimal value strongly depends on the pointing errors standard deviation. Furthermore, the outage probability varies for several orders of magnitude depending on the transmitter beam waist.

Outage capacity of FSO link with pointing errors and link blockage.

In this paper, we analyze the outage capacity performance of free-space optical (FSO) systems. More precisely, taking the stochastic temporary blockage of the laser beam, atmospheric turbulence, misalignment between transmitter laser and receiver photodiode and path loss into account, we derive novel accurate analytical expressions for the outage capacity. The intensity fluctuations of the received signal are modeled by a Gamma-Gamma distribution with parameters directly related to the wide range of atmospheric conditions. The analytical results are validated by Monte Carlo simulations. Furthermore, when the intensity fluctuations are caused only by atmospheric turbulence, derived expressions are reduced to the simpler forms already presented in literature. The numerical and simulation results show that the link blockage causes appearance of the outage floor that is a significant energetic characteristic of an FSO system. The results also show that there exists an optimal value of the laser beam radius at the waist for minimizing outage probability in order to achieve the specified outage capacity. This optimal value depends on atmospheric turbulence strength and standard deviation of pointing errors, but it is also strongly dependent on the probability of link blockage.

Outage Analysis of Mixed FSO/WiMAX Link

In this paper, we study the outage performance of a complex system consisting of a free-space optical (FSO)/radio-frequency (RF) link. Using radio over free-space optics technology, the FSO link carries Worldwide Interoperability for Microwave Access (WiMAX) signals from a core network to a WiMAX base station, delivering traffic to multiple end RF users. A novel closed-form analytical expression for overall outage probability is derived when M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) are applied. The analysis is performed when the FSO link is under the influence of the Gamma-Gamma turbulence, path loss, and misalignment between the transmitter and receiver apertures, and the RF part is influenced by the Gamma-shadowed Nakagami-m multipath fading. To illustrate the usefulness of the derived expressions, we present some numerical results that enable us to estimate the effects of different transceiver and channel parameters on the outage probability. The results are used for optimizing the transmitter laser beam radius at the waist to achieve the minimal overall outage probability in the case of different conditions over the RF part. The numerical and simulation results show that multipath fading severity and shadowing spread over the RF part have a significant effect on the optimal value of the laser beam waist and can decrease the overall outage probability for several orders of magnitude.

Average BER performance of FSO SIM-QAM systems in the presence of atmospheric turbulence and pointing errors

This paper presents the exact average bit error rate (BER) analysis of the free-space optical system employing subcarrier intensity modulation (SIM) with Gray-coded quadrature amplitude modulation (QAM). The intensity fluctuations of the received optical signal are caused by the path loss, atmospheric turbulence and pointing errors. The exact closed-form analytical expressions for the average BER are derived assuming the SIM-QAM with arbitrary constellation size in the presence of the Gamma–Gamma scintillation. The simple approximate average BER expressions are also provided, considering only the dominant term in the finite summations of obtained expressions. Derived expressions are reduced to the special case when optical signal transmission is affected only by the atmospheric turbulence. Numerical results are presented in order to illustrate usefulness of the derived expressions and also to give insights into the effects of different modulation, channel and receiver parameters on the average BER performance. The results show that the misalignment between the transmitter laser and receiver detector has the strong effect on the average BER value, especially in the range of the high values of the average electrical signal-to-noise ratio.

On the Effects of Correlation on Outage Performance of FSO-Unbalanced Multibranch SC Receiver

In this letter, we study the outage performance of unbalanced multibranch selection combining receiver operating over free-space optical gamma-gamma turbulence link. The analysis is performed in the case when the position of closely placed photodiodes corresponds to the constant correlation model. Novel analytical expressions for the probability density function and cumulative distribution function of receiver signal-to-noise ratio (SNR) are derived in the infinite series form whose convergence is numerically determined. Based on these analytical results, we examine the simultaneous effects of the spatial correlation, diversity order, photodiodes diameter, and turbulence strength on outage performance. The results illustrate that spatial correlation has a strong effect on SNR gain decreasing, especially for the higher values of diversity order.

Mixed RF/FSO Relaying Systems

In this chapter, we are focused on wireless optical communications utilizing in overcoming a connectivity gap between the backbone and last mile access networks. The outage performance of dual-hop amplify-and-forward (AF) relaying systems, composed of mixed radio frequency (RF)/free-space optical (FSO) links is presented, when the partial relay selection is considered based on outdated channel state information (CSI). We analyze an example when the RF link is subjected to Rayleigh fading, while the FSO link is affected by atmospheric turbulence, which results in the intensity fluctuations of the optical signal, following the Gamma–Gamma distribution with taking the pointing errors into account. Analytical expressions for the outage probability are presented. The effects of atmospheric turbulence strength, pointing errors standard deviation, number of relays and rank of selected relay, are observed, considering the effect of time correlation between current and outdated CSI of the source-relay channel.

Impact of correlation on outage performance of FSO system with switch-and-stay diversity receiver

In this paper, we analyze diversity reception of optical signals transmitted over terrestrial free-space optical (FSO) links. The irradiance fluctuations of the received signal are modeled by a Gamma-Gamma probability density function whose parameters are directly linked to propagation conditions. The switch-and-stay combining technique at the receiver is utilized for signal reception. Due to insufficient separation of photodiodes, there is a correlation between received signals at different branches. We analyze the effects of spatial signal correlation and switching threshold value on the outage probability. The analytical expression for outage probability is derived in the form of rapidly convergent series. The numerical results illustrate that spatial correlation causes penalty in electrical signal-to-noise ratio of about 5 dB for outage probability of 10-7. The results obtained here also show that proper selection of switching threshold can decrease the outage probability for an order of magnitude.

Effects of pointing errors on average capacity of FSO links over gamma-gamma turbulence channel

In this paper, we derive new closed-form expression for the average channel capacity of the free space optical (FSO) system with intensity-modulation/direct detection (IM/DD). The intensity fluctuations at receiver are described by combined model which assumes turbulence effects, pointing errors and path loss. The numerical results are presented. The effects of normalized jitter variance, propagation distance and turbulence strength are discussed.

Outage Performance of the Mixed RF/FSO Relaying Channel in the Presence of Interference

We present novel closed-form expressions for the outage probability of the amplify-and-forward dual-hop semi-blind relaying channel, composed of mixed radio frequency (RF)/free space optical (FSO) links, while the relay is corrupted by both co-channel interferences and noise. The RF link is assumed to follow Nakagami-m distribution, while the FSO link is under the influence of atmospheric turbulence modelled by the Gamma–Gamma fading taking pointing errors into account. The analytical results are validated by Monte Carlo simulations. The obtained general expressions are simplified when RF link is noise-limited. The numerical results show the existence of the outage probability floor, which can be taken into account in the system design.