Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

The bit error rate (BER) performance of the free space optical (FSO) link suffers from the atmospheric turbulence. By employing additional transmit and receive apertures at the transmitter and receiver, respectively, the error rate of the FSO communication system can be significantly improved. However, the pointing errors (PEs), generated because of the building sway, have the potential to eradicate the benefits of the multiple transmit and/or receive apertures-based FSO communication system. Therefore, for a general and realistic study of the FSO multiple-input multiple-output (MIMO) system, the effect of PEs in the Gamma–Gamma (GG) fading atmospheric fluctuations is considered in this paper. We study two schemes for the FSO MIMO systems: 1) equal gain combining (EGC), and 2) maximal ratio combining (MRC). A new power series-based representation is proposed for the probability density function of the GG fading FSO links with PEs. This new series representation contains only the terms with exponent of the random variable (RV) as compared to the closed-form representation, which contains the Meijer-G function of the RV. Then, we derive the average BER for both combining schemes over the GG fading FSO links with PEs. By using the derived BER expressions, we derive the asymptotic BER for both schemes. The analytical diversity order and combining gains for both systems are also obtained. The effect of PEs over the performance of the schemes is analyzed under different scenarios and it is observed that the PEs significantly degrade the diversity of the FSO MIMO system. It is deduced by simulation and analysis that though the EGC scheme is simpler to implement in practice but the MRC scheme is more rugged to the large PEs.

Performance Analysis of Gamma–Gamma Fading FSO MIMO Links With Pointing Errors

In recent studies, the average capacity for optimal rate adaptation (ORA) of free-space optical channels in turbulent atmosphere has been derived in closed form, mainly based on the application of Meijer's G-function. To this end, the channel was assumed to be memoryless, stationary and ergodic, with independent and identically distributed fading statistics. It was also assumed that scintillations follow a gamma–gamma distribution so as to appropriately describe moderate-to-strong turbulence conditions. In the current contribution, the author will extend this work in two aspects: (i) using the properties of Meijer's G-function, it is shown that the average capacity provides also a closed-form solution for adaptation policies other than ORA, namely optimal power and rate adaptation, channel inversion with fixed rate and truncated channel inversion with fixed rate; (ii) if the additional loss caused by a misalignment between transmitter and receiver (pointing error) is taken into account, it is demonstrated that the developed analytical framework applies straightforwardly.

Further results on the capacity of free-space optical channels in turbulent atmosphere

In this paper, we consider a heterogenous scenario where free-space optical (FSO) and radio-frequency (RF) technologies are deployed together as a dual-hop communication system, and we investigate the end-to-end outage performance of this so-called mixed RF/FSO system. The RF and FSO links are, respectively, modeled as Rayleigh fading (due to multipath propagation) and M-distributed fading (due to atmospheric turbulence). We derive exact closed-form expressions for the outage probability and demonstrate that the existing outage results in the literature for mixed FSO systems can be obtained as special cases of our results. The effect of pointing errors in the FSO link is further investigated.

End-to-end performance of mixed RF/FSO transmission systems

In this paper, a study on the end-to-end performance of multihop free-space optical wireless systems over turbulence-induced fading channels, modeled by the gamma-gamma distribution, is presented. Our analysis is carried out for systems employing amplify-and-forward channel-state-information-assisted or fixed-gain relays. To assess the statistical properties of the end-to-end signal-to-noise ratio for both considered systems, we derive novel closed-form expressions for the moment-generating function, the probability density function, and the cumulative distribution function of the product of rational powers of statistically independent squared gamma-gamma random variables. These statistical results are then applied to studying the outage probability and the average bit error probability of binary modulation schemes. Also, for the case of channel-state-information-assisted relays, an accurate asymptotic performance analysis at high SNR values is presented. Numerical examples compare analytical and simulation results, verifying the correctness of the proposed mathematical analysis.

Serial Free-Space Optical Relaying Communications Over Gamma-Gamma Atmospheric Turbulence Channels

An expression for the bit error rate of a multiple subcarrier intensity-modulated atmospheric optical communication system employing spatial diversity is derived. Spatial diversity is used to mitigate scintillation caused by atmospheric turbulence, which is assumed to obey log-normal distribution. Optimal but complex maximum ratio, equal gain combining (EGC) and relatively simple selection combining spatial diversity techniques in a clear atmosphere are considered. Each subcarrier is modulated using binary phase shift keying. Laser irradiance is subsequently modulated by a subcarrier signal, and a direct detection PIN receiver is employed (i.e. intensity modulation/direction detection). At a subcarrier level, coherent demodulation is used to extract the transmitted data/information. The performance of on-off-keying is also presented and compared with the subcarrier intensity modulation under the same atmospheric conditions.

/pdf/free-space-optical-communication-employing-subcarrier-4dxrbht4gd.pdf

Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel

Free-space optical communication is reputable for its ability to proffer solution to the access network bottle-neck but when used for long range communication, it suffers from scintillation caused by atmospheric turbulence. The probability of outage based performance of subcarrier intensity modulated free-space optical communication in log normal atmospheric turbulence is hereby presented. The bit-error-rate of subcarrier intensity modulated FSO employing phase shift keying (PSK) is also discussed. The atmospheric turbulence is modelled using log normal distribution and its effect mitigated by using an array of PIN photodetectors.

Joe Allen

Papers

Free-space optical communication employing subcarrier modulation and spatial diversity in atmospheric turbulence channel

Performance of Subcarrier Modulated Free- Space Optical Communications