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Table Of Integrals Series And Products

Introduction to linear and nonlinear programming

Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

Matrix Differential Calculus with Applications in Statistics and Econometrics

Tables of integrals

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 this paper, the transmission of signals in a hybrid satellite-terrestrial link is considered. In particular, we address the problem of amplify-and-forward (AF) relaying in a hybrid satellite-terrestrial link, where a masked destination node receives the relayed transmission from a terrestrial link and direct transmission from the satellite link. The satellite-relay and satellite-destination links are assumed to follow the Shadowed-Rician fading; and the channel of the terrestrial link between the relay and destination is assumed to follow the Nakagami-m fading. The average symbol error rate of the considered AF cooperative scheme for M-ary phase shift keying constellation is derived for these generalized fading channels. Moreover, analytical diversity order of the hybrid system is also obtained.

Performance Analysis of AF Based Hybrid Satellite-Terrestrial Cooperative Network over Generalized Fading Channels

In this work, the performance and the capacity analysis of a fixed-gain amplify-and-forward (AF)-based dual-hop asymmetric radio frequency–free space optical (RF–FSO) communication system is performed. The RF link experiences Nakagami-m fading and the FSO link experiences Gamma–Gamma turbulence. For this mixed RF–FSO cooperative system, novel and finite power series-based mathematical expressions for the cumulative distribution function, probability density function, and moment generating function of the end-to-end signal-to-noise ratio are derived. Using these channel statistics new finite power series-based analytical expressions are obtained for the outage probability, the average bit error rate (BER) for various binary and M-ary modulation techniques, and the average channel capacity of the considered system. The same analysis is also performed for the scenario when the FSO link undergoes significant pointing errors along with the Gamma–Gamma distributed turbulence. As a special case analytical expressions for the outage probability, BER, and channel capacity are also presented for a dual-hop asymmetric RF–FSO system where the RF link is Rayleigh distributed. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence, and pointing error are studied on the outage probability, average BER, and the channel capacity.

Performance of an amplify-and-forward dual-hop asymmetric RF–FSO communication system

Performance of cooperative spectrum sensing with multiple antennas at each cognitive radio (CR) is discussed in this paper. The CRs utilize selection combining of the decision statistics obtained by an improved energy detector for making a binary decision of the presence or absence of a primary user (PU). The improved energy detector uses an arbitrary positive power p of amplitudes of samples of the PU's signals. The decision of each CR is orthogonally forwarded over imperfect reporting channels to a fusion center, which takes the final decision of a spectrum hole. We derive expressions of the probabilities of false alarm and missed detection of the proposed cooperative spectrum sensing scheme. By minimizing the total error rate (sum of the probability of missed detection and the probability of false alarm) we derive a closed-form solution of the optimal number of CRs required for cooperation. It is shown by simulations that by using multiple antennas at the CRs, it is possible to significantly improve reliability of spectrum sensing with extremely low interference levels to the PU at very low (much less than 0 dB) signal-to-noise ratio of the PU-CR link.

https://web.iitd.ac.in/~manav/CL2011-1884.pdf

Cooperative Spectrum Sensing in Multiple Antenna Based Cognitive Radio Network Using an Improved Energy Detector

We analyze performance of the decode-and-forward (DF) protocol in the free space optical (FSO) links following the Gamma-Gamma distribution. The cumulative distribution function (cdf) and probability density function (pdf) of a random variable containing mixture of the Gamma-Gamma and Gaussian random variables is derived. By using the derived cdf and pdf, average bit error rate of the DF relaying is obtained.

Manav R. Bhatnagar

Papers

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

Performance Analysis of AF Based Hybrid Satellite-Terrestrial Cooperative Network over Generalized Fading Channels

Performance of an amplify-and-forward dual-hop asymmetric RF–FSO communication system

Cooperative Spectrum Sensing in Multiple Antenna Based Cognitive Radio Network Using an Improved Energy Detector

Performance Analysis of Decode-and-Forward Relaying in Gamma-Gamma Fading Channels