The Gamma-Gamma (GG) distribution has recently attracted the interest within the research community due to its involvement in various communication systems. In the context of RF wireless communications, GG distribution accurately models the power statistics in composite shadowing/fading channels as well as in cascade multipath fading channels, while in optical wireless (OW) systems, it describes the fluctuations of the irradiance of optical signals distorted by atmospheric turbulence. Although GG channel model offers analytical tractability in the analysis of single input single output (SISO) wireless systems, difficulties arise when studying multiple input multiple output (MIMO) systems, where the distribution of the sum of independent GG variates is required. In this paper, we present a novel simple closed-form approximation for the distribution of the sum of independent, but not necessarily identically distributed GG variates. It is shown that the probability density function (PDF) of the GG sum can be efficiently approximated either by the PDF of a single GG distribution, or by a finite weighted sum of PDFs of GG distributions. To reveal the importance of the proposed approximation, the performance of RF wireless systems in the presence of composite fading, as well as MIMO OW systems impaired by atmospheric turbulence, are investigated. Numerical results and simulations illustrate the accuracy of the proposed approach.In communication theory, channel statistical modeling is very crucial, since it can be applied in the design and performance evaluation of various communication systems. A distribution which has recently attracted the interest within the research community due to its involvement in various communication systems, is the so-called Gamma-Gamma (GG) distribution. This distribution is equivalent to the squared Generalized-K (K G ) distribution [1] and can be derived from the product of two independent Gamma random variables (RVs). Moreover, for certain values of its parameters, it coincides with the K-distribution, which in the past has been widely used in a variety of applications, including the statistical characterization of the intensity of SAR images [2], as well as to model the statistics of the reverbation intensity in underwater communications [3]-[4]. Of particular interest is the application of the GG distribution in optical wireless (OW) systems, where transmission of optical signals through the atmosphere is involved. In these systems, a major performance limiting factor is the turbulence induced fading, i.e., rapid fluctuations of the irradiance of the propagated optical signals caused by atmospheric turbulence, which can be accurately modeled using the statistics of the GG distribution [5]. Furthermore, in recent years, GG distribution has also been applied in the field of RF wireless communications; specifically, to model the power statistics in composite fading channels [1], [6]. Additionally, since it includes the well known Double-Rayleigh model [7], GG distribution can be further e...
Abstract-We present a novel architecture for hybrid radio frequency (RF)/ free space optical (FSO) wireless systems without feedback or channel state information (CSI) at the transmitter. Under the assumption that 60 GHz RF and FSO systems support the same data rates, the proposed implementation transmits the same data over both links, using phase shift keying (PSK) as a common modulation scheme, and combines the signals from each individual link at the receiver on a symbol-bysymbol basis. Two popular diversity combining schemes are considered, namely, selection combining (SC) and maximal ratio combining (MRC), while tractable analytical approximations for the bit error rate (BER) are obtained. Investigations over various weather conditions and link distances revealed that the proposed implementation fully exploits the complementary nature of RF and FSO channels, even when one of the two available links fails. Furthermore, the comparison of the combining schemes demonstrates MRC as the optimum combining scheme, offering link distance gains compared to SC.
We investigate transmission protocols for relay-assisted free-space optical (FSO) systems, when multiple parallel relays are employed and there is no direct link between the source and the destination. As alternatives to all-active FSO relaying, where all the available relays transmit concurrently, we propose schemes that select only a single relay to participate in the communication between the source and the destination in each transmission slot. This selection is based on the channel state information (CSI) obtained either from all or from some of the FSO links. Thus, the need for synchronizing the relays' transmissions is avoided and the slowly varying nature of the atmospheric channel is exploited. For both relay selection and all-active relaying, novel closed-form expressions for their outage performance are derived, assuming the versatile Gamma-Gamma channel model. Furthermore, based on the derived analytical results, the problem of allocating the optical power resources to the FSO links is addressed, and optimum and suboptimum solutions are proposed. Numerical results are provided for equal and non-equal length FSO links, which illustrate the outage behavior of the considered relaying protocols and demonstrate the significant performance gains offered by the proposed power allocation schemes. Index TermsAtmospheric turbulence, cooperative diversity, distributed switch and stay relaying, free-space optical communications, relay-assisted communications, relay selection, power allocation. This paper has been submitted in part to the IEEE Global Communications Conference (GLOBECOM'11). DRAFT SUBMITTED TO THE IEEE TRANSACTIONS ON COMMUNICATIONS 1 I. INTRODUCTIONThe constant need for higher data rates in support of high-speed applications has led to the development of the Free Space Optical (FSO) communication technology. Operating at unlicensed optical frequencies, FSO systems offer the potential of broadband capacity at low cost [1], and therefore, they present an attractive remedy for the "last-mile" problem. However, despite their major advantages, the widespread deployment of FSO systems is hampered by major impairments, which have their origin in the propagation of optical signals through the atmosphere. Rain, fog, and atmospheric turbulence are some of the major atmospheric phenomena that cause attenuation and rapid fluctuations in the received optical power in FSO systems, thereby increasing the error rate and severely degrading the overall performance [2].In the past, several techniques have been applied in FSO systems for mitigating the degrading effects of the atmospheric channel, including error control coding in conjunction with interleaving [3], multiple-symbol detection [4], and spatial diversity [5]- [7]. Among these techniques, spatial diversity, which is realized by deploying multiple transmit and/or receive apertures, has been particularly attractive, since it offers significant performance gains by introducing additional degrees of freedom in the spatial dimension. Thus, numerous FSO systems...
Direct-conversion radio (DCR) receivers can offer highly integrated low-cost hardware solutions for spectrum sensing in cognitive radio (CR) systems. However, DCR receivers are susceptible to radio frequency (RF) impairments, such as in-phase and quadrature-phase imbalance, low-noise amplifier nonlinearities and phase noise, which limit the spectrum sensing capabilities. In this paper, we investigate the joint effects of RF impairments on energy detection based spectrum sensing for CR systems in multi-channel environments. In particular, we provide novel closed-form expressions for the evaluation of the detection and false alarm probabilities, assuming Rayleigh fading. Furthermore, we extend the analysis to the case of CR networks with cooperative sensing, where the secondary users suffer from different levels of RF imperfections, considering both scenarios of error free and imperfect reporting channel. Numerical and simulation results demonstrate the accuracy of the analysis as well as the detrimental effects of RF imperfections on the spectrum sensing performance, which bring significant losses in the spectrum utilization.
We propose an adaptive transmission technique for free space optical (FSO) systems, operating in atmospheric turbulence and employing subcarrier phase shift keying (S-PSK) intensity modulation. Exploiting the constant envelope characteristics of S-PSK, the proposed technique offers efficient utilization of the FSO channel capacity by adapting the modulation order of S-PSK, according to the instantaneous state of turbulence induced fading and a pre-defined bit error rate (BER) requirement. Novel expressions for the spectral efficiency and average BER of the proposed adaptive FSO system are presented and performance investigations under various turbulence conditions and target BER requirements are carried out. Numerical results indicate that significant spectral efficiency gains are offered without increasing the transmitted average optical power or sacrificing BER requirements, in moderate-to-strong turbulence conditions. Furthermore, the proposed variable rate transmission technique is applied to multiple input multiple output (MIMO) FSO systems, providing additional improvement in the achieved spectral efficiency as the number of the transmit and/or receive apertures increases.
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