Nestor D. Chatzidiamantis

On the Distribution of the Sum of Gamma-Gamma Variates and Applications in RF and Optical Wireless Communications

The Gamma-Gamma (Γ Γ ) distribution has recently attracted the interest of the research community due to its involvement in various communication systems. In the context of RF wireless communications, Γ Γ 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 Γ Γ 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 Γ Γ variates is required. In this paper, we present a novel and simple closed-form approximation for the distribution of the sum of independent, but not necessarily identically distributed Γ Γ variates. It is shown that the probability density function (PDF) of the Γ Γ sum can be efficiently approximated either by the PDF of a single Γ Γ distribution, or by a finite weighted sum of PDFs of Γ Γ 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.

Adaptive Subcarrier PSK Intensity Modulation in Free Space Optical Systems

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, turbulence models, 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, especially 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.

Generalized Maximum-Likelihood Sequence Detection for Photon-Counting Free Space Optical Systems

We investigate detection methods for on-off keying (OOK) photon-counting Free Space Optical (FSO) systems in the presence of turbulence-induced fading, assuming no channel state information at the receiver. To recover the performance loss which is associated with symbol-by-symbol detection in such a scenario, we consider sequence detection techniques, exploiting the temporal correlation of the FSO channel. Due to its high complexity in the calculation of its metric, optimal maximum likelihood sequence detection (MLSD) is infeasible for most practical purposes. Hence, we propose a suboptimal low-complexity detection rule, which is based on the generalized maximum-likelihood sequence estimation. The proposed scheme allows the detection of sequence lengths that are prohibitive for conventional MLSD, without using any kind of channel knowledge. Monte Carlo simulation results show its performance to be very close to the optimum for large sequence lengths and various fading models.

On the Capacity of Generalized-

This correspondence explores the ergodic capacity of multiple-input multiple-output (MIMO) systems operating in generalized- K fading conditions. Using some recent results on majorization theory, we derive an analytical capacity bound which is applicable for arbitrary values of the signal-to-noise ratio (SNR) and number of antenna elements. In addition, we deduce simple bound approximations in the high-SNR regime and demonstrate that the effects of small and large-scale fading are decoupled. A similar statistical analysis is carried out for MIMO channels under K-fading, which represents a special case of generalized-K fading that can be tackled via the Wishart matrix theory. The implications of the model parameters on the bound performance are also investigated via Monte Carlo simulations.

K

This paper provides a systematic characterization of Zero-Forcing (ZF) detectors over multiple-input multiple-output (MIMO) channels that experience both small and large-scale fading. In particular, we consider the generic K distribution (Rayleigh/gamma distribution) to model the composite fading fluctuations and also assume the general case of semi-correlated small-scale fading. In the following, novel exact analytical expressions for the achievable sum rate are derived, followed by asymptotic expressions in the high and low Signal-to-Noise ratio (SNR) regimes. In these limiting cases, two common and insightful affine expansions are studied followed by new, closed-form upper and lower bounds on the sum rate that remain tight for all SNRs. In the second part of the paper, we present exact tractable expressions along with first-order expansions for the symbol error rate (SER) and outage probability; we also quantify the performance of ZF detectors in terms of diversity order and array (or coding) gain. The implications of the model parameters on the ZF detector performance are investigated via Monte-Carlo simulations which also validate the theoretical analysis.

Fading MIMO Channels

We propose the inverse Gaussian distribution, as a less complex alternative to the classical log-normal model, to describe turbulence-induced fading in free-space optical (FSO) systems operating in weak turbulence conditions and/or in the presence of aperture averaging effects. By conducting goodness of fit tests, we define the range of values of the scintillation index for various multiple-input multiple-output (MIMO) FSO configurations, where the two distributions approximate each other with a certain significance level. Furthermore, the bit error rate performance of two typical MIMO FSO systems is investigated over the new turbulence model; an intensity-modulation/direct detection MIMO FSO system with Q-ary pulse position modulation that employs repetition coding at the transmitter and equal gain combining at the receiver, and a heterodyne MIMO FSO system with differential phase-shift keying and maximal ratio combining at the receiver. Finally, numerical results are presented that validate the theoretical analysis and provide useful insights into the implications of the model parameters on the overall system performance.

ZF Detectors over Correlated K Fading MIMO Channels

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-by-symbol 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.

Inverse Gaussian Modeling of Turbulence-Induced Fading in Free-Space Optical Systems

In this paper, we propose a statistical channel model, named as Double-Weibull, to describe the irradiance fluctuations in moderate and strong turbulence for free-space optical (FSO) systems. The proposed stochastic model is based on the scintillation theory and derived via the product of two Weibull random variables. Closed-form expressions of probability and cumulative density functions are provided in terms of Meijers G-function. We also compare the new model with the classical gamma-gamma model and assess their accuracy via a set of simulations when both plane and spherical waves are considered. We finally evaluate the performance of an FSO system over the Double-Weibull turbulence channel and derive closed-form expressions for the bit-error rate, assuming intensity-modulation/direct detection with On-Off keying, and the outage probability.

Diversity Combining in Hybrid RF/FSO Systems with PSK Modulation

A major performance-limiting factor in terrestrial optical wireless (OW) systems is turbulence-induced fading. Exploiting the additional degrees of freedom in the spatial dimension, multiple laser transmitters combined with multiple receive apertures provide an effective solution for fading mitigation. Although multiple-input multiple-output (MIMO) OW systems have been extensively studied in recent years, most of these works are mainly limited to symbol-by-symbol decoding. MLSD exploits the temporal correlation of turbulence-induced fading and promises further performance gains. In this paper, we investigate MLSD for intensity-modulation/direct-detection MIMO OW systems over log-normal atmospheric turbulence channels. Even with a low-order modulation scheme such as OOK, which is typically used in OW systems, the complexity of MLSD might be prohibitive. We therefore present an iterative sequence detector based on the expectation-maximization (EM) algorithm. The complexity of the proposed algorithm is considerably less than a direct evaluation of the log-likelihood function, and it is independent of the channels fading statistics. The Monte Carlo simulation results demonstrate that the EM-based algorithm outperforms the symbol-by-symbol decoder and achieves a performance, which lies within 0.3 dB of that of the optimal MLSD.

New results on turbulence modeling for free-space optical systems

We present a novel and analytical lower bound on the ergodic capacity of distributed multiple-input multiple-output (D-MIMO) systems operating in composite Rayleigh/lognormal (RLN) fading and assuming double-sided spatial correlation. The proposed lower bound is applicable for finite number of antennas and remains tight across the entire Signal-to-Noise (SNR) regime. In addition, we perform a detailed low-SNR analysis that provides useful insights into the implications of the system parameters on MIMO capacity.