In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

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Fading channels: information-theoretic and communications aspects

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

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An overview of limited feedback in wireless communication systems

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.

Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels: A Stochastic Geometry Approach

In this paper, we consider the transmission of confidential information over a $\kappa $ – $\mu $ fading channel in the presence of an eavesdropper who also experiences $\kappa $ – $\mu $ fading. In particular, we obtain novel analytical solutions for the probability of strictly positive secrecy capacity (SPSC) and a lower bound of secure outage probability (SOP $^{L}$ ) for independent and non-identically distributed channel coefficients without parameter constraints. We also provide a closed-form expression for the probability of SPSC when the $\mu $ parameter is assumed to take positive integer values. Monte-Carlo simulations are performed to verify the derived results. The versatility of the $\kappa $ – $\mu $ fading model means that the results presented in this paper can be used to determine the probability of SPSC and SOP $^{L}$ for a large number of other fading scenarios, such as Rayleigh, Rice (Nakagami- $n$ ), Nakagami- $m$ , One-Sided Gaussian, and mixtures of these common fading models. In addition, due to the duality of the analysis of secrecy capacity and co-channel interference (CCI), the results presented here will have immediate applicability in the analysis of outage probability in wireless systems affected by CCI and background noise (BN). To demonstrate the efficacy of the novel formulations proposed here, we use the derived equations to provide a useful insight into the probability of SPSC and SOP $^{L}$ for a range of emerging wireless applications, such as cellular device-to-device, peer-to-peer, vehicle-to-vehicle, and body centric communications using data obtained from real channel measurements.

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Secrecy Capacity Analysis Over $\kappa $ – $\mu $ Fading Channels: Theory and Applications

Unified exact average capacity results for L-branch coherent diversity receivers including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel generic framework for the capacity analysis of $L$-branch EGC/MRC over generalized fading channels. The framework is used to derive new results for the Gamma shadowed generalized Nakagami-m fading model which can be a suitable model for the fading environments encountered by high frequency (60 GHz and above) communications. The mathematical formalism is illustrated with some selected numerical and simulation results confirming the correctness of our newly proposed framework.

A Unified MGF-Based Capacity Analysis of Diversity Combiners over Generalized Fading Channels

The channel capacity in the presence of Gaussian noise is the same whether the signal suffers fluctuations or not, so high gains may be expected in the fading case. The main tool considered towards this goal is rotation of constellations in signal space, as applied by Boutros (1996) to lattices.

J. Boutros

Papers

On communication over fading channels