Showing papers on "Fading distribution published in 2007"

The $\alpha$ - $\mu$ Distribution: A Physical Fading Model for the Stacy Distribution

Abstract: This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution-the alpha-mu distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated alpha-mu variates are obtained, and they are directly related to the physical fading parameters

Relay-Assisted Free-Space Optical Communication

Abstract: In this paper, we present relay-assisted transmission as a powerful fading mitigation tool for free-space optical systems operating in atmospheric turbulence channels. We study both serial (i.e., multi-hop transmission) and parallel (i.e., cooperative diversity) relaying encoupled with amplify-and-forward and decode-and-forward modes. We consider an aggregated channel model which takes into account both path-loss and turbulence-induced log-normal fading. Since fading variance is distance-dependent in free-space optical systems, relay-assisted transmission takes advantage of the resulting shorter hops and yields significant performance improvements. We derive outage probability of the relaying schemes under consideration which are further confirmed through Monte-Carlo simulations. Our outage probability analysis demonstrates that an impressive performance improvement of 18.5 dB is possible with the use of a single relay at a target outage probability of 10-6.

$N{\ast}$ Nakagami: A Novel Stochastic Model for Cascaded Fading Channels

Abstract: A generic and novel distribution, referred to as Nakagami, constructed as the product of N statistically independent, but not necessarily identically distributed, Nakagami-m random variables (RVs), is introduced and analyzed. The proposed distribution turns out to be a very convenient tool for modelling cascaded Nakagami-m fading channels and analyzing the performance of digital communications systems operating over such channels. The moments-generating, probability density, cumulative distribution, and moments functions of the N *Nakagami distribution are developed in closed form using the Meijer's G -function. Using these formulas, generic closed-form expressions for the outage probability, amount of fading, and average error probabilities for several binary and multilevel modulation signals of digital communication systems operating over the N *Nakagami fading and the additive white Gaussian noise channel are presented. Complementary numerical and computer simulation performance evaluation results verify the correctness of the proposed formulation. The suitability of the N *Nakagami fading distribution to approximate the lognormal distribution is also being investigated. Using Kolmogorov--Smirnov tests, the rate of convergence of the central limit theorem as pertaining to the multiplication of Nakagami-m RVs is quantified.

A case for considering hyper-Rayleigh fading channels

Abstract: This work is motivated by the problem of characterizing small-scale radio propagation environments for wireless sensor networks. If sensors are statically deployed near the ground or within structures, temporal fading may not exist but the channel may nevertheless experience severe frequency-selective behavior. The work presents real-world, frequency-selective fading data measured for in-vehicle wireless sensor applications. This fading data often exhibit statistics more severe than predicted by the Rayleigh fading model; a scenario referred herein as to as being hyper-Rayleigh. A two-ray, small-scale model is proposed as a new worst-case for this application space.

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

Abstract: We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation.

Diversity reception over generalized-K (KG) fading channels

Abstract: A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.

Ergodic and Outage Capacities of Spectrum-Sharing Systems in Fading Channels

Abstract: In this fast growing technology world, where communications play a major rule for connecting people and machines together, the growth in wireless applications have caused an increasing demand for gaining access to the radio spectrum. However, the outdated spectrum utilization policies, imposed by the regulatory bodies in the past century, have caused the spectrum to look over-saturated. Recently, the concept of opportunistic spectrum access has been introduced as a tool to overcome the scarcity of the spectrum. The latter technology offers a tremendous potential to improve the utilization of the radio spectrum by implementing an efficient sharing of the licensed spectrum, whereby a secondary user may utilize the primary user's licensed band as long as its interference to the primary receiver remains below a tolerable level. In this paper, we investigate the capacity gains offered by this spectrum-sharing approach in Rayleigh fading environments. In particular, we derive the fading channel capacity of a secondary user subject to both average and peak received-power constraints at the primary's receiver. Considering both constraints, we derive the ergodic and outage capacities along with their optimum power allocation policies for Rayleigh flat-fading channel, and provide closed-form expressions for these capacity metrics. Furthermore, numerical simulations are conducted to corroborate our theoretical results.

An Additive Model as a Physical Basis for Shadow Fading

Abstract: Received signal power in mobile wireless communications is typically modeled as a product of three factors: distance-dependent average path loss law, variation in the local mean power (shadow fading), and small-scale fading. Of these three factors, the least investigated is the shadow fading, which is usually explained as a result of multiplication of large number of random attenuating factors in the radio channel. In this paper, the authors propose an additive model as an alternative physical basis for shadow fading within an "extended local area" where path loss is constant. Starting from a sum-of-sinusoids signal model, they show that under mild statistical assumptions on the powers of the sinusoids, the resulting signal power will have approximately Gaussian distribution in logarithmic scale. A cluster-based model for shadow fading emerges as a special instance of the general result. They present simulation and measurement results that support their theoretical findings. The new physical basis for shadow fading also provides insights into simulation and modeling of radio channels

Diversity and Multiplexing Tradeoff in General Fading Channels

Abstract: The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance

Evaluation of Nakagami fading behaviour based on measurements in urban scenarios

Abstract: It is well known that the short-term fading conditions of the received envelope in wireless communications channels can be modelled by means of the Nakagami distribution. The value of the m parameter, also called shape factor , indicates the severity of multipath fading, and is a measure of channel quality, making its estimation necessary in many applications. In this letter, a range of possible values of the m parameter based on the analysis of a measurements campaign in urban scenarios is presented.

Measurements and Statistical Analysis of On-Body Channel Fading at 2.45 GHz

Abstract: The fading of an on-body transmission channel at 2.45 GHz is investigated. For the first time a large amount of data has been gathered in practical environments, for realistic activities, and has been subject to statistical analysis. It is clear that significant variations of the path gain and fading can occur due to the movements of body. Extensive statistical analysis has shown that fading in on-body channels is a non stationary process. This letter presents results of a number of significant statistical parameters, including level crossing rate and average fade duration.

On the Secrecy Capabilities of ITU Channels

Abstract: We consider the secrecy inherent in the reciprocal nature of multipath fading channels and present a technique to generate a shared perfectly secret key by two terminals observing a multipath fading channel. Using this technique we quantify the secrecy that can be generated from ITU cellular channels for the 2 GHz frequency range.

Sum of Squared Shadowed-Rice Random Variables and its Application to Communication Systems Performance Prediction

Abstract: The distribution of the sum of non-negative random variables plays an essential role in the performance analysis of diversity schemes for wireless communications over fading channels. While for common fading models such as the Rayleigh, Rice, and Nakagami, the performance of diversity systems is well understood, a minor attention has been devoted to the shadowed-Rice (SR) case, namely a Rice fading channel with fluctuating (e.g. random) Line of Sight (LOS) component. Indeed, the analytical performance evaluation of diversity systems on SR fading channels requires the availability of handy expressions for the distribution of the combined received power. To this end, the rationale of this paper is twofold: first, to evaluate the distribution of the sum of SR random variables, both for the case of independent as well as correlated LOS components, and then to carry out an extensive performance analysis of maximal ratio combining (MRC) detection scheme on SR fading channels.

Measurement of Large-Scale Cluster Power Characteristics for Geometric Channel Models

Abstract: Directional urban radio channel measurements are analyzed in this paper. The mean powers, the shadow fading, and the lifetimes of individual propagation clusters extracted from the measured data are studied. The cluster shadow fading is an input parameter of several directional channel models, but measured values for the fading have not been published previously. Also, measured numbers of strong, significant propagation clusters are essential for the channel models.

Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

Abstract: A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.

Higher Order Statistics for Lognormal Small-Scale Fading in Mobile Radio Channels

Abstract: Lognormal small-scale fading has recently been reported in a number of indoor propagation studies. However, until now, no method of generating higher order statistics for this distribution in short-term fading channels has appeared in the literature. In this letter, we present a lognormal fading model which is based on the Bessel-derived autocorrelation function frequently used in Rayleigh-, Rice-, and Nakagami-fading simulators. In addition, we present exact, closed-form expressions for the level crossing rate and average fade duration (AFD) observed in lognormal small-scale fading channels for arbitrary and . The accepted ability of the lognormal distribution to approximate Nakagami second-order statistics for high values of the Nakagami- parameter is used in combination with simulated data, generated using a rank-matching approach, to validate the new model. Theoretical second-order distributions are also compared with empirical measurements obtained for mobile indoor on-body propagation channels. In all cases, the theoretical equations and test data are in good agreement.

An experimental study of exploiting multipath fading for robot communications

Abstract: A simple approach for mobile robots to exploit multipath fading in order to improve received radio signal strength (RSS), is presented. The strategy is to sample the RSS at discrete points, without deviating too far from the desired position. We first solve the problem of how many samples are needed for given communications performance and how they should be spaced. Second, we propose a circular and a grid trajectory for sampling and give lower bounds on how many samples they will yield. Third, we estimate the parameters of our strategy from measurements. Finally we demonstrate the validity of our analysis through experiments.

Performance Analysis of Dual-Hop Relaying Communications Over Generalized Gamma Fading Channels

Abstract: In this paper, we present closed form expressions for tight lower bounds of the performance of dual-hop non- regenerative relaying over independent non-identical generalized gamma fading channels. The generalized gamma distribution is very versatile and accurately approximates many of the commonly used channel models for multi-path, shadow, and composite fading. Since it is hard to find a closed form expression for the probability density function (PDF) of the signal-to-noise ratio (SNR) for the generalized gamma distribution, we use an approximate value instead. Novel closed form expressions for the PDF, outage probability and the moments of the approximate value of the SNR at the destination are derived. Also, the average SNR and amount of fading are determined. Moreover, closed form expressions (in terms of the tabulated Meijer's G-function) are found for the average symbol error probability (for several modulations schemes) as well as the Shannon capacity. It should be noted that the Meijer's G-function is widely available in many scientific software packages, such as MATHEMATICAreg and MAPLEreg. Finally, simulations results are also shown to verify the analytical results.

Performance of BPSK Pre-detection MRC Systems over Two-Wave with Diffuse Power Fading Channels

Abstract: The bit-error rate (BER) analysis for BPSK pre-detection maximal ratio combining (MRC) systems in two-wave with diffuse power (TWDP) fading is presented. In TWDP fading, the received signal is composed of two specular components in addition to the diffuse signal. The analysis shows that in TWDP fading, the BER of the MRC system is given by the weighted sum of the BERs of a number of MRC systems in Rician fading. The methodology used in the analysis is verified through simulation.

Accurate and efficient simulation of multiple uncorrelated Rayleigh fading waveforms

Abstract: Simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels often demands the generation of multiple uncorrelated Rayleigh fading waveforms. In this letter, two appropriate parameter computation methods, namely the method of exact Doppler spread (MEDS) and Lp -norm method (LPNM), for deterministic sum-of-sinusoids (SoS) channel simulators are investigated to guarantee the uncorrelatedness between different simulated Rayleigh fading processes. Numerical and simulation results show that the resulting deterministic SoS channel simulator can accurately and efficiently reproduce all the desired statistical properties of the reference model.

MIMO-OFDM Systems in the Presence of Phase Noise and Doubly Selective Fading

Abstract: In this paper, we analyze the effects of phase noise to multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems over doubly selective Rayleigh fading channels. Similar to single-antenna OFDM, MIMO-OFDM suffers from significant performance degradation due to phase noise and time-selective fading, which causes inter- carrier interference (ICI). We derive the expressions of carrier- to-interference and signal-to-interference-plus-noise ratios. After characterizing the common phase error (CPE) caused by phase noise and ICI caused by phase noise, as well as time-selective fading, we then derive a minimum mean-squared error-based scheme to mitigate the effect of both phase noise and time-selective fading. We also evaluate and compare the performances of various detection schemes combined with the proposed CPE mitigation scheme. Through numerical results, we examine the relative performances and the potential error floors of these detection schemes.

Sum-of-Sinusoids-Based Simulation of Flat Fading Wireless Propagation Channels Under Non-Isotropic Scattering Conditions

Abstract: This paper presents a modified version of the method of equal areas (MEA) for designing simulation models for frequency non-selective mobile fading channels under non- isotropic scattering conditions. The proposed method, called modified MEA (MMEA), is well suited for channel simulators based on a finite sum of complex sinusoids. The combination of the MMEA with the principle of set partitioning is also proposed here as an efficient way to improve the performance of the simulator and to reduce the computational costs. Such a combination results in a new parameter computation method called MMEA with set partitioning (MMEA-SP). The MMEA and the MMEA-SP are quite general and can be applied on any given distribution of the angle of arrival (AOA). However, to exemplify the good performance of both methods, it is assumed that the AOA follows the von Mises distribution. The obtained results demonstrate that the two proposed methods approximate the autocorrelation function (ACF) of non-isotropic scattering channels with high precision.

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

Abstract: A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.

Recursive Power Allocation in Gaussian Layered Broadcast Coding with Successive Refinement

Abstract: A transmitter without channel state information wishes to send a delay-limited Gaussian source over a slowly fading channel that has a finite number of discrete fading states. The source is coded in layers, with each layer successively refining the description in the previous one. These coded source layers are then superimposed and simultaneously transmitted to the receiver. The receiver decodes the layers that are supported by the realization of the channel, and combines the descriptions in the decoded layers to reconstruct the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the given number of source layers. For two layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For multiple layers, the overall expected distortion can be written as a set of recurrence relations, and the minimum expected distortion is found by recursively applying the two-layer optimization procedure at each recurrence step.

A Simple and Accurate Approximation to the SEP of Rectangular QAM in Arbitrary Nakagami-m Fading Channels

Abstract: Recently, Karagiannidis presented a closed-form solution for an integral which can be used to compute the average symbol error probability of general order rectangular quadrature amplitude modulation (QAM) in Nakagami-m fading channels with integer fading parameters. In this letter, using an accurate exponential bound for the Gaussian Q-function, we derive a simple approximate solution for that integral. In particular, the solution can be used to compute the average SEP of general order rectangular QAM over arbitrary Nakagami-m fading. Numerical results are presented to verify the accuracy of the solution

Optimum Pilot Symbol Assisted Modulation

Abstract: Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.

Severely Fading MIMO Channels: Models and Mutual Information

Abstract: In most wireless communications research, the channel models considered experience less severe fading than the classic Rayleigh fading case. In this work, however, we investigate MIMO channels where the fading is more severe. In these environments, we show that the coefficient of variation of the channel amplitudes is a good predictor of the link mutual information, for a variety of models. We propose a novel channel model for severely fading channels based on the complex multivariate t distribution. For this model, we are able to compute exact results for the ergodic mutual information and approximations to the outage probabilities for the mutual information. Applications of this work include wireless sensors, RF tagging, land-mobile, indoor-mobile, ground-penetrating radar, and ionospheric radio links. Finally, we point out that the methodology can also be extended to evaluate the mutual information of a cellular MIMO link and the performance of various MIMO receivers in a cellular scenario. In these cellular applications, the channel itself is not severely fading but the multivariate t distribution can be applied to model the effects of inter-cell interference.

On the Capacity of Generalized-K Fading Channels

Abstract: This paper investigates the capacity of generalized- K fading channels. This very general model describes accurately composite multipath/shadowing fading channels which are widely encountered in real-world environments. We derive closed-form expressions for three adaptive transmission techniques, namely, i) optimal rate adaptation with constant power, ii) optimal power and rate adaptation, and iii) channel inversion with fixed rate. The analytical expressions obtained match perfectly the results obtained by computer simulations. These expressions provide a good tool to assess the spectral efficiency of the aforementioned adaptive transmission techniques over composite channels.

The η-μ Joint Phase-Envelope Distribution

Abstract: This paper derives a simple and closed-form expression for the phase-envelope joint distribution of the η-μ distribution, a general fading model that includes the Hoyt and the Nakagami-m models as special cases. In the same way, the marginal distribution of the phase is also obtained. These analytical expressions reduce in an exact manner to those of the particular cases comprised by the η-μ distribution. Some plots illustrate the behavior of the phase for several fading conditions.

Error Performance of Rotated Phase Shift Keying Modulation over Fading Channels

Abstract: In this paper, the modulation diversity is used to improve the performance of M-PSK modulation over fading channels. Modulation diversity can be achieved by rotating the signal constellation and using component interleaving. We derive symbol error probability expressions for rotated uncoded M-PSK over Ricean fading channels and obtain optimal rotation angles for M-PSK (M = 2, 4, 8). We show that rotated signal constellations with component interleaving improve the performance of M-PSK significantly as compared to the unrotated one over Rayleigh and Ricean fading channels. For example, when the ratio of the direct path power to the multipath signal power, K is 0 and 10, 8 and 1.5 dB gains are obtained, respectively, at a symbol error probability of 10?3 for 8PSK modulation. We also show that as K gets larger, the gain obtained by the rotation rapidly decreases. We develop a new asymmetric 8PSK signal constellation obtained from two QPSK signal constellations that are optimally rotated by different angles. This asymmetric 8PSK and also the rotated 8PSK signal constellation together with component interleaving are applied to four-state trellis-coded schemes. Simulation results show that these new schemes provide good performance improvements over the original TCM schemes and previous relevant works over Rayleigh and Ricean fading channels.