Nazih Hajri

A study on the statistical properties of double hoyt fading channels

This paper deals with a study on the statistical properties of narrowband amplify-and-forward relay fading channels for Hoyt multipath propagation environments. We consider the basic radio link topology, where only one fixed relay station is used for the amplification. In this case, the envelope of the signal received over the overall multipath channel is modeled by the so-called double Hoyt fading process. Considering this multipath propagation channel model, analytical expressions for the first and second order statistics are provided. Specifically, the mean value, variance, probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) of double Hoyt processes are derived. In addition, an expression for the PDF of the corresponding channel phase is also provided. Since the double Rayleigh fading channel is a special case of the double Hoyt model, it will be shown how the derived expressions can be reduced to the results known for the double Rayleigh fading channel. Moreover, the validity of the derived quantities is confirmed by computer simulations.

Performance analysis of binary DPSK modulation schemes over Hoyt fading channels

This paper presents a performance analysis of differential phase shift keying (DPSK) modulation schemes over Hoyt fading channels. Based upon the theory of DPSK modulation and a recently derived formula for the probability density function (PDF) of the differential phase between two Hoyt vectors contaminated by additive white Gaussian noise (AWGN), the bit error probability (BEP) for DPSK systems with noncoherent demodulation over Hoyt channels is analyzed. In the analysis, the correlation between adjacent bits is taken into account. The obtained theoretical results are fully validated first by reducing them to the corresponding known solutions for the Rayleigh fading distribution being a special case of the Hoyt distribution and second by comparing them with results obtained from computer simulations. The analysis of the BEP performance is illustrated by numerical examples given for the case of a mobile-to-mobile (M2M) Hoyt fading channel by considering various values of the fading channel characteristics and the system parameters. It is demonstrated that the Hoyt fading channel leads to poor BEP performance compared to the Rayleigh fading channel.

Statistical Analysis of the Channel Capacity Outage Intervals in Massive MIMO Systems with OSTBC over Rayleigh Fading Channels

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the outage intervals only over its initial part. By applying the asymptotic behavior of level crossings of Gaussian processes, an alternative expression, valid only for low capacity thresholds, is obtained, which, in turn, is applied to determine an approximate solution for the kth-order moments of the outage intervals. Also presented is the PDF of the so- called instantaneous capacity loss with respect to the average capacity. Simulation results have been shown to be in good agreement with the theoretical approximations, thereby confirming their validity. Although, the focus of the study is on massive MIMO systems, it has been observed that the approximations are accurate even for a moderate number of antennas such as the case of 4×4 MIMO-OSTBC systems.

Outage statistics for beckmann fading channels in non-isotropic scattering environments

In this paper, the outage statistics are studied for non-isotropic Beckmann fading channel model. Non-isotropic scattering generally results in an asymmetrical Doppler power spectral density (PSD). In this context, an expression for the outage probability (OP) (or equivalently the cumulative distribution function (CDF)) of the fading envelope is first derived. Then, the probability density function (PDF) of the rate of change of the fading envelope is investigated. Thereafter, an expression for the average rate of outages (ARO) (or equivalently the level-crossing rate (LCR)) is provided. Finally, by making use of the analytical results of the ARO and OP, an expression for the average duration of outages (ADO) (or equivalently the average duration of fades (ADF)) is attained. The obtained results, which are given in the form of finite-range integrals that can efficiently be computed numerically, are verified to include a variety of already known expressions for models that are special cases of the Beckmann model. Numerical and simulation results are provided to verify the validity of the derivations and to analyze the effect of the fading parameters on the obtained metrics.

On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels

In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are supposed to be symmetric about the carrier frequency. Under these fading conditions, we derive first an expression for the joint probability density function (jpdf) of the phase process and its rate of change. Capitalizing on this jpdf formula, we then investigate the probability density function (pdf) and cumulative distribution function (cdf) of random FM noise. Moreover, the average crossing rate of phase processes, as well as that of the Laplacian distributed in-phase and quadrature components of the complex channel gain, are obtained. Aside from the aforementioned statistics, we also provide exact expressions for the pdf, cdf, and second-order moment of the random FM noise at the output of a selection combiner, operating on independent and identically distributed (i.i.d.) branches. The validity of the analysis has been carried out by reducing the derived expressions to already-known results for single Rayleigh channels and by comparing our analytical results with the corresponding simulation results.

Level-Crossing Rate and Average Duration of Fades in Non-Isotropic Hoyt Fading Channels with Applications to Selection Combining Diversity

In this paper, we investigate the second-order statistics of Hoyt fading channels under non isotropic scattering scenarios. Assuming an asymmetrical Doppler power spectral density (PSD), we derive, in the form of single finite-range integrals, expressions for the level-crossing rate (LCR) and average duration of fades (ADF). These new results are then applied to obtain the LCR and ADF of selection combining (SC) diversity over non-isotropic Hoyt channels. In addition to their importance for studying the system performance and characterizing the dynamic behavior of multipath fading channels, the formulas derived are general in that they can be applied to many non-isotropic scattering situations. Furthermore, they are shown to unify some existing results for Rayleigh and Hoyt channels. The validity of the analytical expressions is verified by means of computer simulations where a mobile-to-mobile (M2M) propagation scenario is considered in which the angle of departure (AOD) and angle of arrival (AOA) of multipath components are both described by the von Mises distribution.

On the First- and Second-Order Statistics of Selective Combining over Double Nakagami-m Fading Channels

This paper studies the statistical properties of selective combining (SC) diversity schemes over double Nakagami-m fading channels. It is assumed that all diversity branches follow independent and identically distributed (i.i.d.) double Nakagami-m fading processes, where the serial concatenated Nakagami-m processes making up the double Nakagami-m fading branches are assumed to be independent, but not necessarily identically distributed. Starting from already known statistics on double Nakagami-m processes, analytical expressions are derived for the cumulative distribution function (CDF), probability distribution function (PDF), level- crossing rate (LCR), and average duration of fades (ADF) of SC diversity schemes. A general expression is derived for the moments of the instantaneous signal-to-noise ratio (SNR). By using the general expression, we study the mean SNR, amount of fading (AoF), and the diversity gain. The derived expressions include also the corresponding results for double Rayleigh, double one-sided Gaussian, and one-sided Gaussian×Rayleigh channels as special cases. A good agreement is observed between theory and simulation, which confirms the validity of the obtained analytical expressions.

On the statistical properties of selection combining cooperative diversity over double Rice fading channels

This paper investigates the statistical properties of selection combining (SC) cooperative diversity over double Rice narrow-band fading channels under the transparent or amplify-and-forward (AF) strategy. It is assumed that the source, the destination, and relay stations are all equipped with single antenna. The Doppler power spectral density, associated with each of the double Rice fading processes, is considered to be symmetrical about the carrier frequency. Under the above conditions, analytical integral expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the SC fading envelopes. Also, expressions for the level crossing rate (LCR) as well as the average duration of fades (ADF) are determined. For some cases, the integral expressions are shown to be approximated using the Laplaces method of integration. The approximations are verified to be accurate when the number of relay stations is large. The obtained results include those corresponding to the double Rayleigh and combined Rayleigh×Rice models as special cases of the double Rice fading channel. The validity of all the presented theoretical results are checked by computer simulations.

A Study on the Phase Crossing Statistics and Random FM Noise in M2M Double Rayleigh Fading Channels

In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in mobile-to-mobile (M2M) double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are assumed to be symmetric about the carrier frequency. Under these fading conditions, we derive at first an expression for the joint probability density function (JPDF) of the phase process and its rate of change, i.e., random FM noise. Second, and based on this JPDF formula, we investigate the probability density function (PDF) and cumulative distribution function (CDF) of random FM noise. Moreover, the average crossing rate of phase processes as well as that of the Laplace distributed inphase and quadrature components of the channel complex gain are obtained. It is found that the presented analytical expressions encompass known results corresponding to the case of single Rayleigh fading channels (unlike the case of the amplitude fading where the statistics of single scattering channels cannot, in general, be attained from those of double fading processes). For the verification of the validity and accuracy of the presented theoretical expressions, we compare them with those ones obtained by means of computer simulations. Excellent agreements are shown between theoretical and simulation quantities.

BEP performance of M2M communications over frequency flat double Hoyt fading channels

The performance analysis of mobile-to-mobile (M2M) radio communications over double Hoyt fading channels perturbed by additive white Gaussian noise (AWGN) is considered. First, the probability density function (PDF) of the instantaneous signal-to-noise ratio (SNR) per bit is derived under the assumption that the fading channel is a concatenation (product) of two independent but not necessarily identically distributed Hoyt processes. Then, an expression for the bit error probability (BEP) is investigated for several modulation schemes commonly used in wireless communication systems. In the derivation, the underlying propagation channel is assumed to be slowly varying and having the frequency-flat fading characteristics. Numerical results, considering the impact of the fading severity on the BEP, are presented. Furthermore, the validity of the theoretical results is checked by means of computer simulations for some of the modulation schemes used in the analysis. The obtained BEP expression is general and includes, as special cases, results corresponding to the channel combinations given by Rayleigh×Hoyt, Rayleigh×one-sided Gaussian, Hoyt×one-sided Gaussian, double one-sided Gaussian, and double Rayleigh fading channels.