Analysis of the level-crossing rate and average duration of fades of WSSUS channels

Studies of the level-crossing rate (LCR) and the average duration of fades (ADF) are so far only devoted to stochastic processes being a function of one independent variable, which is usually time or in some few cases frequency. In this paper, we study the LCR (ADF) of wide-sense stationary uncorrelated scattering (WSSUS) processes in the time-frequency domain. A closed-form solution will be derived for the so-called time-frequency LCR (ADF) of the absolute value of the time-variant transfer function (TVTF) of WSSUS processes. It is shown that the LCR (ADF) is circularly symmetric in the normalized time-frequency domain. The derived time-frequency LCR contains the time LCR and frequency LCR…

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 s…

Performance Analysis of M-DPSK Modulation over Fast-Hoyt Fading Channels under Non-Isotropic Scattering Conditions

In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range …

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 durati…

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 p…

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 rand…

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

On the statistical properties of the capacity of double Hoyt fading channels

The statistical properties of the capacity of narrowband double Hoyt fading channels are studied. Toward this end, analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous channel capacity process are derived. Furthermore, for the characterization of the dynamical behavior of the time-varying channel capacity, expressions are provided for the level-crossing rate (LCR) and the average duration of fades (ADF). Since the double Rayleigh fading channel is a special case of the double Hoyt model, it is shown that the derived expressions can be reduced to the corresponding results already known for the capacity of the double…

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 situati…

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 …

Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems

In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average…