Outage Probability Curves Research Articles

On the Statistics of the Maximum of α-F Variates and Their Applications

In this letter, a statistical characterization is provided for the instantaneous signal-to-noise ratio (SNR) resulting from the maximum of independent and non-identically distributed random variables characterized by the <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> distribution. Based on this study, new expressions are derived for the probability density function, cumulative distribution function and moment generating function of the resulting instantaneous SNR. Asymptotic expressions are also provided. The aforementioned new expressions can be used to determine metrics for the performance evaluation of multiple branch selection combining based receivers. In this context, bit error probability and outage probability curves are presented for different parameters that characterize the channel. All the expressions are corroborated by Monte-Carlo simulations.

Outage Probability of the Product of Two Beaulieu–Xie, $\eta$–$\mu$, $\kappa$–$\mu$, or $\alpha$–$\mu$ Random Variables

In this letter, new and simple expressions are presented for the outage probability (OP) of the product of two Beaulieu–Xie, $\eta$ – $\mu$ , $\kappa$ – $\mu$ , or $\alpha$ – $\mu$ random variables. The OP expressions obtained in this letter are determined using the Gauss–Laguerre quadrature, and are corroborated by computational simulations performed with the Monte Carlo method. Several theoretical, and simulated OP curves are shown, with a great adherence between the curves, considering different values of the parameters that characterize the fading distributions.

Performance analysis of underwater wireless optical communication systems over a wide range of optical turbulence

The propagation of optical signal under water is affected by three major degrading phenomena, namely absorption, scattering, and turbulence. The statistical distribution of turbulence-induced fading though has not yet been well characterized. In this paper, in order to investigate the effect of different probability density functions (PDFs) proposed for the statistical behavior of fading under water, we evaluate the performance of underwater wireless optical communication (UWOC) systems with respect to the well-known statistical distributions for the optical turbulence such as lognormal, Gamma, K, Weibull, and exponentiated Weibull distributions. For the sake of accuracy, we adopt a general channel model where both absorption and scattering effects are appropriately taken into account based on the Monte Carlo (MC) numerical method, and consider the fading effect as a multiplicative coefficient with the aforementioned PDFs. We derive the closed-form expressions for the average bit error rate (BER) and outage probability, as the system performance metrics, with respect to all of the channel degrading effects and the aforementioned statistical distributions. Our results demonstrate that as the turbulence strength, measured by the scintillation index value, increases, the gap between the system performance predicted by different statistical distributions becomes more, and this gap mainly appears in the form of changing the slope of average BER or outage probability curves versus the average transmitted power per bit. This further emphasizes the importance of accurate channel models for the design of UWOC systems.

Optimization of Scalable Broadcast for a Large Number of Antennas

In this paper, for a system incorporating a large number of antennas, we address the optimal space–time coding of multimedia scalable sources, which require unequal target error rates in their bitstream. First, in terms of the number of antennas, we analyze the behavior of the crossover point of the outage probability curves for the vertical Bell Laboratories space–time (V-BLAST) architecture with a linear or a maximum-likelihood receiver, and orthogonal space–time block codes (OSTBCs). We prove that, as the number of antennas increases with the transmission data rate fixed, the crossover point in outage probability monotonically decreases. This holds for any data rate employed by the system and is valid over propagation channels such as spatially correlated Rayleigh or Rician fading channels, as well as independent and identically distributed Rayleigh channels. We next show that, over such propagation channels with a large number of antennas, those analytical results can be used to simplify the computational complexity involved with the optimal space–time coding of a sequence of scalable packets, with no performance degradation.

Scalable Source Transmission with Unequal Frequency Reuses in MIMO Cellular Networks

This paper studies the optimal frequency reuse for the transmission of multimedia scalable sources, such as embedded images or scalable video, which need unequal error protection or unequal transmission rates in the bitstream. First, we analyze the crossover of the outage probabilities for full and partial frequency reuse cases in terms of the data rate. We prove that we can find a crossover of the outage probability curves for a data rate lower than a given threshold, which is a function of the parameters such as the partial frequency reuse factor and the user location in the cell. Moreover, the crossover point in the signal-to-noise ratio (SNR) is a strictly increasing function of the data rate. On the other hand, for a data rate higher than or equal to the threshold, there is no crossover; for all SNRs, the outage probability of full-frequency reuse is lower than that of partial-frequency reuse. The results are proven for the arbitrary location of a user in a cell, and for an arbitrary partial frequency reuse factor. Furthermore, the results hold, regardless of the numbers of transmit and receive antennas in the multiple-input multiple-output systems of orthogonal space-time block codes, and of the vertical Bell Labs space-time architecture with a zero-forcing linear receiver. Based on the analysis, we propose unequal-frequency reuse for the optimal transmission of scalable sources. The numerical results show that the peak-SNR performance improves when a sequence of scalable packets is transmitted at the subbands governed by unequal-frequency reuse in cellular networks.

Optimization of Multimedia Progressive Transmission Over MIMO Channels

This paper studies the optimal transmission of multimedia progressive sources, which require unequal target error rates in their bitstream, over multiple-input–multiple-output (MIMO) channels. First, we derive the information outage probability expression of a space–time code for an arbitrarily given piecewise-linear diversity–multiplexing tradeoff (DMT) function and the conditions for the existence of a crossover point of the information outage probability curves of the space–time codes. We prove that as long as the crossover point of the outage probabilities exists, as spectral efficiency increases, the crossover point in the signal-to-noise ratio (SNR) monotonically increases, whereas that of the outage probability monotonically decreases. This analysis can be applied to any space–time code, receiver, and propagation channel with a given DMT function. As a specific example, we analyze the two-layer diagonal Bell Labs space–time architecture (D-BLAST) with a group zero-forcing receiver, the vertical BLAST (V-BLAST) with a minimum mean-square error receiver, and orthogonal space–time block codes (OSTBCs), and prove the monotonic behavior of the crossover point for those codes. Based on that, with respect to D-BLAST, V-BLAST, and OSTBC, we derive a method for the optimal space–time coding of a sequence that contains numerous progressive packets. We show that by employing the optimization method rather than exhaustive search, the computational complexity involved with optimal space–time coding can be exponentially reduced without losing any peak SNR performance.

The Bottleneck Effect of Rician Fading in Dissimilar Dual-Hop AF Relaying Systems

New infinite-series expressions are obtained for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) of dual-hop amplify-and-forward (AF) relaying systems operating over Rician fading channels and dissimilar dual-hop AF systems operating over mixed Nakagami- $m$ /Rician fading channels. Precise analytical solutions for outage probability, as well as precise single-integral solutions for the ergodic capacity and the average symbol error probability, are obtained. Simulation results are used to verify the solutions obtained. It is shown that the limiting slopes of the average symbol error probability curves and the outage probability curves are not affected by the Rician fading parameter in contrast to the case of Nakagami- $m$ fading links. For the case of mixed fading links, the exact performance metrics are compared to performance bounds in the literature. It is shown that the existing performance bounds are not tight for medium ranges of SNR. The effects of the Rician and Nakagami- $m$ fading parameters on the system performance are also studied. It is shown that, while increasing the Rician parameter results in a notable SNR gain, increasing the Nakagami- $m$ parameter results in a negligible improvement in the system performance.

Optimum Power Randomization for the Minimization of Outage Probability

The optimum power randomization problem is studied to minimize outage probability in flat block-fading Gaussian channels under an average transmit power constraint and in the presence of channel distribution information at the transmitter. When the probability density function of the channel power gain is continuously differentiable with a finite second moment, it is shown that the outage probability curve is a nonincreasing function of the normalized transmit power with at least one inflection point and the total number of inflection points is odd. Based on this result, it is proved that the optimum power transmission strategy involves randomization between at most two power levels. In the case of a single inflection point, the optimum strategy simplifies to on-off signaling for weak transmitters. Through analytical and numerical discussions, it is shown that the proposed framework can be adapted to a wide variety of scenarios including log-normal shadowing, diversity combining over Rayleigh fading channels, Nakagami-m fading, spectrum sharing, and jamming applications. We also show that power randomization does not necessarily improve the outage performance when the finite second moment assumption is violated by the power distribution of the fading.

Throughput-reliability tradeoff in decode-and-forward cooperative relay channels: A network information theory approach

Cooperative transmission protocols are always designed to achieve the largest diversity gain and the network capacity simultaneously. The concept of diversity-multiplexing tradeoff (DMT) in multiple input multiple output (MIMO) systems has been extended to this field. However, DMT constrains a better understanding of the asymptotic interplay between transmission rate, outage probability (OP) and signal-to-noise ratio. Another formulation called the throughput-reliability tradeoff (TRT) was then proposed to avoid such a limitation. By this new rule, Azarian and Gamal well elucidated the asymptotic trends exhibited by the OP curves in block-fading MIMO channels. Meanwhile they doubted whether the new rule can be used in more general channels and protocols. In this paper, we will prove that it does hold true in decode-and-forward cooperative protocols. We deduce the theoretic OP curves predicted by TRT and demonstrate by simulations that the OP curves will asymptotically overlap with the theoretic curves predicted by TRT.

Detection Outage and Detection Diversity in a Homogeneous Distributed Sensor Network

The distributed detection problem over a binary target is considered with wireless sensors sending local decisions to a fusion center over slow-fading orthogonal multiple access channels, where the J-divergence between the distributions under different hypotheses is used as the performance criterion. Given the slow-fading channels between the sensors and the fusion center, two new concepts called detection outage and detection diversity are introduced to quantify the long-term system performance, where the detection outage probability is defined as the probability that the instantaneous J-divergence is smaller than a certain threshold. Based on the detection outage probability, detection diversity order is defined as the slope of the outage probability curve (versus system power consumption) when things are plotted in logarithm domain. It is shown that even with a simple uniform transmission strategy, full detection diversity can be achieved on the order of K with K the total number of sensors in the network. We further show that if the transmission power is optimized across sensors, an adaptive power gain can be achieved in addition to the full diversity gain.

The Throughput–Reliability Tradeoff in Block-Fading MIMO Channels

We build on Zheng and Tse's elegant formulation of diversity-multiplexing tradeoff (DMT) to provide a better understanding of the asymptotic interplay between transmission rate, error probability, and signal-to-noise ratio (SNR) in block-fading multiple-input multiple-output (MIMO) channels. In particular, we identify the limitation imposed by the notion of multiplexing gain and develop a new formulation called the throughput-reliability tradeoff (TRT), that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of block-fading MIMO channels.

Outage probability for lognormal-shadowed Rician channels

A new general outage probability expression for a Rician signal received among L Rician interferers is derived. This result is shown to cover previous published expressions involving Rayleigh signal/interferers as special cases. A new method is then applied to further extend the result to include the effect of lognormal shadowing on the outage probability (for microcellular mobile radio systems in Rician/Rician fading environments). New Rician/Rician outage probability curves against the normalized reuse distance and cluster size with and without lognormal shadowing effect are presented and discussed.

BER and outage probability performance of /4 DQPSK for Rice–lognormal channels

A new general expression is derived for the bit error rate (BER) of π/4 DQPSK in a channel modelled by a combination of Rice and lognormal statistics. This Rice–lognormal channel model is shown to cover other well known channel models such as the Suzuki and the Loo models. New BER and outage probability curves are presented and discussed.

Spectrum efficiency for log-normal shadowed Rician/Rician channels

Analysis is carried out on the spectrum efficiency in a microcellular mobile radio environment using a fourth power path loss law. A new technique for evaluating outage probabilities for channels affected by Rician fast fading and log-normal shadowing is presented, and new spectrum efficiency against outage probability curves for these channels are obtained and discussed.

Outage probability for a Rician signal in L Rician interferers

A new general outage probability expression for a Rician signal received among L Rician interferers is derived. This result is shown to cover previously published expressions involving Rayleigh signal/interferers as special cases. New Rician/Rician outage probability curves are presented and discussed.