Fluctuating Two-Ray Fading Research Articles

The Fluctuating Two-Ray Fading Model With Independent Specular Components

We introduce and characterize the independent fluctuating two-ray (IFTR) fading model, a class of fading models consisting of two specular components which fluctuate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">independently</i> , plus a diffuse component modeled as a complex Gaussian random variable. The IFTR model complements the popular fluctuating two-ray (FTR) model, on which the specular components are fully correlated and fluctuate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jointly</i> . The chief probability functions of the received SNR in IFTR fading, including the PDF, CDF and MGF, are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. Then, the IFTR model is empirically validated using multiple channels measured in rather diverse scenarios, including line of sight (LOS) millimeter-wave, land mobile satellite (LMS) and underwater acoustic communication (UAC), showing a better fit than the original FTR model and other models previously used in these environments. Additionally, the performance of wireless communication systems operating under IFTR fading is evaluated in closed-form in two scenarios: ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) exact and asymptotic bit error rate for a family of coherent modulations; and ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) exact and asymptotic outage probability.

Alternative Formulations for the Fluctuating Two-Ray Fading Model

We present two alternative frameworks for the statistical characterization and performance evaluation of the fluctuating two-ray (FTR) fading model which simplify previous approaches. The new formulations are based on the fact that the FTR fading distribution can be described, for arbitrary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , as an underlying Rician Shadowed (RS) distribution with continuously varying parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K_{r}$ </tex-math></inline-formula> (ratio of specular to diffuse power components), while for the special case of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> being an integer, it is demonstrated that the FTR fading model can be described in terms of a finite number of underlying squared Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> distributions. It is shown that any performance metric that is computed by averaging over the probability density function (PDF) of the FTR fading model can be expressed in terms of a finite-range integral over the corresponding performance metric for the simpler RS (for arbitrary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> ) or Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> (for integer <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> ) fading models, for which many results are available in closed-form. New expressions for some Laplace-domain statistics of interest are also obtained; these are used to analyze the outage probability of FTR fading under co-channel interference, as well as to obtain closed-form expressions for the main statistics of a composite wireless channel model encompassing FTR fading and shadowing.

Error analysis of SISO and dual-branch communications with generalized Gaussian noise over FTR fading channels

In this paper, we present error probability analysis for single-input single-output (SISO) and asymmetric dual-branch networks with additive white generalized Gaussian noise (AWGGN) over millimeter-wave (mmW) fluctuating two-ray (FTR) fading channels. Then, we examine the error probability evaluation of a SISO system with imperfect phase errors over mmW FTR fading channels. The probability density function (PDF) approach is employed for the error probability performance evaluation and the novel PDF of the asymmetric dual-branch system over Nakagami-m/mmW FTR fading channels is obtained. Specifically, closed-form expressions are derived for the error probability of the SISO and asymmetric dual-branch networks. The derived error expressions facilitate in effectively evaluating the performance of considered networks in the presence of AWGGN and imperfect phase noise with optimal fading parameters and modulation type. The theoretical derivations are extensively confirmed through exact simulations.

Performance of Remote Radio Unit Selection in Millimeter-Wave Distributed Antenna Systems Over Fluctuating Two-Ray Fading

Millimeter wave (mmWave) is a promising future wireless communication technology. To overcome the high path loss in mmWave band, distributed antenna systems (DASs) with each base station (BS) connecting to multiple remote radio units (RRUs) is a candidate solution. To better characterize the small-scale fading of mmWave channels, the fluctuating two-ray (FTR) was recently proposed. In this letter, we study the performance of RRU selection in mmWave DASs over the FTR fading. First, simplified closed-form expressions are, respectively, provided for the probability density function (PDF) and cumulative distribution function (CDF) of signal-to-noise ratio (SNR). Then, we derive the exact closed-form expressions and their high-SNR approximations for the outage probability and ergodic rate, respectively. The effect of RRU number and FTR-fading parameters on the performance are further revealed from these high-SNR approximations. Simulations validate our analytical results.

Performance Analysis in Terms of Bit Error Rate Over Fluctuating Two-Ray (FTR) Fading Channels

The fluctuating two-ray (FTR) channel is currently taken as a suitable small-scale fading model for fifth-generation millimeter-wave communications. This paper analyzes the performance in terms of the average bit error rate (ABER). The expressions of ABER of coherent and non-coherent modulation are evaluated using probability density function over FTR fading channels. Moreover, the behaviors of each modulation schemes are also studied based on the fading parameters. A comparison of the modulation schemes is also presented over FTR fading channels. The evaluated expressions are then verified with expected outcomes and Monte Carlo simulation.

Wireless-Powered Full-Duplex UAV Relay Networks Over FTR Channels

A thorough understanding of fundamental limits of wireless-powered unmanned aerial vehicle (UAV) relay networks in millimeter waves is still missing. We narrow this gap by investigating the outage performance of a UAV-assisted wireless network over fluctuating two-ray (FTR) channels. The FTR fading model is particularly appealing since well characterizes the wireless propagation in a wide range of frequencies, including those in millimeter waves. The proposed setup consists of a source-destination pair communicating with the assistance of a UAV, which is a wireless-powered relay station operating in full-duplex mode under the amplify-and-forward protocol. For the wireless energy harvesting at the UAV, wireless power transfer (WPT), simultaneous wireless information and power transfer (SWIPT), and self-recycling energy techniques are employed together. To characterize the system outage probability, we obtain an integral-form expression derived from an approximate analysis and a simple closed-form expression derived from an asymptotic analysis at the high signal-to-noise ratio (SNR) regime. Monte Carlo simulations are provided to validate the correctness of our theoretical results and provide insights on the network performance in terms of key system parameters. Interestingly, obtained results show that the FTR fading parameters corresponding to the first hop and second hop play no role on the system outage performance at high SNR. Instead, it is mainly governed by the effect of the residual self-interference at the UAV, leading to outage floors.

Performance of dual-branch selection combining receiver over Fluctuating Two-Ray (FTR) fading channels for 5G mmWave communications

The fluctuating two-ray (FTR) fading channels is a suitable model of small-scale fading environment for fifth-generation millimeter-wave and beyond communications. This paper evaluates the performance of selection combining (SC) of the received signals through an independent FTR fading channels. A dual-branch SC receiver is considered because of its lower complexity and significant improvement from the non-diversity system. The probability distribution function (PDF) expression of the received signal to noise ratio (SNR) of the SC receiver is obtained from the cumulative distribution function of SNR for FTR fading channels. The average bit error rate of coherent and non-coherent modulation schemes are derived using the obtained received PDF expression. The impacts of the fading parameters on the performance of the system are analyzed numerically. The numerically estimated expressions are verified with standard outcomes and Monte Carlo simulation.

The Performance of Coherent and Non-coherent Modulation in FTRF Channels

The Fifth-Generation (5G) communication targets to provide a high-speed data rate in the wireless system. The data rate of 1000Mbps can able to provide using an unlicensed millimeter wave (mmWave) spectrum. Fluctuating Two-Ray Fading (FTRF) channels is the best accurate model for the small-scale fading environment of the 5G mmWave communication. In this paper, a new probability density function (PDF) expression for FTRF channels is evaluated. Moreover, the average bit error rate for coherent and non-coherent modulation over FTRF channels is also presented using a PDF-based approach. Finally, a comparison is also presented among the modulation schemes. The numerically estimated expressions are verified with standard outcomes and Monte Carlo simulation.

Cascaded Fluctuating Two-Ray Fading Channels

In this letter, we derive the exact probability density function (PDF), cumulative distribution function (CDF), and generalized moment generating function of a product of $N$ independent fluctuating two-ray (FTR) random variables. Capitalizing on the derived expressions, new expressions for the PDF and CDF of the FTR fading model, i.e., $N=1$ , are obtained in terms of elementary functions, where the existing ones are expressed in terms of special functions. The derived distributions are then used to derive exact analytical expressions for the outage probability and average bit error rate. Monte Carlo simulations have been carried out to validate the correctness of our results.

Sum of Squared Fluctuating Two-Ray Random Variables With Wireless Applications

The fluctuating two-ray (FTR) channel fading offers good fit for small-scale experimental data in millimeter wave communications. We first investigate the statistical characterizations of the sum of independent nonidentically distributed squared FTR random variables. More specifically, the exact and approximate analytical expressions for moment generating function, probability density function, and cumulative distribution function are derived. Then, the performance of the maximal-ratio combining system over FTR fading channels is assessed in terms of the outage probability (OP) and the average bit error probability (ABEP). Moreover, asymptotic OP and ABEP expressions are obtained to obtain physical insights into the impact of the system and channel parameters on the overall performance. Finally, the correctness of our results is verified by simulation results.

Performance of maximum ratio combining of fluctuating two‐ray (FTR) mmWave channels for 5G and beyond communications

AbstractRecently, a millimeter‐wave band channel model for fifth generation and beyond communications, called fluctuating two‐ray (FTR) model, has been introduced, which accurately tracks the behavior of wireless communication links in that band. In this paper, the performance of maximum ratio combining (MRC) of signals received through independent FTR channels is evaluated. Closed‐form expressions for the probability distribution of the signal‐to‐noise ratio at the output of the MRC combiner, outage probability of the system, and a tight upper bound for average bit error probability are derived. From the results obtained, it is shown that MRC for FTR channels achieves the same diversity order as MRC for Rayleigh fading, and equal to the number of diversity branches. Additionally, the effects of the FTR fading model parameters on the system performance have been investigated via numerical results obtained from analytical derivations. Comparison between analytical and simulation results show that they are in excellent agreement. To the best of our knowledge, this is the first work to analyze the performance of MRC for FTR channels.

Unveiling the Hyper-Rayleigh Regime of the Fluctuating Two-Ray Fading Model

The recently proposed Fluctuating Two-Ray (FTR) model is gaining momentum as a reference fading model in scenarios where two dominant specular waves are present. Despite the numerous research works devoted to the performance analysis under FTR fading, little attention has been paid to effectively understanding the interplay between the fading model parameters and the fading severity. According to a new scale defined in this work, which measures the hyper-Rayleigh character of a fading channel in terms of the Amount of Fading, the outage probability and the average capacity, we see that the FTR fading model exhibits a full hyper-Rayleigh behavior. However, the Two-Wave with Diffuse Power fading model from which the former is derived has only strong hyper-Rayleigh behavior, which constitutes an interesting new insight. We also identify that the random fluctuations in the dominant specular waves are ultimately responsible for the full hyper-Rayleigh behavior of this class of fading channels.

Average Symbol Error Rate Analysis of QAM Schemes Over Millimeter Wave Fluctuating Two-Ray Fading Channels

In this study, analytical expressions are derived by using probability density function approach over millimeter wave fluctuating two-ray (FTR) fading channels for average symbol error rate (ASER) of rectangular quadrature amplitude modulation (RQAM) and cross quadrature amplitude modulation (XQAM) schemes. First, an exact ASER expression for RQAM over millimeter wave FTR fading channels is derived. Second, two different upper bound ASER expressions of RQAM scheme under millimeter wave FTR fading conditions are obtained by using Chernoff and Chiani approximations of Gaussian Q-function. In addition to this, an asymptotic ASER expression for RQAM is also proposed. Then, an analytical formulation is presented for XQAM signaling over millimeter wave FTR fading channels in terms of infinite series representations which rapidly converge. Finally, the numerical results of the proposed analytical expressions are compared with the simulation results in order to validate the analytical findings in this work.

Physical Layer Security Over Fluctuating Two-Ray Fading Channels

Ensuring the physical layer security (PHY-security) of millimeter-wave (mmWave) communications is one of the key factors for the success of 5G. Recent field measurements show that conventional fading models cannot accurately model the random fluctuations of mmWave signals. To tackle this challenge, the fluctuating two-ray (FTR) fading model has been proposed. In this correspondence, we comprehensively analyze the PHY-security in mmWave communications over FTR fading channels. More specifically, we derive analytical expressions for significant PHY-security metrics, such as the average secrecy capacity, the secrecy outage probability, and the probability of strictly positive secrecy capacity, with simple functions. The effect of channel parameters on the PHY-security has been validated by numerical results.

New Results on the Fluctuating Two-Ray Model With Arbitrary Fading Parameters and Its Applications

The fluctuating two-ray (FTR) fading model provides a much better fit than other fading models for small-scale fading measurements in millimeter wave communications. In this paper, using a mixture of gamma distributions, new exact analytical expressions for the probability density and cumulative distribution functions of the FTR distribution with arbitrary fading parameters are presented. Moreover, the performance of digital communication systems over the FTR fading channel is evaluated in terms of the channel capacity and the bit error rate. The interaction between channel fading parameters and system performance is further investigated. Our newly derived results extend and complement previous knowledge of the FTR fading model.

The Fluctuating Two-Ray Fading Model: Statistical Characterization and Performance Analysis

We introduce the Fluctuating Two-Ray (FTR) fading model, a new statistical channel model that consists of two fluctuating specular components with random phases plus a diffuse component. The FTR model arises as the natural generalization of the two-wave with diffuse power (TWDP) fading model; this generalization allows its two specular components to exhibit a random amplitude fluctuation. Unlike the TWDP model, all the chief probability functions of the FTR fading model (PDF, CDF and MGF) are expressed in closed-form, having a functional form similar to other state-of-the-art fading models. We also provide approximate closed-form expressions for the PDF and CDF in terms of a finite number of elementary functions, which allow for a simple evaluation of these statistics to an arbitrary level of precision. We show that the FTR fading model provides a much better fit than Rician fading for recent small-scale fading measurements in 28 GHz outdoor millimeter-wave channels. Finally, the performance of wireless communication systems over FTR fading is evaluated in terms of the bit error rate and the outage capacity, and the interplay between the FTR fading model parameters and the system performance is discussed. Monte Carlo simulations have been carried out in order to validate the obtained theoretical expressions.