Two-ray Fading Channel Research Articles

Relay-assisted communication over a fluctuating two-ray fading channel

ABSTRACT The intricacies of relay-aided device-to-device (D2D) communication within the novel fluctuating two-ray (FTR) model is inspected in this study. Two cases with respect to co-channel interference are considered here, in case A, co-channel interferences due to unmanned aerial vehicles affect the relay while at the D2D receiver, the co-channel interferences follow the FTR model. In case B, interferences due to unmanned aerial vehicles affect the D2D receiver and the relay now experiences interferences over the FTR channels. The channel of a co-channel interference due to unmanned aerial vehicle is assumed to be a recently proposed single-shadowing based composite fading model. Further enhancing operational efficiency, the D2D receiver incorporates a power splitting mechanism for power harvesting. In this analysis a characteristic function-based approach is applied, which serves as the foundational cornerstone for deriving expressions that govern the outage and success probabilities. These intricate expressions are connected with critical factors, such as the dynamics of path-loss phenomena, the spatial separation between the interferers and the relay, the varying distances between the interferers and the D2D receiver, and the physical gap bridging the relay and the D2D receiver. Building upon the derived expressions, an extensive numerical analysis unfurls them for both interference cases.

Performance of GFDM system with channel estimation error over FTR mmWave channels for 5G and beyond communication

Millimeter-wave (mm-Wave) communication are the building block of the beyond 5G (B5G) generations. For mm-Wave communication, the fluctuating two-ray (FTR) fading channels serve as an appropriate model for the small-scale fading. Generalized frequency division multiplexing (GFDM) is envisioned as one of the potential candidate to fulfil the requirements of B5G communication systems. This paper presents the performance analysis of a GFDM system over the FTR fading environment. In this analysis, both GFDM and space–time coded (STC) GFDM system has been considered, and an exact closed-form expression of the average symbol error rate (ASER) is derived for the μ-QAM modulation technique under imperfect channel estimation condition. The simulation results demonstrate excellent agreement with the numerical results obtained for GFDM and STC-GFDM systems with different channel and system parameters such as m, Kf, Δ, TA, RA, ϱA2 and μ. An asymptotic analysis is also done for both systems.

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 Analysis of mmWave Communications With Selection Combining Over Fluctuating-Two Ray Fading Model

In this letter, the performance of millimeter-wave (mmWave) communications with selection combining (SC) over non-identical fluctuating two-ray (FTR) fading channels is analyzed. Consequently, the exact expressions and asymptotic approximations at high signal-to-noise ratio (SNR) regime of the moment generating function (MGF) and probability density function (PDF) of the maximum of non-identical FTR variates are provided. To this effect, mathematically tractable expressions of the outage probability (OP), outage capacity (OC), average bit error probability (ABEP), and average channel capacity (ACC) are derived. The truncation of the infinite series of the cumulative distribution function (CDF) for a specific number of terms is also given. A comparison between the numerical and simulated results is performed to verify the validation of our analysis.

Physical-Layer Security for Frequency Diverse Array-Based Directional Modulation in Fluctuating Two-Ray Fading Channels

The frequency diverse array (FDA)-based directional modulation (DM) technology plays an important role in the physical-layer security (PLS) transmission of 5G and beyond communications. In order to meet the tremendous increase in mobile data traffic, a new memory-efficient design for the FDA-DM-based PLS transmission is urgently demanded. In this article, an analytical symmetrical multi-carrier FDA model is proposed in three dimensions, namely, range, azimuth angle, and elevation angle, differing from the conventional analytical approach with only range and azimuth angle considered. Then, a single-point (SP) artificial noise (AN) aided FDA-DM scheme is proposed, which reduces the memory consumption significantly compared with the conventional zero-forcing (ZF) and singular value decomposition (SVD) approaches. Moreover, the PLS performance of the proposed FDA-DM scheme is analyzed in fluctuating two-ray (FTR) fading channels for the first time, including the average secrecy capacity (ASC) and the secrecy outage probability (SOP). More importantly, the closed-form expressions for the lower bound on ASC and the upper bound on SOP are derived, respectively. The effectiveness of the analytical expressions is verified by numerical simulations. This work opens a way to lower the memory requirements for DM-based PLS transmission of 5G and beyond communications.

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.

Secrecy Performance for Finite-Alphabet Inputs Over Fluctuating Two-Ray Channels in FDA Communications

To provide system design insights for practical communication systems equipped with the frequency diverse array (FDA), this paper investigates the secrecy performance of FDA systems exploiting finite-alphabet inputs over fluctuating two-ray (FTR) fading channels. More specifically, closed-form expressions for the average secrecy rate (ASR) and the secrecy outage probability (SOP) are derived, while their correctness is confirmed by numerical simulations. In addition, we perform asymptotic analysis to quantify the secrecy performance gap between Gaussian and finite-alphabet inputs, for a sufficiently large average signal-to-noise ratio (SNR) of the main channel. Compared with Gaussian inputs-based research, this letter focuses on practical scenarios which sheds lights on properties of FDA systems.

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.

Secrecy outage analysis over fluctuating two‐ray fading channels

In this letter, we analyze the secrecy outage probability (SOP) over fluctuating two-ray fading channels but with a different definition from the one adopted in [5]. Following the new defined SOP, we derive an analytical closed-form expression for our proposed SOP, as well as an asymptotic formula valid in the high signal-to-noise ratio region of the source to destination link. In the numerical results section, we perform some Monte-Carlo simulations to validate the accuracy of our derived expressions, and also present the probability gap between our proposed SOP and the SOP in [5].

Wireless powered UAV relay communications over fluctuating two-ray fading channels

The unmanned aerial vehicle (UAV) relay has recently attracted a large amount of research interests, due to its relative ease of development to enhance cooperative communication performance when the direct link between transmitters and receivers is severely blocked. With simultaneous wireless information and power transfer, the UAV relay can harvest energy from radio frequency and prolong the network lifetime. In this paper, we use the time-switching relaying protocol for UAV energy harvesting (EH) and data forwarding. Different from prior works, the ground-to-air links are modeled as fluctuating two-ray fading channels, which provide a very good fit to the UAV relay communication. In addition, we obtain novel exact analytical expressions for the outage probability, symbol error rate and average capacity of the considered system employing decode-and-forward and amplify-and-forward protocols, respectively. Furthermore, we offer valuable insights into the impact of system and fading parameters on the performance. For example, the optimal EH time can be selected to enhance the system performance. Finally, numerical results are provided to validate the derived results.

Different Power Adaption Methods on Fluctuating Two-Ray Fading Channels

In this letter, we consider a typical scenario where the transmitter employs different power adaption methods, including the optimal rate and power algorithm, optimal rate adaption, channel inversion and truncated channel inversion, to enhance the ergodic capacity (EC) with an average transmit power constraint over fluctuating two-way fading channels. In particular, we derive exact closed-form expressions for the EC under different power adaption methods, as well as corresponding asymptotic formulas for the EC valid in the high signal-to-noise ratio (SNR) region. Finally, we compare the performance of the EC under different power adaption methods, and this also validates the accuracy of our derived expressions for the exact and asymptotic EC.

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.

MGF Approach to the Analysis of Generalized Two-Ray Fading Models

We analyze a class of Generalized Two-Ray (GTR) fading channels that consist of two line of sight (LOS) components with random phase plus a diffuse component. We derive a closed form expression for the moment generating function (MGF) of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.

Efficient bad equalizer in two-ray multipath fading channels

An efficient bidirectional arbitrated decision feedback (BAD) equalizer is presented in single-carrier block transmission system in the two-ray multipath fading channels, where the output from the bidirectional equalizers are combined together directly using maximal ratio combining (MRC) rule to improve the signal-to-noise ratio (SNR) before demodulation. The computational complexity of the BAD equalizer presented is linear with the channel length, which is the same as conventional decision feedback equalizer (DFE) and is significantly lower than that of conventional BAD equalizer as well as the maximum likelihood (ML) algorithm. While the performance of the new scheme depends on the specific channel characteristics, it is shown by simulation results that the performance of the new BAD can surpass the one of DFE dramatically in the minimum or non-minimum phase Two-ray multipath fading channels.

Diversity gains in two-ray fading channels

A two-ray, small-scale fading model was recently proposed as a worst-case fading scenario for certain wireless sensor applications. Empirical data motivated this development for fading was found to be more severe than predicted by Rayleigh fading statistics, a behavior referred to as hyper-Rayleigh fading. Based on the two-ray model, we study the benefits of M-branch diversity in the context of signal-to-noise ratio (SNR) and bit-error rate (BER) performance metrics. While these results are well-known for Rayleigh fading, this work is the first analysis of diversity for the hyper-Rayleigh regime.

A multiple guard interval based frequency error detector for OFDM systems

We deal with the carrier frequency synchronization of the orthogonal frequency division multiplexing (OFDM) system and propose a multiple guard interval based frequency error detector (GIB FED) using a set of consecutive guard interval data for OFDM system. We compare the performance of a multiple GIB FED with two conventional GIB FEDs. Under two-ray multipath fading channel, it is shown that the normalized frequency jitter of the proposed multiple GIB FED is about 2.1/spl sim/4.9 times lower than that of GIB-I FED and 1.2/spl sim/2.1 times lower than that of GIB-II FED. The acquisition time of multiple GIB FED is also about 1.8 and 3.2 times faster than those of GIB-I FED and GIB-II FED, respectively, regardless of the channel condition.

Performance of digital DECT radio links based on semianalytical methods

We report a very efficient semianalytical approach for the performance evaluation of differential detection schemes for GMSK signals of the DECT standard. Precisely, for a given channel, the performance is determined by means of an analytical procedure which includes the saddlepoint approximation. We consider both static channels (with impulse response generated by the simulation program SIRCIM) and two-ray Rayleigh and log-normal fading channels. As a departure from previous works, our receiver includes an all-digital part after the analog differential detection scheme. The digital part includes: (1) a block for the estimation of both the optimum sampling phase and the nonlinear channel coefficients (by making use of the DECT training sequence), (2) a one-tap decision feedback (DF) equalizer, and (3) a block for the evaluation of the approximate optimum bias level (/spl gamma//sub e/) in the threshold detector. Both the DF equalizer coefficient and /spl gamma//sub e/ are based on the nonlinear channel coefficients estimate. For channels with a normalized delay spread up to 0.2, the use of the optimum threshold together with the DF equalizer permits a gain of about 2 dB at BER=10/sup -6/ with respect to a receiver without equalization and a zero-level decision threshold. In addition, we discover that, in indoor environments, the 2-bit GMSK detector performs roughly the same as the 1-bit detector. The threshold optimization is also effective in the presence of channels affected by fading. To support this statement, we report the performance of the 1-bit differential detection scheme combined with antenna selection diversity in the presence of a two-ray log-normal and Rayleigh fading channel.