Cascaded Fading Channels Research Articles

ALAMOUTI SPACE-TIME CODING FOR VEHICULAR COMMUNICATIONS IN THE PRESENCE OF CHANNEL ESTIMATION ERRORS

In this paper, the error performance of the Alamouti space-time coding (STC) scheme is investigated for vehicle-to-vehicle (V2V) communication systems over imperfect cascaded fading channels. In vehicular communication systems, perfect knowledge of the channel state information is not available to the users at all times due to the rapid movement of communicating vehicles and fast change of the rich scattering environment which makes the fading effects in wireless channels more severe. Therefore, in the analysis, we consider the erroneous estimation of the channel gain, which is more realistic for practical scenarios. For this purpose, we first derive the moment-generation function (MGF) of the channel fading coefficient with estimation error in the case of the cascaded Nakagami-m fading conditions. Then, using the MGF, we obtain the closed-form symbol-error-rate (SER) expressions of Alamouti STC with two transmitting and L receiving antennas for the M-PSK and M-QAM modulation schemes. Then, the exact ergodic capacity expression is derived for the proposed system. Furthermore, the analytical results are verified through Monte-Carlo simulations. Numerical results show that the SER performance of V2V communication systems can be improved significantly by using Alamouti STC even in case of harsh fading conditions and full channel-state information is not available due to estimation errors.

Reliability analysis of cascaded η − μ fading channels

AbstractIn this work, the mathematical characterization of the cascaded fading channel based on multiplicative modeling is discussed. The proposed cascaded probability density function is derived by taking the product of statistically independent, but not necessarily identically distributed fading random variables, which encompasses various well‐known distributions as cascaded Nakagami‐m, Hoyt, and Rayleigh distributions. In particular, other statistical measures such as cumulative distribution function, moment generating function, and moment of the cascaded channels, are developed. This set of derived results is further utilized in studying the reliability performance of the wireless cascaded fading channels. The system reliability is comprehensively investigated through various statistical metrics like average symbol error probability, ergodic capacity, outage probability, and effective capacity. All the developed results are of intractable univariate Foxs H‐function form. The accuracy of the numerical results is extensively validated through Monte‐Carlo simulation.

Block Error Rate Analysis of Short-Packet Mobile-to-Mobile Communications Over Correlated Cascaded Fading Channels

This paper thoroughly investigates the performance of short-packet communications over cascaded fading channels that have a variety of applications in mobile-to-mobile (M2M) communications. By considering the wide occurrence of the correlation among cascaded fading processes, cascaded 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> channel model with general correlation is adopted. However, the presence of channel correlation poses significant challenges on the analysis of block error rate (BLER), which is the most fundamental performance metric in short-packet communications. For tractability, Mellin transform is first invoked to derive the BLER in terms of the representation of an infinite summation. This result then enables the asymptotic analysis of BLER with useful insights, including the diversity order, the negative impact of correlation and the extension to infinite blocklength regime. Furthermore, to implement the infinite series representation of BLER, an effective truncation approach is proposed with controllable calculation accuracy. More importantly, our analytical results lay the foundation for the optimal system design. In the end, extensive Monte Carlo simulations verify our analysis.

Performance Analysis of Intelligent Reflecting Surface Aided Wireless Networks With Wireless Power Transfer

The low efficiency of wireless power transfer (WPT) poses a key challenge for energy-constrained wireless networks. To address this issue, in this letter, the integration of intelligent reflecting surface (IRS) into a WPT network is investigated. To this end, an accurate approximation for the probability density function of the end-to-end cascaded fading channel is presented. By leveraging the derived result, accurate closed-form expressions of the outage probability (OP) and average symbol error probability (ASER) are derived for the proposed IRS-aided WPT system. To gain further insight into the system performance, asymptotic closed-form expressions for the ASER and OP are further derived and interesting observations are reported. Particularly, our asymptotic analysis reveals that the achievable diversity in the underlying scenario is independent of the reflective elements of the IRS. The analytical derivations, corroborated by simulation results, demonstrate that IRSs can be promising candidates for the realization of a highly efficient power transfer enabled wireless network.

Secrecy Analysis Over Cascaded $\kappa -\mu$ Fading Channels With Multiple Eavesdroppers

In this paper, secrecy performance is investigated over the cascaded fading channel for the κ-μ distribution. The probability density function (PDF) and the cumulative distribution function (CDF) for the cascaded κ-μ fading channels as well as for some of its special cases, such as the Rayleigh and Rician fading channels are derived. A communication system operating over the cascaded κ-μ fading channel is analyzed in which the outage probability (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ), the average symbol error probability (ASEP), and the average channel capacity (ACC) are obtained in terms of the Meijer G-function. In addition, the secrecy is examined for a system model where we have a transmitter, a receiver, and multiple colluding eavesdroppers attempting to overhear the information received. The secrecy performance is investigated in terms of the secrecy outage probability (SOP) and the probability of non-zero secrecy capacity (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nzc</sup> ). The analyses illustrate that increasing the number of eavesdroppers in the network degrades the secrecy of the system. Furthermore, increasing the cascade level in the channel degrades the system performance as well as the information security. In addition, the impact of the wiretap channel parameters and the average received signal-to-noise-ratio (SNR) at the eavesdroppers over the security are studied. To verify the accuracy of the derived analytical expressions, Monte-Carlo simulations are utilized.

Vertical Underwater Visible Light Communication Links: Channel Modeling and Performance Analysis

Underwater visible light communication (UVLC) has been introduced to support emerging high data rate applications such as real-time image and video transmission. Initial works on UVLC build upon the assumption of fixed turbulence strength through the transmission range which can be justified only for horizontal links. In vertical underwater links, the gradient of temperature and salinity changes with depth. This effectively results in ocean stratification where water with different values of salinity and temperature form non-mixing layers. In this paper, we first model the vertical underwater link as a cascaded fading channel where fading coefficients associated with different layers are modeled as independent and non-identical distributed. Based on the cascaded lognormal and Gamma-Gamma distributions respectively for weak and moderate/strong turbulence conditions, we first derive closed-form expressions for the bit error rate (BER) performance of UVLC systems. Then, we analyze the asymptotic BER performance and determine the diversity orders. In addition, we derive closed-form expressions for the average ergodic capacity of underwater cascaded fading channels under consideration. We present simulation results to confirm the analytical findings.

Performance Analysis of Opportunistic Relay Selection Cooperative Communication in Cascaded Fading Channels

Cooperative communication enables users to transmit information in a cooperative way, which is one of the key technologies used in wireless communication systems to improve spectral efficiency. A cascade Nakagami-m fading function is proposed to describe the fading characteristics of complex wireless channels, and a communication model of decoding-and-forward opportunistic relay selection (DF-ORS) cooperative communication under total power constraints is established. Theoretical analysis and simulation results show that DF-ORS cooperative communication can effectively reduce outage probability and improve spectrum efficiency under total power constraints and complex cascade Nakagami-m fading channels. The transmission power allocation of source node and relay node has an important impact on communication performance. Equal power allocation scheme cannot guarantee the optimal system performance, and the obtained conclusions have more general applicability.

Product and Ratio of Product of Fisher-Snedecor ℱ Variates and Their Applications to Performance Evaluations of Wireless Communication Systems

This article considers the product, and the ratio of the product of Fisher-Snedecor $\mathcal {F}$ random variables (RVs), which can be used in modeling fading conditions that are encountered in realistic wireless transmission. To this end, exact analytical expressions are derived for the probability density function (PDF) and cumulative distribution function (CDF) of the product of $N$ statistically independent, but not necessarily identically distributed, Fisher-Snedecor $\mathcal {F}$ RVs. Capitalizing on these, exact analytical expressions are then derived for the outage probability, average channel capacity and average bit error probability over cascaded fading channels. Moreover, some important statistical metrics such as amount of fading, channel quality estimation index, kurtosis, and skewness are also provided, since they provide useful insights on the characteristics of the encountered fading conditions. In addition, with the aid of the central limit theorem, an approximation for the PDF of $N*$ Fisher-Snedecor $\mathcal {F}$ RVs is proposed using a lognormal density, and its accuracy is quantified in terms of the resistor-average distance. Finally, novel expressions for the PDF and CDF of the $N$ -fold product ratio of Fisher-Snedecor $\mathcal {F}$ RVs are also derived. As a potential application of our new results, a spectrum sharing network is considered, for which exact analytical expressions for the outage probability, delay-limited capacity, and ergodic capacity are derived. For the cascaded fading scenario and the spectrum sharing network, numerical examples are provided to show the impact of different channel-related parameters, such as fading severity, shadowing, peak and average interference power on the system performance, which is rather useful in the design of conventional and emerging wireless communication systems. Monte-Carlo simulation results are provided to corroborate the presented mathematical analysis.

Outage probability bound of decode and forward two‐way relay employing optical spatial modulation over gamma‐gamma channels

In this study, free space optical communication has been studied for different atmospheric conditions. Spatial modulation (SM) has been used to improve the performance of two-way relay cooperative communication. The proposed system employs decode and forward (DF) relaying technique along with physical layer network coding, hence it has been named as optical SM based DF two-way relay. It enables full-duplex communication thereby enhancing the system efficiency. The transmit optical source index as well as the information are exchanged between the two bidirectional nodes. Performance analysis of the system has been carried out in terms of lower and upper bounds of outage probability and average data rate for N -γ cascaded fading channels. The analytical results have been validated by means of Monte Carlo simulations. The variation of the performance due to change in different parameters has also been reported in this study.

Secrecy performance analysis over cascaded fading channels

In this study, the authors investigate the secrecy performance at the physical layer of wireless communication systems where the channels are modelled as cascaded fading channels, in which the fading effects are worse than those in the cellular communication channels like Rayleigh and Nakagami- m . Analytic results are derived for the cascaded Nakagami- m fading channel model comprising the cascaded Rayleigh, 2*Nakagami- m , the generalised- K , and the conventional cellular channel models as well. By evaluating the information-theoretic physical layer security performance, they obtain the closed-form expressions of the average secrecy capacity and probability of the positive secrecy capacity in case of that channel-state-information of the eavesdropper is known by the source. Then they obtain the exact closed-form secrecy outage probability (SOP) when the eavesdropper is passive. Analytic results are computed in terms of the bivariate and univariate Meijer's G functions and later on are successfully validated through Monte Carlo simulations. The simulation results show that the secrecy performance worsens with the increasing cascading degree of the fading channels. For example, in 2*Nakagami- m fading channels where the cascading degree is 2, extra 4 dB signal-to-noise ratio is required to achieve the same SOP value in comparison with the classical Nakagami- m fading channels.

Outage probability bound of decode and forward two‐way full‐duplex relay employing spatial modulation over cascaded α − μ channels

SummaryThe system performance of mobile‐to‐mobile (D2D) cooperative communication has been improved by utilizing spatial modulation (SM) in this paper. The proposed system employs decode and forward (DF) relaying technique along with physical layer network coding (PLNC); hence, it has been named as SM‐based decode and forward two‐way relay (DFTWR). It enables full‐duplex communication thereby enhancing the system efficiency. Information bits are exchanged between the two bidirectional nodes. For two bits of information exchange, the antenna index is conveyed by the least significant bit (LSB) of the data symbol while the most significant bit (MSB) carries the message. The system performance has been investigated by analyzing certain performance metrics like lower and upper bounds of outage probability and average data rate for N‐α‐μ cascaded fading channels. The change in the system performance by varying certain parameters like relative geometrical gain, fading coefficients, and number of cascaded components has also been put forth in this paper.

STTC design for vehicular communication systems employing fixed‐gain AF PLNC over cascaded fading channels

In this study, the authors combine physical layer network coding (PLNC) and space-time trellis coding (STTC) techniques to improve the error performance of vehicle-to-vehicle (V2V) communication systems where all fading channels are assumed to undergo double Rayleigh fading (DRF) which is worse than Rayleigh fading used in cellular communications. In the authors' analysis, they show that the DRF channels can be modelled by using the mixture gamma distribution. After that, pairwise error probability (PEP) analysis is performed for a fixed-gain amplify-and-forward PLNC V2V system employing STTC over the DRF channels, and an upper bound for the PEP is obtained. By examining the behaviour of the upper bound expression in the high SNR region, they derive a new design criterion for STTCs. Finally, using this criterion they propose novel STTCs with 4 and 8 states for V2V systems employing PLNC over the DRF channels.

Product of Two Envelopes Taken From $\alpha $ - $\mu $ , $\kappa $ - $\mu $ , and $\eta $ - $\mu $ Distributions

This paper presents exact, novel formulations for the probability density function and cumulative distribution function for the product of two independent and non-identically distributed $\alpha $ - $\mu $ , $\kappa $ - $\mu $ , and $\eta $ - $\mu $ variates. The expressions are given in terms of both 1) generalized Fox H-function and 2) easily computable series expansions. The formulations derived can be directly used to explore the performance of a number of wireless communication processes, including multihop systems, cascaded channels, radar communications, multiple-input multiple-output links, and others. Due to the high flexibility of the above-mentioned distributions, the results presented here comprise a substantial number of useful product distributions. As application examples, performance metrics for the cascaded fading channel are derived. The validity of the expressions is confirmed via Monte Carlo simulation. It is noteworthy that, because any composite multipath-shadowing fading model is obtained as a particular case of the product of two fading variables, the results given here provide a plethora of composite multipath-shadowing fading scenarios.

Effects of RF Impairments in Communications Over Cascaded Fading Channels

Direct-conversion architectures can offer highly integrated low-cost hardware solutions to communication transceivers. However, it has been demonstrated that radio frequency (RF) impairments such as amplifier nonlinearities, phase noise, and in-phase/quadrature-phase imbalances (IQI) can lead to severe degradation of the performance of such systems. Motivated by this, the present work is devoted to the quantification and evaluation of the effects of RF IQI on wireless communications in the context of cascaded fading channels for both single-carrier and multicarrier systems. To this end, closed-form expressions are first derived for the outage probability (OP) over $N^{\ast}$ Nakagami- $m$ channels for the cases of ideal transmitter (TX) and receiver (RX), ideal TX and IQI RX, IQI TX and ideal RX, and joint TX/RX IQI. The offered expressions, along with several deduced corresponding special cases, are subsequently employed in vehicle-to-vehicle (V2V) communications to justify their importance and practical usefulness in the context of emerging communication systems. The offered analytic results are corroborated by extensive comparisons with respective results from computer simulations. It is shown that considering non-ideal RF front-ends at the TX and/or RX introduces nonnegligible errors in the OP performance that can exceed 20% under several communication scenarios. It is further demonstrated that the effects by cascaded multipath fading conditions are particularly detrimental as they typically result in considerable performance losses of around or over an order of magnitude.

Joint Relay and Antenna Selection in MIMO PLNC Inter-vehicular Communication Systems over Cascaded Fading Channels

We investigate the joint relay and antenna selection performance in a multiple input multiple output (MIMO) Vehicle-to-Vehicle (V2V) communication system employing physical layer network coding (PLNC) with amplify-and-forward (AF) scheme at the relay antenna. Analytic results are derived under the cascaded Nakagami-m fading channel model assumption, which covers cascaded Rayleigh and conventional cellular channel models as well. We evaluate the performance of the system in terms of joint outage probability of sources and derive closed-form expressions for lower and upper bounds while an exact expression is found as a single integral form. Besides, the asymptotic diversity order is analyzed and quantified as a function of number of relays and antennas installed on the source and relay vehicles, and channel parameters. Finally, we verify the analytic derivations by computer simulations. Our results show that the outage probability performance decreases with the increasing cascading degrees of the channels but joint relay and antenna selection enhances the performance of the system superbly with the increasing number of relays and antennas. Also it is shown throughout all the simulation results, the lower bound for the joint outage probability seems to consistently be well tight for large SNR. Therefore it can be used for practical design of inter-vehicular communication systems which contain multiple relays and antennas.

Energy Detection of Unknown Signals Over Cascaded Fading Channels

Energy detection is a favorable mechanism in several applications relating to the identification of deterministic unknown signals such as in radar systems and cognitive radio communications. The present work quantifies the detrimental effects of cascaded multipath fading on energy detection and investigates the corresponding performance capability. A novel analytic solution is first derived for a generic integral that involves a product of the Meijer G-function, the Marcum Q-function, and arbitrary power terms. This solution is subsequently employed in the derivation of an exact closed-form expression for the average probability of detection of unknown signals over N*Rayleigh channels. The offered results are also extended to the case of square-law selection, which is a relatively simple and effective diversity method. It is shown that the detection performance is considerably degraded by the number of cascaded channels and that these effects can be effectively mitigated by a nonsubstantial increase of diversity branches.

Performance Analysis of Passive UHF RFID Systems Under Cascaded Fading Channels and Interference Effects

In this paper, the performance of monostatic and bistatic passive ultra high frequency radio frequency identification (UHF RFID) systems under the effects of cascaded fading channels and interference is studied. The performance metric used is tag detection probability defined as the probability that the instantaneous received power is higher than the reader's sensitivity. A closed-form expression of the detection probability is derived using cascaded forward and backscatter fading channels and the reader antennas orientation relative to the tag. Furthermore, the performance of passive UHF RFID systems under reader-to-tag interference caused by both the desired RFID signal and multiple RFID interferers is analyzed, and the effect of constructive and destructive interferences is examined. In addition, the maximum reading range in ideal, multipath fading, and interfering environments is presented. To the best of our knowledge, this is the first work that provides a 3-D performance analysis of the passive UHF RFID systems under cascaded fading channels. The obtained results are very useful for the design and optimization of passive UHF RFID systems from an RF physical channel point of view.

Error Rates in Dual Hop Wireless Links Operating in Cascaded Fading Channels

Dual hop wireless links offer a simple means of achieving broad coverage through low power transmitters. But, such systems are not immune from fading present in all wireless systems. While several fading models exist, fading treated as a cascading process, namely the cascaded model, allows flexibility in describing channel conditions that are far worse than those existing in Nakagami channels. In this work, an exact analysis of a dual hop link operating in a cascaded N*Nakagami channel is studied. The error rates were estimated using the exact model and compared to the results obtained using random number simulation. These results show an excellent match suggesting the strength of the approach. While the dual hop systems might offer simplicity, the error rate analysis in such systems illustrates that the performance is worse than what is seen in a conventional direct link.

Diversity in cascaded N*Nakagami channels

Short term fading conditions that are worse than those existing in typical Nakagami channels can be modeled using the cascaded approach where the received signal-to-noise ratio is treated as the product of N identical or nonidentical random variables that are either dependent or independent. Cascaded channels also permit the modeling of fading seen in amplify and forward relaying channels as well as keyhole channels. The simplest of these models, referred to as the N*Nakagami model, assumes that the received signal to noise ratio is the product of N independent and identically distributed gamma variables. The fading mitigation achieved in such cascaded channels through diversity is studied in this work. Through analytical approach and simulation, the performance of wireless channels is examined for the selection combining, equal gain combining, generalized selection combining, and maximal ratio combining algorithms. Results demonstrate the existence of severe degradations in cascaded fading channels and the comparative usefulness of the various algorithms in improving the data transmission capabilities. Even though the analysis was undertaken for the case of a coherent binary shift keying modem, results can easily be extended to other modems.

Novel Approximations to the Statistics of Products of Independent Random Variables and Their Applications in Wireless Communications

A novel analytical framework for evaluating the statistics of the product of independent random variables is proposed. Compared with other methods, which use either infinite series or special functions, the new method provides simple and efficient closed-form approximations, in terms of elementary functions, such as powers and exponentials. Numerical results, which are used to check the accuracy of the new approximations, show that it is quite accurate in most regions of interest. As an application, the proposed analytical results can be efficiently used in wireless communications theory to evaluate in closed form the outage probability of cascaded fading channels, as well as the rate offset of the hybrid automatic repeat request (H-ARQ) transmission. Numerical examples show that the derived expressions provide significant insights on the behaviors of important system parameters as the outage probability and the rate offset.