Expressions For Average Symbol Error Rate Research Articles

Performance analysis of energy harvesting‐enabled relay networks in κ‐μ fading channels

AbstractIn this paper, we investigate the performance of an energy harvesting (EH)‐enabled multiple relay network operating over generalized ‐ fading channels. Our approach involves utilizing a partial relay selection strategy and employing an amplify and forward relay protocol for efficient EH from RF signals. Additionally, we integrate a selection combining scheme at the receiver to combine both direct and relaying path signals. In our research, we first obtain the exact closed‐form expression of the cumulative distribution function (CDF) for the system under investigation. Subsequently, we derive expressions for the outage probability (OP) and the moment generating function (MGF) using the derived CDF expression. Furthermore, with the assistance of a CDF‐based approach, we derive closed‐form expressions for the average symbol error rate (ASER) for coherent quadrature amplitude modulation (QAM) schemes, including rectangular QAM (RQAM) and hexagonal QAM (HQAM). We also analyze the ASER expression for non‐coherent frequency shift keying (NCFSK), leveraging the derived MGF expression. To gain valuable insights into the performance of EH‐enabled multiple relay networks, we assess the asymptotic expression of the OP. The outcomes indicate how the behavior of the system is affected by various factors such as time switching ratio, channel fading components, number of relays, and the distance between nodes. To corroborate the accuracy of the analytical findings, Monte Carlo simulations are executed.

On the performance of energy harvesting‐assisted Nth best relay cooperative networks in Nakagami‐m fading

SummaryWe study the energy harvesting (EH)‐assisted system model based on the performance of a dual‐hop cooperative communication system that is subjected to Nakagami‐ fading. Through the partial relay selection method, the selection of th best relay (BR) is performed among amplify and forward (AF) relays, which can harvest energy from radio frequency signals. At the receiver, the selection combining scheme is considered to select between the signals of th best relaying path and the direct path. For this considered system, we compute the closed‐form expressions of outage probability (OP) and the average symbol error rate (ASER) for higher order quadrature amplitude modulation (QAM) techniques, especially for rectangular QAM, cross QAM, and hexagonal QAM. Further, a new moment‐generating function expression is obtained which is used to derive the ASER expression related to the generalized non‐coherent modulation technique. We also give the asymptotic expression of OP to find out the diversity order. Furthermore, we study the effect of fading parameters, th BR, and other factors on system behavior. Finally, we verify the derived expressions with Monte Carlo simulations.

Multihop IRS-assisted free space optics communication with DF relaying: a performance analysis.

Free space optics communication (FSO) offers several advantages over its counterpart radio frequency (RF) systems in terms of bandwidth, data rates, and cost efficiency. However, FSO, being a line-of-sight (LoS) communication system, is hindered by various environmental factors. In this paper, we propose a multihop decode-and-forward (DF) relaying-based intelligent reflecting surface (IRS)-assisted FSO system with an aim to deal with the impediments in FSO communication, and it is assumed that each IRS consists of multiple reflecting elements. Specifically, we derive end-to-end expressions for cumulative distribution function (CDF) of output instantaneous signal-to-noise ratio (SNR). Furthermore, with the aid of the CDF statistics, we study the performance of the proposed system by obtaining the expressions for outage probability (OP) and average symbol error rate (ASER) in terms of multivariate Fox's H-function. Moreover, we have quantified the system performance by numerical results. The numerical results show that the multihop IRS-assisted FSO system provides better performance when compared to a single-hop IRS-assisted FSO system and multihop FSO system without IRS. Finally, the derived expressions of OP and ASER are validated using Monte-Carlo simulations.

ASER analysis of generalized hexagonal QAM schemes for NOMA systems over Nakagami‐m fading channels

SummaryTo achieve high data rates expected from beyond 5G communications, higher‐order modulation techniques have been explored. The energy‐efficient modulation technique with a high data rate has encouraged researches towards an optimum two‐dimensional hexagonal‐shaped constellation, namely, hexagonal quadrature amplitude modulation (HQAM). Thus, in this work, we analyze the average symbol error rate (ASER) of HQAM schemes by considering a two‐user nonorthogonal multiple access (NOMA) pair. Closed‐form expressions for ASER of HQAM schemes for users are derived over generalized Nakagami‐ fading channels. Further, for the HQAM constellation feasibility in two‐user downlink NOMA systems, the power allocation criterion for the users is presented. Furthermore, the impact of modulation order of the users over the systems ASER analysis is investigated and valuable insights are drawn.

On the ASER performance of RF energy harvesting multiple relay networks

We present the average symbol error rate (ASER) of quadrature amplitude modulation (QAM) for radio frequency energy harvesting assisted dual-hop multiple amplify-and-forward (AF) relay network. In this relaying network, partial relay selection scheme is employed to select best relay among multiple relays, while selection combining is considered at destination to combine the signals coming from the direct path and the relaying path. In particular, we derive the exact ASER expressions of rectangular QAM (RQAM), hexagonal QAM and cross QAM schemes for the considered systems over independent and non-identically distributed Nakagami-m fading channels using cumulative distribution function method. Moreover, the asymptotic ASER expression of RQAM is determined to examine the system’s diversity order. Further, to verify the correctness of derived expressions, numerically evaluated results are compared with Monte Carlo simulations. Furthermore, the effects of fading parameter, number of relay, time switching ratio, and large scale fading are studied on the ASER performance.

On the ASER performance of SC receiver with RQAM and HQAM over [formula omitted]-[formula omitted] fading

In this paper, we consider a multi-branch selection combining receiver over independent and non-identically distributed κ-μ fading channels. We derive new exact expressions for moment generating function of output signal-to-noise-ratio (SNR), average symbol error rate (ASER) of coherent rectangular and hexagonal quadrature amplitude modulations, and ASER of non-coherent frequency shift-keying modulation schemes. Further, an asymptotic ASER expression is also derived to determine the diversity order of the system. The analytical results are validated using Monte-Carlo simulations for a wide range of SNRs and fading parameters. Finally, the impact of channel parameters and the number of branches on the ASER performance is also studied.

On the ASER Performance of UAV-Based Communication Systems for QAM Schemes

In this letter, we derive an average symbol error rate (ASER) expression of rectangular quadrature amplitude modulation (RQAM) scheme for unmanned aerial vehicle-enabled communication systems operating over double-shadowing and double-scattering composite fading channel. A moment generating function for the receiver output signal-to-noise ratio is obtained to analyze the ASER expression of non-coherent modulation schemes. An asymptotic expression of ASER for RQAM scheme is also derived to examine diversity order of the considered system. Further, the impact of composite fading parameters and path loss on ASER performance is highlighted. Finally, we validate all the theoretical results through Monte Carlo simulations.

ASER of SISO system with rectangular QAM scheme over α-μ fading channels

ABSTRACT In this study, analytical expressions are developed for average symbol error rate (ASER) of rectangular quadrature amplitude modulation (RQAM) scheme over fading channels. Initially, the ASER expression for RQAM under fading channels is acquired by applying Chernoff approximation of Gaussian -function. Further, another ASER expression of RQAM scheme covering fading conditions is derived by adopting Chiani approximation of Gaussian -function.

Generic evaluation of FSO system over Málaga turbulence channel with MPPM and non‐zero‐boresight pointing errors

Free space optical (FSO) communication channels are affected by fluctuations in irradiance due to atmospheric turbulence and pointing errors. Recently, a generalized statistical model knows as Malaga ( M ) was developed to describe irradiance fluctuations of the beam propagating through a turbulent medium. In this paper, an approximate finite-series probability density function (PDF) for composite M turbulence with pointing errors is verified. Considering multiple pulse-position-modulation (MPPM) with intensity modulation and direct detection, specific closed-form expressions for average symbol error rate (ASER) and outage probability are obtained. Moreover, asymptotic expressions for ASER and outage probability over the Malaga channel with pointing errors are presented. Finally, ASER and outage probability expressions are deduced in three turbulence regimes, strong, moderate, and weak. Therefore, simulation results are given to confirm the accuracy of the proposed expressions. The results show that the optimum beam divergence angle is 1 mrad for zero-boresight displacement and 2 mrad for nonzero-boresight at a distance of 1 km. By increasing the range to 5 km, atmospheric turbulence is found to have the dominant effect over boresight displacement. Moreover, the system performance at the optimized divergence angle is studied in terms of transmit power, normalized boresight, and link distance.

Error performance of QAM schemes for SIMO and MIMO networks

In this paper, we analyze the average symbol error rate (ASER) of single-input multiple-output (SIMO) networks for rectangular quadrature amplitude modulation (RQAM) and cross-QAM (XQAM) subject to Rayleigh fading. Then, we investigate the performance of RQAM for a SIMO system under κ-μ fading conditions. And also, we consider a multiple-input multiple-output with single transmit antenna selection and maximal ratio combining over Rayleigh fading environments. To analyze the key parameters on the network performances, we propose the analytical expressions of ASER for the considered networks. Assuming flat fading, the obtained exact and approximate expressions for ASER based on the probability density function approach. Furthermore, we present asymptotic expressions of RQAM and XQAM schemes for a SIMO system over Rayleigh fading at the high signal to noise ratio to evaluate the network performance in terms of diversity gain. Finally, simulations are ensured to confirm the correctness of our frameworks in this study.

Approximate ASER analysis of MIMO TAS/MRC networks over Weibull fading channels

In this paper, the average symbol error rate (ASER) evaluation of multiple-input-multiple-output (MIMO) systems with transmit antenna selection (TAS) and maximal ratio combining (MRC) are analysed under Weibull fading conditions. The impact of additive white Gaussian noise (AWGN) and additive white generalized Gaussian noise (AWGGN) on the ASER evaluation of the MIMO TAS/MRC networks are considered. Closed form approximate and asymptotic ASER expressions of the considered network with AWGN for different quadrature amplitude modulation techniques are derived based on the probability density function approach. The closed-form approximate and asymptotic ASER expressions for the AWGGN case are also obtained. In addition, a comprehensive analysis of the ASER performance for the MIMO TAS/MRC networks is demonstrated by varying the fading parameter values, numbers of transmitter-receiver antennas and constellation size. Finally, the obtained theoretical results are confirmed through the exact simulation results.

Different QAM schemes analyses for ARS fading channels

AbstractQuadrature amplitude modulation (QAM) techniques are employed for various communication systems due to its advantages such as efficient bandwidth and high rate. In this paper, the average symbol error rate (ASER) performances of single‐input single‐output networks are investigated to address the different QAM schemes combined use. The link in the network experiences the alternate Rician shadowed (ARS) fading which has the benefit of contributing left or right‐sided bimodality. Four different QAM schemes such as rectangular QAM, cross‐QAM, hexagonal QAM, and square QAM are used for the considered network. Under these assumptions, new closed‐form expressions for the ASER in terms of elementary functions and Meijer's G functions are derived. The derived ASER expressions are obtained by employing the Prony approximation with two terms which has fractional coefficients to provide precise results. Based on the second‐order exponential function approximation for Gaussian Q‐function, the ASER expressions of the considered system are also proposed. Additionally, we provide other important engineering insights based on the high signal‐to‐noise‐ratio analysis of the ASER performance over ARS fading channels. Finally, all our theoretical results are confirmed with simulations.

On the Performance Analysis of Higher Order QAM Schemes Over Mixed RF/FSO Systems

In this work, the performance of a dual-hop variable gain amplify-and-forward (AF) mixed radio frequency (RF)/free space optics (FSO) system is analyzed in details. As variable gain AF relay network is considered, processing delay results in outdated channel state information (CSI) during amplification at the relay. For general applicability, the RF link is modeled with the generalized Nakagami-m fading. The FSO link is modeled with the Gamma-Gamma distribution which is affected with the atmospheric turbulence and pointing error impairments, and both the intensity modulation with direct detection (IM/DD) and heterodyne detection are employed at the FSO receiver. In this context, analytical expressions of outage probability and ergodic capacity are derived in terms of Meijer-G function and extended generalized bivariate Meijer-G function. For diversity order, asymptotic outage probability expression is also derived. Further, cumulative distribution function based generalized average symbol error rate expressions for various quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived in terms of Meijer-G function. Furthermore, a detailed comparative study of various modulation schemes is presented and the impact of pointing error, atmospheric turbulence, outdated CSI, and Nakagami-m parameter are highlighted on the system performance. Finally, all the analytical results are verified through Monte-Carlo simulations.

On ASER performance of higher order QAM schemes in two‐way multiple‐relay networks under imperfect CSI

In this study, the authors present an analytical approach to evaluate the performance of a two-way multi-relay system with direct link using a three-phase analogue network coding and opportunistic relay selection scheme. Herein, the imperfect channel state information is considered over independent and non-identically distributed Nakagami-m fading channels with integer-valued fading parameter. For analysis, initially, the closed-form expressions of cumulative distribution function and moment generating function (MGF) for the considered system are derived. Further, by using the MGF-based approach, generalised expressions of average symbol error rate (ASER) for higher-order quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived. They then analyse the asymptotic behaviour of ASER expression to evaluate the system's diversity order. Furthermore, a comparative analysis of the ASER performance for various QAM constellations is illustrated and impact of the number of relays, fading parameter, relay location, and channel estimation error are highlighted on the system's performance. Finally, all the analytical results are validated through Monte-Carlo simulations.

On ASER Analysis of Energy Efficient Modulation Schemes for a Device-to-Device MIMO Relay Network

In this paper, we investigate the performance of a device-to-device (D2D) multiple-input and multiple-output (MIMO) communications using an amplify-and-forward relaying for various energy-efficient modulation schemes. For analysis, transmit antenna selection strategy is employed at the transmitter to select the best transmit antenna which maximizes the received signal power. In the analysis, we optimized the relay location to obtain the lowest outage probability possible and derived the generalized upper-bound average symbol error rate expressions of energy-efficient futuristic modulation schemes such as square quadrature amplitude modulation (QAM), rectangular QAM, cross QAM, and hexagonal QAM for D2D network. Further, we have derived the ergodic capacity expression to calculate the achievable rates. Comparative analysis of different QAM schemes for various constellation orders is also presented. Furthermore, the impact of the relative position of relay, path loss, and the number of antennas are also highlighted. Finally, the derived analytical results are verified through Monte-Carlo simulations.

Average Symbol Error Rate Analysis for Non-Orthogonal Multiple Access With $M$ -Ary QAM Signals in Rayleigh Fading Channels

This letter investigates a symbol error rate (SER) performance of the downlink non-orthogonal multiple access (NOMA) scheme with symbol-level successive interference cancellation (SIC). Exact and closed-form expressions for average SERs of individual users are derived under Rayleigh fading channels considering imperfect SIC when the square quadrature amplitude modulation (QAM) symbols of two users are superposed and transmitted using NOMA. In addition, a power allocation criterion of NOMA is provided for the design of feasible QAM constellations when the modulation orders of two users are given.

Error performance of digital modulations over Fisher-Snedecor F fading channels

In this paper, symbol error probability (SEP) and the average symbol error rate (ASER) of digital modulation schemes are derived in the presence of Fisher-Snedecor F fading. First, an analytical SEP expression is proposed based on complementary cumulative distribution function (CDF) for M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Then, an asymptotic solution is also presented for the SEP of M-PSK and M-PAM modulations in order to get more insights on the performance at high signal-to-noise ratio (SNR) regime. Finally, an exact ASER expression for rectangular quadrature amplitude modulation (RQAM) is derived and then, the ASER performance is analyzed based on two different upper bound approximations of Gaussian Q-function in Fisher-Snedecor F fading channels. The proposed expressions are not only valid for integer values of fading and shadowing parameters but also valid for non-integer values. The performance results which are in good agreement with the exact simulations are illustrated for different modulation schemes and various configurations of fading and shadowing parameters.

An Approximate Error Expression for RQAM Scheme under α-η-µ Fading Conditions

In this paper, average symbol error rate (ASER) performance of rectangular quadrature amplitude modulation (RQAM) scheme is analyzed over α-η-µ fading channels. First, an ASER expression is derived based on Chernoff approximation of Gaussian Q-function. Then, an asymptotic ASER formula is obtained for analyzing system behavior at high signal-to-noise ratio (SNR) regime. The ASER performance is presented for different modulation levels and fading parameter values. In addition, relative truncation error (RTE) is illustrated in order to determine how many terms are needed for the computation of proposed expression. It is shown that analytical results are in close agreement with exact results.

QAM signaling over [formula omitted] shadowed fading channels

In this study, average symbol error rate (ASER) expressions for rectangular quadrature amplitude modulation (RQAM) and cross quadrature amplitude modulation (XQAM) over κ−μ shadowed fading are proposed by considering two different system models. In the first system model, a single-input–single-output (SISO) scheme is considered while a multiple-input–multiple-output (MIMO) with single transmit antenna selection and maximal ratio combining (TAS/MRC) is investigated as a second system model. First, the exact, approximate and asymptotic ASER expressions of RQAM and XQAM for a SISO system model are proposed based on probability density function (PDF) of instantaneous signal-to-noise ratio (SNR). Second, ASER expressions of RQAM and XQAM schemes for a MIMO system with TAS/MRC are obtained by using the PDF of instantaneous SNR at the receiver side. Then, ASER performances of RQAM and XQAM for the considered two system models are compared in the presence of different fading configurations. Finally, our numerical results illustrate that the analytical ASER expressions proposed in this study are well agreement with their simulations.

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.