Expressions For Symbol Error Rate Research Articles

Comprehensive performance analysis of hybrid FSO/RF space–air–ground integrated network

Free space optics (FSO) communication due to its large optical carrier bandwidth offers better data rates close to gigabits per second (GBPS) compared to radio frequency (RF) communication and can support seamless ubiquitous high-speed broadband connectivity, which is a significant requirement for sixth-generation (6G) communication. It is also envisioned that the data transmission in 6G communication will be over space–air–ground integrated network (SAGIN) to provide broadband global mobile connectivity. Thus, our main aim in this paper is to investigate the performance of a dual-hop (DH) system model utilizing high-altitude platform station (HAPS) as a relay station with FSO communication for SAGIN scenario, which is expected to be featured in 6G communication. Despite various advantages, HAPS-based FSO satellite communication (SATCOM) is undermined by several factors such as atmospheric turbulence, pointing errors, and atmospheric attenuation. To improve the system performance in terms of capacity and reliability, hybrid FSO/RF communication with RF link as a backup is utilized between ground station (GS) and HAPS. Further, comprehensive end-to-end system performance is investigated by deriving unified closed-form expressions for outage probability and average symbol error rate (SER). We also obtain approximate upper bound expressions for ergodic capacity and outage capacity. The asymptotic expressions are also derived to obtain the diversity order. Here, FSO and RF links are modelled using generalized Malaga distribution with non-zero boresight pointing errors and shadowed κ−μ distribution, respectively. Further, the closed-form expressions for optimum switching threshold signal-to-noise ratio (SNR) are derived and the obtained optimal SNR values are verified using a numerical optimization technique. Finally, the results show that the proposed DH SAGIN-based hybrid FSO/RF SATCOM system is more reliable as well as achieves higher capacity compared to the FSO-based SATCOM systems.

Asymptotic performance of FBMC-PAM systems in frequency-selective Rayleigh fading channels

This paper deals with the performance analysis of the recently introduced FBMC-PAM system, a multicarrier scheme that represents a promising alternative to OFDM to meet the requirements of cognitive radio or machine type communications. An analytical expression of the symbol error-rate (SER) of the single-tap sub-channel (SC) equalizer designed as the inverse of the complex gain that multiplies the symbol of interest at the output of the filter matched to each subcarrier, is derived. Specifically, an asymptotic (i.e., for a large number of subcarriers) analytical expression of the SER of the SC receiver operating in frequency-selective Rayleigh fading channel is obtained and compared via simulation results. Moreover, a simple approximate closed-form expression of the asymptotic SER of the SC receiver is obtained by taking into account, for each active subcarrier, only inter-symbol interference (ISI) terms due to the considered subcarrier and adjacent subcarriers, and, moreover, inter-carrier interference (ICI) terms due to adjacent subcarriers.

Performance Analysis of Dual-Hop THz Transmission Systems Over α-μ Fading Channels With Pointing Errors

In this article, the performance of a dual-hop relaying terahertz (THz) wireless communication system is investigated. In particular, the behaviors of the two THz hops are determined by three factors, such as the deterministic path loss, fading effects, and pointing errors. Assuming that both THz links are subject to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> fading with pointing errors, we derive exact expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR). With these statistical expressions, some important performance metrics are evaluated, such as the outage probability (OP), average bit error rate (BER), and average channel capacity (ACC). Moreover, the asymptotic analyses are presented to obtain more insights. The results show that the dual-hop relaying scheme has better performance than the single THz link. Furthermore, the system diversity order depends on the fading parameters and pointing errors of both THz links. In addition, we extend the analysis to a multirelay cooperative diversity system and derive the asymptotic symbol error rate (SER) expressions. Finally, the derived analytical expressions are verified by the Monte Carlo simulation.

On the maximal-ratio combining of FSO and RF links over generalized distributions and its applications in hybrid FSO/RF systems

Recently, generalized fading distributions have gained substantial research interest due to their applicability and adaptability in practical scenarios. In this paper, we derive the exact closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the maximal-ratio combining (MRC) of the free space optics (FSO) and radio frequency (RF) links over the most generalized Malaga and α-η-κ-μ fading models. Further, with the help of derived MRC channel statistics (i.e. PDF and CDF), closed-form expressions for outage probability and average symbol error rate (SER) for the hybrid FSO/RF system based on MRC and adaptive combining schemes are derived. In an adaptive combining scheme, the MRC of FSO and RF links is employed at the receiver, if the operating FSO link quality is unacceptable for transmission. Further, the derived expressions are unified for both intensity modulation/direct detection (IM/DD) and heterodyne detection (HD) techniques. We have considered the effects of atmospheric path loss, atmospheric turbulence-induced fading and non-zero boresight pointing errors in case of the FSO link. We have also determined the optimum switching threshold and beam waist values for the adaptive combining scheme to achieve optimal performance. Moreover, computationally less complex asymptotic expressions are calculated and the diversity gains of MRC and adaptive combining schemes are determined. Finally, the performances of single-link FSO, hard-switching-based hybrid FSO/RF, MRC, and adaptive-combining-based hybrid FSO/RF systems are compared and the inferences are reported under various turbulence conditions, link distances, weather conditions, and severity of the pointing errors.

Performance analysis of a UAV-based IRS-assisted hybrid RF/FSO link with pointing and phase shift errors

Intelligent reflecting surface (IRS)-assisted wireless communication has recently become a promising technology to relax the line-of-sight requirement and also to provide a communication link in uncovered and remote areas. In this work, an alternate implementation of unmanned aerial vehicle (UAV)-based IRS-assisted hybrid free space optics/radio frequency wireless communications is presented. Phase shift errors occur due to the presence of reflecting elements in the IRS and affect the reflected beam. We consider the effect of phase shift error along with atmospheric turbulence, which is modeled as gamma-gamma distribution. Furthermore, a statistical model is considered for pointing errors due to the position and orientation fluctuation of the mounted IRS on the UAV. We derive closed-form expressions of the average symbol error rate and spectral efficiency of the considered system, under the combined effects of atmospheric turbulence, pointing error, and phase shift error. In addition, we present asymptotic analysis of the average symbol error rate of the system in a high SNR region and evaluate the diversity order and coding gain. The derived results are further validated using Monte Carlo simulation.

On the performance of a relay assisted hybrid RF-NLOS UVC system with imperfect channel estimation

Non-line-of-sight (NLOS) ultraviolet communication (UVC) is emerging as an attractive optical wireless communication technology that enables wireless connectivity in radio-frequency (RF) prohibited areas with no LOS availability. NLOS UVC, however, suffers from a very high path loss, thereby restricting its usage to smaller link distances. In this paper, we address the challenge of providing long-distance wireless connectivity to RF prohibited areas by mixing NLOS UVC with RF communication using a decode-and-forward relay. The RF link is modeled using Rayleigh distribution, and the NLOS UV link is modeled using lognormal distribution under weak turbulence conditions. A framework for analytical expressions of the outage probability and probability density function (PDF) of the end-to-end signal-to-noise ratio is presented by considering the practical scenario of imperfect channel state information (CSI) at the receiver. Subsequently, a PDF based novel closed-form analytical expression of the average symbol error rate is deduced for spectrally efficient higher-order modulation schemes, including rectangular quadrature modulation (RQAM), square QAM (SQAM), cross-QAM (XQAM), and hexagonal QAM (HQAM). Numerical investigations are conducted, and the impact of CSI imperfections on the system performance is evaluated. It is shown that the RF link is more vulnerable to channel estimation error (CEE) than the NLOS UV link. Further, it is illustrated that for constellation sizes greater than four, HQAM always performs better than the RQAM, SQAM, and XQAM schemes, irrespective of the amount of CEE present. Furthermore, it is shown that an elevation angle of 70° or less in the NLOS UVC link results in better outage performance. Correctness of the derived analytical expressions is supported through extensive Monte Carlo simulations.

On Performance of IRS-Assisted Hybrid Satellite-Terrestrial Cooperative Communication

In this paper, an Intelligent Reflecting Surface (IRS)-assisted hybrid satellite-terrestrial cooperative system is considered, where direct transmission between satellite and destination is not present due to masking effect and destination node receives amplify-and-forward (AF) relayed transmission through an IRS. It is assumed that the channel between satellite and relay undergoes Shadowed-Rician fading, while the cascaded relay-IRS-destination link follow Rayleigh distribution. The performance of the considered system is evaluated by deriving an approximate closed-form expression for the average symbol error rate (SER) of the considered system for <i>M</i>-ary phase shift keying modulation. Further, analysis for diversity order is also carried out using the asymptotic SER. In addition to this, analytical expressions for upper bound on ergodic capacity and outage probability of considered system are also obtained.

Single- and Multi-Carrier Systems Affected by Impulsive Noise: Covid-19 View

In this work we present a fully stochastic model of performance analysis of single- and multi-carrier modulations (SCM and MCM) in communication systems affected by impulsive noise. The key performance of the model is the symbol error rate (SER), which is fully determined as a function of the system parameters, including the frame length, symbol power, white noise power, impulsive noise power, and the probability of the impulse events. We derive closed-form analytical expressions for the systems SER and compare them with simulation results, showing very good agreement for all the impulsive noise scenarios. Specifically, we show under which conditions a MCM system performs better than a SCM one, and vice versa, which can be used to apply an optimal switching policy that minimizes SER. The model developed for SCM and MCM systems is conceptually applied to the Covid-19 phenomenology and, consequently, the results obtained for SCM and MCM scenarios are interpreted to inform decision and management policies of social distancing (lock/roam). Specifically, we also show when the “roam” strategy performs better than the “lock” strategy, and vice versa, thus enabling the design of an optimal control policy that minimizes the mortality rate (MR). However, the proposed model for Covid-19, which assumes a similarity with SCM/MCM systems, may not be easy to be tested in practice in the absence of adequate statistical data. Therefore, any management decision should not be based (only) on the proposed model adapted to Covid-19, and necessarily requests the integration of experts opinions.

Successive Interference Cancellation Decoding With Adaptable Decision Regions for NOMA Schemes

In this work, we propose adaptable decision regions in the successive interference cancellation (SIC) decoder for the three-user uplink/downlink non-orthogonal multiple access (NOMA) scheme by exploiting the knowledge of the channel gains. We present scenarios in which the modified SIC decoder outperforms the traditional one and is able to replicate the performance achieved by a deep learning-based decoder. We present analytical symbol error rate (SER) expressions for the three users, compare them to simulation results, and discuss possible consequences of our analysis, such as the optimal power allocation. We also employ heatmaps to analyze the joint influence on the SER of some system parameters, such as signal-to-noise ratio and channel gains.

Performance Analysis of Satellite Communication Systems With Randomly Located Ground Users

Satellite communication (SatCom) is an essential component of next-generation wireless communication to achieve a goal of ubiquitous connectivity on globe. The outage event of SatCom link connecting to a network is more critical in an infrastructure-deficient remote area. In this paper, we analyze outage probability (OP) and symbol error rate (SER) over SatCom downlink channels when the users are randomly located in single beam and multibeam area. The downlink beams will suffer from propagation loss and the shadowed-Rician fading depending on the user location which is assumed to follow a Poisson point process. For mathematically tractable, informative, and insightful interpretation, we obtain the asymptotic OP and SER expressions of user link under several channel conditions in the high power regime. Finally, numerical results are presented to verify the analysis and show the accuracy of the asymptotic results.

Ergodic Capacity and Symbol Error Rate Analysis of a Wireless System with α-μ Composite Fading Channel

A composite α-µ/Lognormal fading channel is proposed with several channel performance criteria. This model considers the most effective occurrences in a fading channel, mainly non-linearity, multi-cluster nature of propagation medium, and shadowing effects. The new generation of communication systems is moving towards the use of millimetre waves (mmW). In this type of propagation, large-scale effects of fading channel on the received signal are significant, so in the proposed composite model, the lognormal distribution is considered to model large-scale effects of fading, which is the most accurate distribution to model shadowing. The Gaussian-Hermite quadrature sum is used to approximate the probability distribution function (PDF) of the proposed model. After calculating the statistics, the symbol error rate (SER) and ergodic capacity are computed. The Mellin transform technique is used to calculate the SER expression of different modulation schemes; then, ergodic capacity is computed for a diverse frequency spectrum. Finally, the Monte Carlo method is used to evaluate the analyses.

Symbol Error-Rate Analytical Expressions for a Two-User PD-NOMA System with Square QAM

Power domain non-orthogonal multiple access (PD-NOMA) is one of the most perspective multiplexing technologies that allows improving the capacity of actual networks. Unlike orthogonal multiple access (OMA), the PD-NOMA non-orthogonally schedules multiple users in the power domain in the same orthogonal time-spectrum resource segment. Thus, a non-orthogonal multiplexed signal is a combination of several user signals (usually, modulation and coding schemes (MCS) based on quadrature amplitude modulation) with different power weights. The symbol error rate (SER) and bit error rate (BER) performances are one of the main quality characteristics of any commutation channel. The issue is that a known analytical expression for BER and SER calculation for conventional OMA cannot be applied in terms of the PD-NOMA. In the following work, we have derived the SER and BER analytical expressions for gray-coded square quadrature amplitude modulation (QAM) user channels that are transmitted in two-user PD-NOMA channel under additive white Gaussian noise (AWGN). Through the simulation, the verification of the provided expressions is presented for four multiplexing configurations with various user power weights and QAM order combinations.

MIMO Hybrid FSO/RF System Over Generalized Fading Channels

Free-space optics (FSO) communication is often unreliable, especially for long distances, as it suffers from attenuation due to foggy weather, atmospheric turbulence, and pointing errors. To avoid communication link failure, radio frequency (RF) communication, which is unaffected from these effects, is utilized when FSO communication is in outage. Diversity is known to counteract the adverse fading effects, therefore, this paper presents a transmit aperture/antenna selection (TAS) and selection combining (SC)-based multiple-input-multiple-output (MIMO) hybrid FSO/RF system. The proposed system consists of a MIMO FSO and RF sub-systems. The MIMO FSO sub-system is given higher priority to transmit and receive using the selected best link. The best link of the MIMO RF sub-system is used when the FSO sub-system is in outage. The probability density function (PDF) and cumulative distribution function (CDF) expressions for TAS/SC-based MIMO FSO and RF sub-systems are derived. The derived PDF and CDF expressions are used further to derive the exact and asymptotic expressions for outage probability, average symbol error rate (SER), and capacity of the hybrid system. From the asymptotic SER expressions, the diversity order of the proposed system is determined. The optimum values for the threshold SNR and transmit beam waist, which minimize the average SER, are obtained. Further, the obtained optimal values using analytical expressions are verified using numerical optimization technique. The effect of multiple apertures/antennas, pointing errors, and atmospheric attenuation over the system performance is analyzed extensively by varying the FSO and RF channel parameters. The results show that the proposed hybrid FSO/RF system is more reliable compared to the individual MIMO FSO and RF systems and achieves higher capacity compared to the MIMO RF system.

ASER Analysis of Hybrid Receiver Based SWIPT Two-Way Relay Network

In this paper, we investigate the performance of a hybrid receiver-based simultaneous wireless information and power transfer (SWIPT) two-way relay network over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> faded channels. A hybrid receiver is adopted at the relay node that utilizes both the time switching (TS) and power splitting (PS) protocols for energy harvesting and information transmission. Amplify-and-forward relaying protocol is utilized at the relay node to process the information in half-duplex mode. In the considered network, impact of a practical non-linear power amplifier (NLPA) at the relay node is considered. Selection combining is performed at the destination node to utilize the direct-link and relay assisted signals. For the considered system, the analytical expressions of outage probability (OP) and asymptotic OP are derived over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> faded channels for both the integer and non-integer value of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> . The analytical expression of the system throughput and energy efficiency of the considered network are also derived. Further, the analytical expression of ergodic capacity is derived in terms of the Meijer-G function. By utilizing a cumulative distribution function based approach, analytical expressions of average symbol error rate (ASER) for general order hexagonal quadrature amplitude modulation (QAM), general order rectangular QAM, and 32-cross QAM schemes are derived. For different QAM constellations, a comparative ASER analysis is also illustrated. Furthermore, the impact of TS factor, PS ratio, energy conversion efficiency, NLPA, and threshold data-rates on the considered network is also highlighted. Finally, Monte-Carlo simulations are performed for validation of the derived analytical expressions.

Design and analysis of spatial modulation based orthogonal time frequency space system

In this paper, we design a spatial modulation based orthogonal time frequency space (SMOTFS) system to achieve improved transmission reliability and meet the high transmission rate and high-speed demands of future mobile communications, which fully utilizes the characteristics of spatial modulation (SM) and orthogonal time frequency space (OTFS) transmission. The detailed system design and signal processing of the SM-OTFS system have been presented. The closed-form expressions of the average symbol error rate (ASER) and average bit error rate (ABER) of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function (MGF). Meanwhile, the system complexity has been evaluated. Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio (SNR) regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing (SM-OFDM) system with limited complexity increase under mobile conditions, especially in high mobility scenarios.

Spectrally efficient M‐ary QAM based multi‐antenna cooperative system over TWDP fading channel

AbstractTo cater the ever‐increasing demand of wireless high‐speed data access and mobile users, one of the potential enablers toward the sustainable improved network capacity is the network densification at different layers of the radio access system. In this article, a possible solution to achieve a spectrally efficient, ultradense network (UDN) for cellular communication is analyzed. In particular, the performance of the generalized M‐ary quadrature amplitude modulation (M‐QAM) scheme for multiantenna cooperative decode‐and‐forward (DF) system over two‐wave with diffuse power (TWDP) fading is presented. The TWDP fading is evaluated using the moment generating function (MGF) based approach on spectral efficient QAM transmission. In this article, novel closed‐form expressions for the exact average symbol error rate (ASER) for the generalized rectangular‐QAM (R‐QAM) and square‐QAM (S‐QAM) schemes are presented. The obtained expressions are in the form of Appell's and Laureicella's confluent hypergeometric function which can be evaluated mathematically either in the series or the integral‐form. Further, the asymptotic analysis is also presented for the considered system to get better insights into the system. The analytical results derived are corroborated by simulations to validate the accuracy of the analysis.

Intelligent Reflecting Surfaces Assisted UAV Communications for IoT Networks: Performance Analysis

The increasing demand for wireless connectivity and the emergence of the notion of the Internet of Everything require new communication paradigms that will ultimately enable a plethora of new applications and new disruptive technologies. In this context, the present contribution investigates the use of the recently introduced intelligent reflecting surface (IRS) concept in unmanned aerial vehicles (UAV) enabled communications aiming to extend the network coverage and improve the communication reliability as well as spectral efficiency of Internet of Things (IoT) networks. In particular, we first derive tractable analytic expressions for the achievable symbol error rate (SER), ergodic capacity, and outage probability of the considered set up. Following this, we also derive tight upper and lower bounds on the average signal-to-noise ratio (SNR). Our derivations are then compared with the corresponding asymptotic performance, based on the central limit theorem (CLT) assumption, which reveals that the asymptotic SNR falls within the area between derived bounds, and approaches either bound depending on the number of reflective elements (REs). We further show that the asymptotic SER becomes in a tight agreement with the corresponding exact simulation SER for N ≥ 16. In addition, the offered results demonstrate that the use of the IRS is significantly effective as they assist in improving the achievable SER by five orders of magnitude. We further demonstrate that, in terms of achievable ergodic capacity, IRS-assisted UAV communication systems can exhibit ten times higher capacity compared to conventional UAV communications. Based on the above, these results and related insights are anticipated to be useful in the design and deployment of IRS-assisted UAV systems in the context of beyond 5G communications, such as 6G communications.

SER performance of MIMO full-duplex relay system with channel estimation errors and transceivers hardware impairments

In practice, traditional wireless communication systems are often affected by various negative factors such as channel estimation errors (CEE) and transceiver hardware impairments (THI). For in-band full-duplex (FD) communication systems, besides CEE and THI impacts, imperfect self-interference cancellation will significantly degrade the system performance because of residual self-interference (RSI). This paper aims to investigate the performance of a multiple-input multiple-output (MIMO) FD relay (FDR) system in realistic scenarios where the impacts of CEE, THI, and RSI are taken into account. We mathematically derive the exact closed-form expression of symbol error rate (SER) of the considered MIMO-FDR system and validate the derived expression by Monte-Carlo simulations. Numerical results indicate that the impacts of three imperfect factors (CEE, THI, and RSI) are remarkable. Specifically, with the considered values of CEE, THI, and RSI, the impact of CEE on the SER is most substantial. Additionally, compared with the ideal system (perfect channel estimations, transceiver hardware, and self-interference cancellation), the SER of the considered system is significantly higher and goes to the error floor fast. Therefore, it is crucial to apply all solutions for reducing the CEE, THI, and RSI in the considered MIMO-FDR system.

Error performance analysis of optical communication over Lognormal-Rician turbulence channel using Gram-Charlier Series

Abstract In this paper, the symbol-error rate (SER) performance of a coherent free-space optical (FSO) communication system in lognormal-Rician turbulence channel is analyzed using the generalized Gram-Charlier (GCC) series. We proposed the differential evolution (DE) algorithm to solve the parameters in GCC efficiently. It is shown that highly accurate closed-form SER expressions are obtained for M-ary phase-shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) schemes with maximum ratio combining (MRC) technique. The asymptotic error rate analysis is presented to reveal the performance behavior in the high signal-to-noise (SNR) regime. The effects of imperfect phase noise compensation on the error rate performance are also studied, and it is found that the impact of phase compensation error can be small enough with loop SNR ρ c more than seven.

Study of SER and BER in NOMA Systems

At present, non-orthogonal multiple access (NOMA) techniques have attracted broad attentions, since they could improve the throughput of cellular networks efficiently. However, the symbol error rate (SER) and bit error rate (BER) have not been studied comprehensively in the NOMA, even they play a key role in communication system control, e.g., power allocation. To address such an issue, this paper studies the SER and BER with consideration of the downlink/uplink transmission, the number of information streams, and the channel coding jointly. For analyzing the impact of channel coding, Gray coding is introduced for the downlink transmission. The derived SER and BER are given by closed-form expressions, by which the transmission performance could be evaluated efficiently. We also show an approximate SER/BER when the transmitter could employ Gray-coding. Additionally, associating with the derived closed-form expressions, we show that there exists no error propagation/error accumulation phenomenon when the successive interference cancellation (SIC) is adopted in signal demodulation, which is treated as a major drawback of SIC demodulation in the NOMA systems. Furthermore, by analyzing the encoding/decoding processes in the current NOMA works, a joint Gray-coding scheme is introduced to reduce the SER and BER in the downlink transmission effectively. Through simulations, we validate the correctness of the derived expressions of SER and BER from different aspects.