Average Symbol Error Probability Research Articles

Constellation design for PD-NOMA-based mmWave inter-satellite communication

The upcoming sixth-generation (6G) networks are supposed to utilize frequencies beyond the fifth-generation (B5G) and serve for satellite communications. During inter-satellite millimeter wave (mmWave) communications, the transmitting satellites may have identical simultaneous power transmissions, leading to the erroneous decoding of their information. This paper describes the application of a power-domain (PD) non-orthogonal multiple-access (NOMA) scheme for both terrestrial and inter-satellite communications consisting of two users or satellites. Specifically, the user (or satellite) symbol decoding is addressed under identical power transmissions. Both the user’s (transmitting satellite’s) data are extracted by minimizing the average probability of symbol errors using a designed constellation. Analytical/graphical results along with the simulation verify decent symbol decoding at a low average noise variance. At a noise variance of 0.01, the achieved average symbol-error probability reaches an order of up to 10−5. The proposed system results in a negligible error-vector magnitude (EVM) of −10 dB at higher end of the considered signal-to-interference-plus-noise ratio (SINR) range. Further, the proposed method alleviates the successive interference cancellation (SIC) pre-requisite of NOMA, strengthening the application of NOMA with mmWaves in next-generation satellite communication systems.

Performance assessment of full-duplex two-way Internet-of-vehicles relay networks under practical imperfect conditions

Contemporary Internet-of-Things (IoT) devices in general and Internet-of-Vehicles (IoV) networks in specific are taking the benefits from using full-duplex (FD) communication with the help of relay nodes to facilitate data transmission. However, self-interference between transmit and receive antennas at the relay node may cause big trouble if self-interference cancellation (SIC) is not applied. In this paper, a rigorous analysis on the performance of FD two-way relay networks (FDTWRNs) for IoV applications under imperfect conditions is provided. Different from earlier studies on the performance of FDTWRNs where one or two imperfect factors were considered, this work simultaneously takes into account many practical issues in the implementation of the IoV networks at the physical layer, including errors in channel state information at all channel links, imperfect SIC and transceiver hardware impairment at all nodes. For relaying protocol, we consider amplify-and-forward with both fixed-gain (FG) and variable-gain (VG) protocols. The exact closed-form expressions (in terms of the system parameters) of key performance factors such as signal-to-interference-plus-noise-distortion-and-error ratio (SINER), outage probability (OP), achievable data rate (ADR), and average symbol error probabilities (ASEP) of the considered system over Rayleigh fading channels and under the combined effect of imperfect CSI, SIC, and transceiver hardware are derived mathematically using probabilistic model analysis. The correctness of the analysis is then verified by Monte Carlo simulations. Drawing upon both analytical and numerical findings, the efficacy of the FDTWRNs under consideration is meticulously and comprehensively assessed in comparison to its performance in ideal conditions characterized by one or multiple critical factors. The disparity between perfect and imperfect scenarios serves as a valuable metric for appraising the practical viability of the considered FDTWRNs when deployed in practical IoV networks.

On Performance of Low-Power Wide-Area Networks With the Combining of Reconfigurable Intelligent Surfaces and Relay

This article proposes an integration of multiple reconfigurable intelligent surfaces (RISs) with a relay to enhance the performance of a low-power wide-area (LPWA) network. Specifically, besides using the traditional relaying approach to assist the transmission between an Internet of Things (IoT) sensor and a gateway, multiple RISs are also utilized to boost the intermediate links between the IoT sensor and the relay and between the relay and the gateway. We mathematically derive the analytical expressions of average outage probability (AOP) and average symbol error probability (ASEP) of this multiple-RIS-relay aided LPWA network over Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channels. The performance of the proposed network is also compared with the performance of the relay-aided LPWA network without using RISs. The analytical results show that the exploitation of RISs can greatly enhances the performance of the LPWA network. Thus, the multiple-RIS-relay aided LPWA network can operate at the high frequency band for long range transmission. Moreover, the effect of various important factors such as the location of the RISs, the Nakagami-<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> parameters, the data transmission rate, and the modulation scheme on the performance of the multiple-RIS-relay aided LPWA network are also investigated in practical scenarios.

Performance analysis of RIS-Assisted wireless networks in the presence of imperfect phase errors

In this article, an analysis of the average symbol error probability (ASEP) for a reconfigurable intelligent surface (RIS)-assisted wireless network with imperfect phase noise errors is proposed. In particular, we focus on a RIS-assisted wireless transmission in which imperfect phase errors are modeled by the Tikhonov distribution. The source (S) and destination (D) nodes are equipped with a single antenna, and the channels between the S-RIS and RIS-D nodes exhibit Rayleigh fading which is a good fit for the non-line-of-sight instances. For this system, we derive novel and exact analytical and asymptotic expressions for the ASEP, and the obtained ASEP expressions are then exploited to evaluate the error performance of under different network configurations. The proposed theoretical analysis is confirmed through the exact simulation results.

Performance Analysis and Optimization of UAV-Assisted Networks: Single UAV With Multiple Antennas Versus Multiple UAVs With Single Antenna

In this article, we make a comparison between the following two unmanned aerial vehicles (UAVs) network models: 1) multiple UAVs equipped with a single antenna and 2) a single UAV equipped with multiple antennas (MAs). In order to assess the performance of the two network models, we derive closed-form expressions for the outage probability, average symbol error probability, ergodic capacity, and energy efficiency of both models. After that, we formulate a joint optimization problem to obtain the optimal power values and UAV altitudes using the particle swarm optimization technique. We consider in the first scenario both uniformly and nonuniformly distributed UAVs assuming 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> fading channels. Numerical results are obtained for different simulation scenarios to validate our proposed model, followed by conclusions to show its effectiveness. The results show the superiority of the multiple uncorrelated antennas single UAV model over a single antenna multiple UAV model. Moreover, several comparisons have been performed between blanket transmission mode (BTM) and single transmission selection mode (STSM) for the multiple UAVs model, which reveal that the BTM outperforms the STSM for different systems parameters.

Gamma-shadowed two-ray with diffuse power composite fading model

In this paper, a novel gamma-shadowed two-ray with diffuse power (GS-TWDP) composite fading model is proposed by assuming that the shadowing-caused mean power variations of the received signal, affected by TWDP multipath fading, are gamma distributed. For the proposed model, the essential statistics such as probability density function (PDF), cumulative distribution function (CDF), moment generating function (MGF) and higher order moments are obtained and used to derive the approximate general order rectangular quadrature amplitude (RQAM) average symbol error probability (ASEP). That expression enabled us to investigate the effect of shadowing on overall error probability, in case when signal is propagating in channels with TWDP multipath fading. The proposed model is verified by comparing analytically obtained results with those measured at 28 GHz and reported in literature, which makes the GS-TWDP model a promising candidate for modeling propagation at millimeter wave (mmWave) frequencies. Analytical results are validated by Monte-Carlo simulation.

Extremely Accurate, Generic and Tractable Exponential Bounds for the Gaussian Q Function With Applications in Communication Systems

In this letter, we apply the Fejer’s Rule of interpolatory integration in a modified manner to obtain a very generic, tractable and extremely accurate approximation for the Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> function. We further show the utility of the proposed approximation by simplifying the error performance metrics like average symbol error probability (ASEP) of popular digital modulation techniques over a very useful κ-μ shadowed fading channel. This eliminates the need of mathematical softwares which require very high processing power (a constraint at the receiver side) yielding simplified and cost effective receiver’s design. In addition, an insight on the asymptotic ASEP (and diversity order thereof) is also highlighted in this letter.

Error Probability Analysis of Intelligent Reflecting Surface-Enabled Non-Orthogonal Multiple Access Systems

We analyze the error performance of intelligent reflecting surface (IRS)-aided non-orthogonal multiple access (NOMA) systems. We deduce novel approximate analytical expressions for average symbol error probability (SEP) for PAM and QAM. We also analyze the multi-user scenario by deriving the novel approximate analytical expressions for (i) the average SEP for multicast transmission and (ii) the average pairwise error probability (PEP) for unicast transmission. We consider Rayleigh fading direct path and independently Rician fading reflected paths from access point to users via IRS. We also formulate and solve a constrained optimization problem to determine the fraction of elements to be activated at any IRS in order to guarantee near-identical SEP performance for both the users. We present results to elucidate that adding few extra IRS elements yields SNR gain for both users, requires allocation of lower power to weaker user and supports communication with higher-order constellation without significant increase in SEP/PEP. Furthermore, a 3-bit programmable IRS yields near-identical performance as an IRS with infinite precision phase-shift. Impact of estimation error on average SEP is also investigated.

A 4-Term Exponential-Quadratic Approximation for Gaussian Q or Error Functions Accurate to $1.65\times 10^{-4}$

Integrals on [0, ∞) where the integrand is of the form Qn(a√x) p(x), where Q is the Gaussian Q function, p(·) a Gamma PDF, n a positive integer and a &gt; 0; or of the form erfn(ax + b) xr exp(-c2x2 + 2dx), where erf(x) is the error function, with integers r ≥ 0, n &gt; 0, arise in performance modelling of communication and machine learning systems. Such integrals cannot be evaluated analytically in general, but they are reducible to a set of key integrals whose integrand is erfn(ax + b) N(x; m, s) where N() is a Gaussian PDF with mean m and variance s. Seeking an efficient and accurate evaluation method, we develop a new 4-term exponential quadratic approximator (EQA) for the error function that includes both linear and quadratic terms in its exponents. The EQA minimises a sum-of-squares cost function with two “spline-type” constraints, i.e., constraints on the function value and its first derivative. This constrained optimisation problem is reduced to an unconstrained one by inverting a 4-D linear system, then solved by gradient descent. The resulting approximator has a maximum absolute error of 1.65 × 10-4 on the real line, and outperforms many other exponential sum approximators for erf(x) on x ∈ [0, 1.5] and for Q(x) on x ∈ [0, 2]. Moreover, due to its functional form, the EQA leads to an analytical formula for the set of key integrals, which, in the n = 1 case, is accurate to 3 to 4 significant figures while being orders of magnitude more efficient than Monte Carlo integration. The EQA can equally be used to obtain closed forms for the average symbol error probability of various modulation schemes on Rayleigh fading channels.

On the correlated Gamma–Gamma distribution and coherent detection performance of optical spatial modulation

The performance of optical spatial modulation (OSM) is severely damaged by correlated atmospheric turbulence (AT) channels for coherent free-space optical (FSO) communication systems. In this paper, we assume correlated AT channels comply with Gamma–Gamma distribution and present a coherent FSO-OSM system model. Based on this, we derive the closed-form approximated expressions of average symbol error probability (ASEP), and discuss the interaction of signal constellation diagram and spatial constellation diagram of the OSM under different conditions. We further illustrate relations of the ASEP caused by signal constellation and spatial constellation to AT strength and correlation. In addition, we explore the impact trends of the correlation coefficients respectively resulted from large-scale and small-scale eddies on the performance of system under different AT conditions. Through simulations, we prove theoretical results and demonstrate that the rise of AT severity and correlation coefficients can degrade the performance of coherent OSM.

Hybrid SAG-FSO/SH-FSO/RF Transmission for Next-Generation Satellite Communication Systems

Recent advances demonstrate satellite communication (SatCom) as a potent enabler for future Terabit/s global connectivity. Existing SatCom systems, however, rely mostly on radio frequency (RF) transmission, whose limited available bandwidth is the main bottleneck for further data rate increases. Free-space optical (FSO) communication links, with huge license-free bandwidth, have emerged as an attractive alternative. Despite their ability to deliver high-throughput transmissions, FSO communications are weather-dependent and susceptible to atmospheric turbulence. Hybrid FSO/RF and space-air-ground (SAG) FSO transmissions are possible solutions to increase the reliability of FSO-based transmission systems. A strategically deployed unmanned-aerial vehicle, acting as a relay, can successfully mitigate the adverse effect of atmospheric turbulence, while the hybrid FSO/RF transmission can address weather-dependent effects. These solutions can also be integrated to create a system with significantly improved performance and reliability. To evaluate the performance of the resulting integrated transmission system, we analyze the outage probability and average symbol error probability in this work. Asymptotic expressions are also derived to get further insight into the system behavior and calculate the overall diversity gain. Furthermore, we consider the optimal design of switching thresholds. The numerical results show that the integrated transmission system achieves about 10 dB performance gain over existing solutions for both downlink and uplink scenarios.

An Asymptotic Framework for Fox's H-Fading Channel With Application to Diversity-Combining Receivers

Unified statistics are valuable in the performance analysis of communication systems. In this context, Fox's H-function has been shown to be eminently suitable for diverse scenarios. Another pivotal requirement is to have a low computational complexity, which is often hard to achieve for generalized models. Given this motivation, in this article we have presented high-power, low-complexity solutions for the outage probability (OP) and the average symbol error probability (SEP). Additionally, diversity techniques are harnessed for mitigating the effect of fading, which are then analysed based on the results derived. The entire methodology is governed by the origin probability density function rather than approximating the performance metrics under high-power. All the presented mathematical expressions are compared and validated through computer simulations (Monte-Carlo) to verify the accuracy of the proposed framework.

Error Probability of a Coherent M-ary PSK FSO System Influenced by Phase Noise

In this paper, we aim to develop an analytical framework for design and analysis of new generation mobile networks fronthaul/backhaul links based on the application of free-space optical (FSO) technology. Taking the receiver hardware imperfections into account, we present an efficient analytical approach in analyzing average symbol error probability (SEP) of the coherent FSO system employing M-ary phase-shift keying (PSK). Optical signal transmission is influenced by pointing errors and atmospheric turbulence. The signal intensity fluctuations caused by atmospheric turbulence are modeled by general Málaga (M) distribution, which takes into account the effect of multiple scattered components. We estimate the range of the signal-to-noise ratio at which the SEP floor appears, as well as the value of this non-removable error floor. The results illustrate that the effect of imperfect phase error compensation on the SEP is more critical under weaker turbulence conditions and for higher order modulation formats. Based on the analytical tools presented here, it is possible to estimate tolerable value of standard deviation of phase noise for the given value of SEP. This value of standard deviation is an important parameter in designing the phase-locked loop filter in the receiver.

Pilot‐aided 1 × 2 and 2 × 2 space‐time line code systems with transmit antenna selection

SummaryThe space‐time line code (STLC), which has been recently proposed in the literature, assumes fully known channel state information at the transmitter and not the receiver. However, the effective channel gain is still required at the receiver to coherently detect ‐ary quadrature amplitude modulation ( QAM) symbols. In this paper, we propose pilot‐aided STLC systems, which do not require the effective channel gain at the receiver to detect the QAM symbols. In order to further improve the error performance of the proposed schemes, we present the pilot‐aided STLC systems with transmit antenna selection (TAS). Using a more direct and simpler approach, we derive the average symbol error probability (ASEP) of the coherent STLC systems with TAS, which represents the lower bound of the pilot‐aided STLC systems with TAS. For comparison, in a similar manner, we also derive the ASEP of the coherent STLC systems without TAS, which represents the lower bound of the pilot‐aided STLC systems. For pilot‐aided STLC systems with TAS, the gap between the simulated symbol error rate (SER) and the derived theoretical ASEP lower bound is very small. For a given number of transmit antennas, the simulated SER and theoretical ASEP also show that the error performance of the pilot‐aided STLC systems with or without TAS is superior to the pilot‐aided STLC systems with TAS by at least 1.8 dB.

Performance Analysis of I/Q Imbalance With Hardware Impairments Over Hyper Fox’s H-Fading Channels

Impairments baseband model in-phase and quadrature-phase Imbalance (IQI) and Residual hardware impairments (RHI) are two key factors degrading the performance of wireless communication systems (WCSs), particularly when high-frequency bands are employed, as in 5G systems and beyond. The impact of either IQI or RHI on the performance of various WCSs has been investigated exclusively in a separate way. To fill this gap, in this paper, the joint effect of both IQI and RHI on the performance of a WCS subject to Hyper Fox’s H-fading (HFHF) channel, is investigated. Such a fading model generalizes most, if not all, of well-known fading and turbulence models. To this end, closed-form expressions for the outage probability (OP), Average channel capacity (ACC) under constant power with optimum rate adaptation (ORA) policy, and average symbol error probability (ASEP) for both coherent and non-coherent modulation schemes are derived. Specifically, all the analytical expressions are derived for three different scenarios: (i) ideal Tx and Rx impaired, (ii) Tx impaired and ideal Rx, and (iii) both Tx and Rx are impaired. Further, asymptotic expressions for OP, ACC under ORA policy, and ASEP are obtained, based on which, insightful discussions on the IQI and RHI impacts are made. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha -\mu $ </tex-math></inline-formula> and Málaga <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {M}$ </tex-math></inline-formula> turbulence with pointing error distribution models have been considered as particular cases of the HFHF distribution. The analytical derivations, endorsed by simulation results, demonstrate that the RF impairments’ effects should be seriously taken into account in the design of next-generation wireless technologies.

Performance analysis of SWIPT assisted cooperative Internet of Things (IoT) network under Optimal and Adaptive Power Splitting Schemes

In this paper, a Simultaneous Wireless Information and Power Transfer (SWIPT) aided Cooperative Relaying (CoR) scheme is employed to perform energy harvesting and information transmission at the same time for a low-powered Internet of Things (IoT) network. A decode and forward power splitting relaying (DF-PSR) protocol is utilized, and performance analysis is made by considering two scenarios, namely (i) Energy Harvesting (EH) relay and non-EH IoT device, and (ii) EH relay and EH-IoT device. Analytical models for computing Average Symbol Error Probability (ASEP) based on an Optimal Power Splitting Scheme (OPSS) for Scenario-1 and Joint Optimal Power Splitting Scheme (JOPSS) for Scenario-2 are presented by considering the effects of relay location. Moreover, an Adaptive Power Splitting Scheme (APSS) is suggested based on instantaneous Symbol Error Probability (SEP) under instantaneous channel conditions. The analytical results are validated through Monte Carlo simulations. The simulation results show that APSS performs better as compared to OPSS under given conditions.

Two Interval Upper-Bound Q-Function Approximations with Applications

The Gaussian Q-function has considerable applications in numerous areas of science and engineering. However, the fact that a closed-form expression for this function does not exist encourages finding approximations or bounds of the Q-function. In this paper, we determine analytically two novel interval upper bound Q-function approximations and show that they could be used efficiently not only for the symbol error probability (SEP) estimation of transmission over Nakagami-m fading channels, but also for the average symbol error probability (ASEP) evaluation for two modulation formats. Specifically, we determine analytically the composition of the upper bound Q-function approximations specified at disjoint intervals of the input argument values so as to provide the highest accuracy within the intervals, by utilizing the selected one of two upper bound Q-function approximations. We show that a further increase of the accuracy, achieved in the case with two upper-bound approximations composing the interval approximation, can be obtained by forming a composite interval approximation of the Q-function that assumes another extra interval and by specifying the third form for the upper-bound Q-function approximation. The proposed analytical approach can be considered universal and widely applicable. The results presented in the paper indicate that the proposed Q-function approximations outperform in terms of accuracy other well-known approximations carefully chosen for comparison purposes. This approximation can be used in numerous theoretical communication problems based on the Q-function calculation. In this paper, we apply it to estimate the average bit error rate (ABER), when the transmission in a Nakagami-m fading channel is observed for the assumed binary phase-shift keying (BPSK) and differentially encoded quadrature phase-shift keying (DE-QPSK) modulation formats, as well as to design scalar quantization with equiprobable cells for variables from a Gaussian source.

On the performance of a hybrid frequency–phase-keying-based MIMO hybrid RF/FSO communication link

A hybrid technique in optical wireless communications is an effective solution to counter impairments and to improve link availability. In this work, a hybrid frequency phase keying (FPK) modulation scheme, based on frequency shift keying (FSK) and phase shift keying (PSK), for a hybrid radio frequency (RF)/free space optical (FSO) communication system is proposed. The hybrid FPK modulation scheme combines advantageous features of FSK and PSK and has the possibility to provide improved link performance in adverse channel conditions. A transmit aperture selection (TAS) and maximal ratio combining (MRC) diversity-based multiple-input–multiple-output (MIMO) hybrid RF/FSO system is considered to mitigate adverse fading effects. Analytical closed-form expressions are derived for the average symbol error probability to trace the performance of the TAS-MRC-based MIMO hybrid RF/FSO system with FPK modulation over fading and pointing error conditions. A comparative analysis of average symbol error performance is presented. The results clearly indicate that the proposed FPK modulation scheme with the MIMO hybrid RF/FSO communication system link is advantageous, as it exploits the complementary properties of both RF and FSO channel characteristics and PSK and FSK modulation schemes. In addition, the proposed MIMO hybrid RF/FSO system with FPK modulation offers superior performance, compared with MIMO RF, FSO, or hybrid RF/FSO systems applied with FSK and PSK modulation schemes. An optimum beam waist is derived analytically, and it is further verified with a numerical optimization technique. All results are validated using Monte Carlo simulation.

Performance Analysis of Cascaded Reconfigurable Intelligent Surface Networks

Reconfigurable intelligent surfaces (RIS) have been presented as a solution to realize the concept of smart radio environments, wherein uninterrupted coverage and extremely high quality of service can be ensured. In this letter, assuming that multiple RIS are deployed in the propagation environment, the performance of a cascaded RIS network affected by imperfect phase estimation is evaluated. Specifically, we derive closed-form expressions for the outage probability, the ergodic capacity and the average symbol error probability that can be utilized to evaluate the coverage of the proposed network, as well as the average capacity and the data transmission accuracy. Finally, we validate the derived expressions through simulations and show that by choosing the number of the participating RIS correctly, a cascaded RIS network can outperform a single RIS-aided system and extend the network’s coverage efficiently.

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.