Expressions For Symbol Error Probability Research Articles

Scaled Selection Combining Receiver for Cooperative NOMA-based 5G Cellular Systems

Non-Orthogonal Multiple Access (NOMA) technology can accommodate more subscribers concurrently and achieve higher spectrum efficiency than Orthogonal Multiple Access (OMA) technologies. This work investigates the performance of the two subscriber downlink cooperative NOMA system with Scaled Selection Combining (SSC) comprising a Base Station (BS), a cell edge subscriber and a near subscriber. Due to the channel conditions, the error performance of the cell edge subscriber is poorer compared to the near subscriber. To mitigate this and enhance the performance, the proposed SSC combines signals from BS and near subscriber and chooses the best signal between them. The Symbol Error Probability (SEP) of this cellular system with M−ary Phase Shift Keying (MPSK) modulation is derived under the Rayleigh fading environment. The optimum scaling factor to reduce the SEP is also obtained. The theoretical SEP expressions of SSC are validated with the Monte-Carlo simulations. The proposed system provides better SEP and outperforms the non-cooperation and traditional Selection Combining (SC) schemes. Additionally, the efficacy of the proposed system under various modulation schemes is studied.

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.

Channel Norm-Based Energy Detection With Diversity Reception for Amplitude-Shift Keying in Rayleigh Fading

Optimum and suboptimum energy detection receivers with diversity reception in Rayleigh fading, that only require limited channel state information based on the channel norm, are introduced. The importance of these channel norm based energy detection (CNBED) receivers is that they achieve the same diversity order as that of a coherent receiver. Furthermore, their performance degradation when compared to a coherent receiver can be made sufficiently low by appropriate choice of parameters. Due to their performance and the low complexity of energy detection, the CNBED techniques have potential applications to internet of things. Analysis of the CNBED receivers is performed for multi-level amplitude-shift keying (ASK). For the optimum receiver, an analytical approximation of the symbol error probability (SEP) as a sum of univariate integrals involving averaging of Gaussian Q-functions is derived. For the suboptimum receiver, closed form expressions for the exact SEP and for the approximate SEP under the condition of high signal-to-noise ratio (SNR) are obtained; in addition, using asymptotic approximations, expressions for the optimal ASK transmit levels with high SNR and large number of receive diversity branches, that minimize the SEP subject to an energy constraint, are found. Numerical results are provided to demonstrate the performance of the receivers.

Symbol error probability of mmWave communications with transmit antenna selection and RISs under the impacts of hardware impairments

SummaryIn practice, hardware impairments (HIs) often exist in wireless devices, especially in low‐cost device systems. However, previous reports usually ignored HIs due to the computational complexity in mathematical derivations, particularly in millimeter‐wave (mmWave) communications. This article proposes the usage of transmit antenna selection (TAS) and multiple reconfigurable intelligent surfaces (RISs) to address HIs in mmWave communications. In particular, TAS is utilized at the source to increase the received signal power at the destination and reduce the effects of HIs. Multiple channel gains from RISs are combined with the classical source‐destination channel gain at the destination. The symbol error probability (SEP) expression of the mmWave communications with TAS and RISs under the effects of HIs (shortened as the TAS‐RISs‐HIs communications) is formulated over Nakagami‐ channels and verified through Monte Carlo simulations. The effects of HIs on the SEP of TAS‐RISs‐HIs communications are demonstrated through numerical illustrations. Specifically, the SEP of the TAS‐RISs‐HIs communications is significantly higher than the SEP of the ideal hardware communications with TAS and RISs, especially in the high transmit power regime. As a result, ignoring HIs when evaluating the SEP of the mmWave communications can result in some inappropriate conclusions. Moreover, the joint and separate advantages of TAS and RISs are thoroughly analyzed when comparing the SEPs in the cases with and without TAS, with and without RISs.

A New Approach to Deriving Closed-Form Bit Error Probability Expressions of MPSK Signals

In conventional approach, the bit error probability (BEP) expressions of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are obtained by using elementary functions-based approximations of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

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.

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.

SYMBOL ERROR PROBABILITY PERFORMANCE FOR GENERALIZED SELECTION COMBINING DIVERSITY RECEPTION OF M-QAM OVER RAYLEIGH FADING CHANNEL

The performance of generalized selection combining (GSC) diversity reception symbol error probability (SEP) of square M-ary quadrature amplitude modulation (M-QAM) signals over frequency-flat Rayleigh fading channels is investigated in this work. The combining techniques considered in this paper are maximum ratio combining and selection combining (SC). We present closed-form approximate expressions for the average combined signal-to-noise ratio (SNR) and SEP in the fading channel for M-QAM signal reception in the GSC using diversity pathways that are independently, identically distributed. The simulation results validate the SEP expressions and demonstrate that, for a given number of accessible diversity paths, combining the strongest paths results in the majority of the diversity gain, and that the SNR declines as the number of combined paths increases. On the other hand, the numerical results demonstrate that, for a certain number of combined paths, increasing the number of available diversity paths can lead to a significant performance improvement.

Optimal Multi-Level Amplitude-Shift Keying Modulation for a Reliable Channel Magnitude Detection-Based Receive Diversity Powerline Communication System

The implementation of a coherent powerline communication (PLC) receiver increases its hardware complexity and energy consumption, which can be tackled by a non-coherent receiver. However, this reduces the reliability of the PLC systems. To meet this trade-off, a novel energy-efficient receiver structure is proposed in this study that exploits the knowledge of the channel magnitude of a receive diversity PLC system. The transmitter employs multi-level amplitude-shift keying (ASK) modulation for data transmission via the PLC channels subjected to Rayleigh multipath phenomenon and corrupted by additive Nakagami-m background noise, which would lead to a superior performance as compared to other modulation schemes owing to the channel magnitude-based proposed receiver. Utilizing the receiver structure, closed-form expression for symbol error probability (SEP) and its asymptotic expression at a high average signal-to-noise ratio (SNR) are derived using a characteristic function approach. Furthermore, to achieve the simultaneous design of an energy-efficient modulation scheme and a reliable PLC system, optimal ASK signaling levels are obtained with a constraint on the total available energy at the transmitter end. The analytical relation of the derived optimal multi-level ASK constellation with the traditional ASK constellation is obtained at high SNR values. The proposed channel magnitude-based receiver is found to achieve full diversity order and numerical results presented provide various insights towards the design of the energy-efficient PLC system.

Exploiting Multiple RISs and Direct Link for Performance Enhancement of Wireless Systems With Hardware Impairments

In this paper, the performance of a wireless system, which is beneficial from utilization of multiple reconfigurable intelligent surfaces (RISs) and the direct link between the source node and the mobile user, is analyzed. Especially, the effect of transceiver hardware impairments (HIs) are taken into consideration. We successfully derive the outage probability (OP), throughput, achievable data rate (ADR), and symbol error probability (SEP) expressions of this multiple-RIS assisted wireless systems with and without HIs (referred as RIS-HI and RIS-ID system, respectively) over 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. The above performance factors are also benchmarked with the case that only a point-to-point (P2P) link without RIS is considered (denotes as as P2P-HI and P2P-ID systems for HI and ideal hardware conditions, respectively). All obtained formulas are verified by Monte-Carlo simulations. It is observed that the RIS-HI system significantly outperforms the P2P-HI system at low transmit power regime, while the performance of the RIS-ID system is always better than that of P2P-ID system. On the other hand, HIs show more severe effect for higher data transmission rates or high modulation orders.

Average symbol error probability and channel capacity of the underwater wireless optical communication systems over oceanic turbulence with pointing error impairments.

The influence of oceanic turbulence and pointing error impairments on the underwater wireless optical communication (UWOC) systems is considered in this study. We propose a generalized fading model, which comprises the path loss due to the absorption and scattering, the oceanic turbulence (modeled by Málaga distribution), and the pointing error impairments resulting from ocean movements. Thereafter, closed-form expressions of the average symbol error probability (SEP) and average channel capacity are proposed for optical waves propagate in oceanic turbulence with the M-ary pulse position modulation (PPM) and under the constraints of the limited average-power and peak-power. The Monte Carlo simulations are conducted to validate the analytical results and demonstrate that the fading parameters, including the mean-squared temperature, the salinity-temperature contribution factor, jitters, and water conditions, significantly affect the system performance. Moreover, the thermal noise and quantum noise in ocean environment have more serious impact than the background noise. Finally, we prove that the UWOC systems with the pure peak-power constraint performs better than that limited by average-power and peak-power.

Performance analysis of vertical multihop cooperative underwater visible light communication system with imperfect channel state information

Visible light communication (VLC) has gained attention due to its ability to provide a high data rate in underwater communication. We consider an underwater VLC (UWVLC) system and vertical propagation through the column of water with L layers (channels) and M relays between the transmitter and the receiver. We consider the real-time adverse effects of depth-dependent weak turbulence and path loss. We model each of the L channels with a log-normal distribution, where its statistical parameters mean and variance are functions of the parameters representing the adverse effects of the turbulence. For this concatenated L layered UWVLC, using Gauss–Hermite integral technique, we derive closed-form expressions of outage probability and average symbol error probability taking square quadrature amplitude modulation and rectangular quadrature amplitude modulation modulations with different configurations and assuming imperfect channel state information available at the receiver for detection. We have observed that there is a drastic degradation in the performance as the depth (distance between the transmitter and the receiver) is increased. However, the severity can be alleviated by installing multiple relays between the transmitter and the receiver.

Mobile Two-Way Molecular Communication via Diffusion Using Amplify-and-Forward and Analog Network Coding.

Mobile molecular communication via diffusion (MCvD) has attracted lots of attentions due to its time-varying channels. In this paper, we investigate a mobile two-way MCvD model, which consists of two mobile source nanomachines and a mobile relay nanomachine. The amplify-and-forward (AF) relaying and analog network coding (ANC) are utilized to implement the exchange of information between two source nanomachines in this model. To explore the performance of the mobile two-way MCvD system, we first adopt the depleted molecule shift keying (D-MoSK) modulation, and then the mathematical expressions of symbol error probability (SEP) and mutual information are derived by using AF and ANC scheme on the basis of maximum a posteriori (MAP) probability detection. Finally, we present the numerical and simulation results. Compared with the AF-No-ANC scheme which is without use of ANC scheme, the scheme of combining AF and ANC can significantly improve the performance of SEP and mutual information. Moreover, the D-MoSK modulation outperforms the molecule shift keying (MoSK) modulation for this mobile two-way MCvD system. In addition, we propose the evaluation and discussion about the impacts of several important parameters on the performance of this system. These results can be used to design mobile two-way MCvD system with lower SEP and higher mutual information.

Performance analysis of non‐orthogonal multiple access assisted cooperative maritime communication system over two‐wave with diffuse power fading

AbstractNon‐orthogonal multiple access (NOMA) and millimeter‐wave (mmWave) communication are two promising technologies to fulfill the high throughput and reliable communication requirements. Maritime communication systems use a generalized fading at near‐sea‐surface channels (for seashore to ship/boat/fishing fleet communication) to provide reliable communication due to atmospheric turbulence. Experimental research on generalized two‐wave diffuse power (TWDP) fading reveal the footprints of mmWave. This article proposes novel exact and asymptotic closed‐form expressions of average symbol error probability (ASEP) of NOMA users for cooperative maritime communication systems over TWDP fading with the different modulations. The end‐to‐end closed‐form expressions are derived in terms of Appell's and Lauricella's hypergeometric functions. Also, the ASEP is shown using the power allocation factor for different modulation schemes. The proposed system provides better transmission reliability using generalized TWDP fading. Further, the outage probability of the system described above is analyzed using the distance, path loss exponent, transmission rate, and Rician factor as performance metrics for both the NOMA users. Effects of fading outage parameters on the system performance are studied. The end‐to‐end exact numerical results have been verified with the Monte‐Carlo simulations that validate with asymptotic results at a high SNR regime.

Performance Analysis of an IRS-Aided Wireless Communication System With Spatially Correlated Channels

An intelligent reflecting surface (IRS) assisted wireless communication system, with statistically correlated channels between the transmitter and the IRS pair and between the IRS and the receiver pair, is studied in the absence of channel state information (CSI). Assuming the phases added by IRS elements to be deterministic, the closed-form analytical expression for the symbol error probability (SEP) and the upper bound on the channel capacity are derived, with the transmitter employing binary phase-shift keying (BPSK) modulation for data transmission. The asymptotic SEP expression is derived and the achievable diversity order of the system is shown to be independent of the number of IRS elements. A search based algorithm is proposed to obtain the optimal phase at IRS minimizing the average SEP, as a equal phase configuration. The optimal equal phase is also found to maximize the average channel capacity. Numerical results are presented for the case of channels following a practical IRS correlation model.

Performance of Cooperative Communication System With Multiple Reconfigurable Intelligent Surfaces Over Nakagami-m Fading Channels

In this paper, the advantages of multiple reconfigurable intelligent surfaces (RISs) assisted wireless systems and direct link between two terminals are exploited by considering a cooperative communication system where reflecting links created by multiple RISs and the direct link are combined at the receiver. We mathematically analyze the performance of the cooperative multiple RISs - direct link (RIS-D) system over 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 by obtaining the symbol error probability (SEP) expression. In addition, the SEP of the single-input single-output (SISO) system without RISs (i.e., there is only direct link between two terminals) is also obtained for convenience in comparison the performance of the cooperative RIS-D and SISO systems. We demonstrate the correctness of the derived expressions via Monte-Carlo simulations. Numerical results show that the SEP of the cooperative RIS-D system significantly lower than that of the SISO system for a certain transmission power of the transmitter. Also, for a certain SEP target, the cooperative RIS-D system can greatly save energy consumption in comparison with the SISO system. Specifically, increasing the number of RISs or the number of reflecting elements (REs) in the RISs can remarkably reduce the SEP of the cooperative RIS-D system. On the other hand, the impacts of the system parameters such as the number of RISs, the number of REs, and the 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 are fully investigated to clearly indicate their influences on the SEP of the cooperative RIS-D system.

Hybrid MPPM-BB84 Quantum Key Distribution Over FSO Channel Considering Atmospheric Turbulence and Pointing Errors

Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.

On Minimizing Symbol Error Rate Over Fading Channels With Low-Resolution Quantization

We analyze the symbol error probability (SEP) of $M$-ary pulse amplitude modulation ($M$-PAM) receivers equipped with optimal low-resolution quantizers. We first show that the optimum detector can be reduced to a simple decision rule. Using this simplification, an exact SEP expression for quantized $M$-PAM receivers is obtained when Nakagami-$m$ fading channel is considered. The derived expression enables the optimization of the quantizer and/or constellation under the minimum SEP criterion. Our analysis of optimal quantization for equidistant $M$-PAM receiver reveals the existence of error floor which decays at a double exponential rate with increasing quantization bits, $b$. Moreover, by also allowing the transmitter to optimize the constellation based on the statistics of the fading channel, we prove that the error floor can be eliminated but at a lower decay exponent than the unquantized case. Characterization of this decay exponent is provided in this paper. We also expose the outage performance limitations of SEP-optimal uniform quantizers. To be more precise, its decay exponent does not improve with $b$. Lastly, we demonstrate that the decay exponent of a quantized receiver can be complemented by receive antenna diversity techniques.

Performance analysis of efficient digital modulation schemes over various fading channels

Using a simple yet accurate two-term exponential based approximation of the Gaussian Q function, in this paper, we simplify the intractable yet significant integrals which are used in the symbol error probability (SEP) expressions of various efficient digital modulation schemes over various well known fading statistics like Rayleigh, Nakagami-m, Nakagami-q and Nakagami-n. Precisely, we express these integrals in terms of simple moment generating function (MGF) whose solution for the aforementioned fading channels can be easily obtained from the literature. This MGF based approach simplifies the cumbersome integrals and eventually makes the SEP expressions tractable. The analytical work is further validated with the help of Monte-Carlo simulations.

Combining RF energy harvesting and cooperative communications for low-power wide-area systems

This paper presents the combination of energy harvesting (EH) at the wireless sensor and cooperative communications for low-power wide-area (LPWA) systems. Firstly, the Internet of Things sensor harvests the energy from the power beacon with multiple transmit antennas via radio frequency signals and then uses the harvested energy to transmit signals to multiple gateways with multiple receive antennas. Then, the cooperative communications is applied at the server based on the gateway outputs. By mathematical analysis, we derive the exact closed-form expressions of outage probabilities (OPs), throughput, and symbol error probabilities (SEPs) of the EH-LPWA system over Nakagami-m fading channel in the cases without and with cooperative communications. Our expressions can be considered as the first results applying EH for LPWA systems with mathematical analysis. Then, we obtain the optimal value of the time switching ratio that minimizes the OPs and SEPs and maximizes the throughput of the considered EH-LPWA system. Numerical results have clarified that, the distances, path loss exponent, and data transmission rate have a strong impact on the OPs, throughput, and SEPs. Particularly, using a half of transmission blocks for EH can maximize the system performance. Moreover, when the number of transmit antennas at power beacon is equal to the number of receive antennas at gateways, the system performance can be improved significantly. Finally, the accuracy of the obtained expressions is demonstrated via Monte-Carlo simulations.