Expressions For Bit Error Probability Research Articles

Analysis of non-linear degradation over NOMA-GFDM communications systems

Generalized frequency division multiplexing (GFDM) and non-orthogonal multiple access (NOMA) schemes are currently regarded as promising techniques for meeting the requirements of sixth-generation (6G) communication systems. While significant attention has been devoted to studying these techniques, specific scenarios still need to be explored. Considering that one essential aspect of any communication system is the utilization of high-power amplifiers, which are typically modeled as non-linear systems, in this paper, we propose a novel methodology to analyze the bit error probability (BEP) of NOMA-GFDM systems operating on memoryless non-linear system. To account for the non-linear distortions induced by high-power amplifiers, a polynomial model is employed, and new theoretical expressions are developed to compute the BEP of the system. Specifically, exact BEP expressions for a two-user downlink NOMA-GFDM system are provided. The numerical results obtained demonstrate that non-linear distortion significantly degrades system performance.

Enhanced connectivity through double RIS uplink MIMO and advanced modulation

Reconfigurable Intelligent Surfaces (RISs) have garnered significant attention in the development of Internet of Things (IoT) networks and vehicular communication systems, offering improved spectral efficiency with reduced power consumption and complexity overhead. However, employing a single RIS (S-RIS) may limit certain application scenarios and prove insufficient for ensuring reliable communication between transmitters and receivers. Consequently, the use of multiple RISs is recommended to further enhance coverage, capacity, and spectral efficiency. In this paper, we introduce the concept of Index Modulation (IM) into the double RIS (D-RIS) uplink Multiple-Input Multiple-Output (MIMO) communications, utilizing the antenna indices at the base station (BS). IM is realized through a combination of Space-Shift Keying (SSK) and Spatial Modulation (SM) techniques. We present an analytical model for the Double RIS based on SSK/SM methods and obtain a closed-form expression for the theoretical bit error probability (BEP), employing a greedy detector. To validate our theoretical BEP derivations for d-RIS-SSK/SM, we compare them with simulated BEP results. Our simulation data reveals an excellent match between the derived BEP and the simulated BEP, especially at lower Signal-to-Noise Ratios (SNRs), specifically -34 dB for SSK and -24 dB for SM. Furthermore, we evaluate the performance of the proposed d-RIS-aided IM methods by contrasting them with conventional d-RIS and single RIS-aided IM systems. Our simulation results demonstrate that the d-RIS-assisted IM outperforms the conventional d-RIS and single RIS-aided IM, achieving lower BEP at lower SNRs. d-RIS aided IM saves 15 dB in SNR compared to d-RIS without IM. Moreover, it saves 9 dB and 7 dB in SNR compared to single RIS-SSK and single RIS-SM, respectively when N = 64 and saves 3.5 dB and 1 dB in SNR with N = 128.

Emission rate optimization in diffusion-based molecular communication among mobile bacteria

In quorum sensing (QS), bacteria exchange information by using molecular signals to work together. In this paper, we study diffusion-based molecular communication with the QS mechanism between the transmitter node and receiver node which are composed of a population of mobile bacteria in a cluster, respectively. The expression of average bit error probability (BEP) at a receiver bacterium is derived. Furthermore, we use the projected gradient descent (PGD) algorithm to solve the optimization problem whose objective is to minimize the average BEP under emission rate constraints which require that the emission rate of each transmitter bacterium has lower and upper bounds. Finally, the numerical results show the PGD algorithm has good convergence behaviors and it is more efficient in finding the optimal emission rate with fewer iterations than genetic algorithm. The obtained results are expected to provide guidance in designing QS-based molecular communication system with lower average BEP.

Joint Code Index Modulation Aided Enhanced Spatial Modulation for High-Rate MIMO Systems

In this paper, a novel scheme, which introduces the technology of the code index modulation (CIM) into the realm of enhanced spatial modulation (ESM), named CIM-ESM, is proposed to achieve high spectral efficiency and high energy efficiency in multiple-input multiple-output (MIMO) systems. In the CIM-ESM scheme, information bits are conveyed not only by modulated symbols and spreading code indices, but also by the indices of the active antenna and constellation combinations. Meanwhile, the mathematical expressions for the average bit error probability (ABEP) in the presence of channel estimation errors, data rate, energy efficiency, and complexity of the CIM-ESM scheme are deduced. To achieve a higher transmission rate and code utilization, we further propose an enhanced scheme, named joint CIM-ESM (JCIM-ESM) scheme. In the JCIM-ESM scheme, spreading codes are jointly selected to form spreading code pairs and the matching indices of the spreading code pairs are utilized to convey extra information bits. Finally, Monte Carlo simulation results corroborate the tightness of the derived ABEP expression in the high signal-to-noise ratio region and reveal that both the CIM-ESM and JCIM-ESM schemes can provide better performance than CIM spread spectrum (CIM-SS), generalized CIM-aided spatial modulation (GCIM-SM), generalized space CIM (GSCIM), and CIM-aided QSM (CIM-QSM) schemes.

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.

Average bit error probability performance of intelligent reflecting surface‐aided wireless communications over Hoyt fading

SummaryIn this article, the performance of a wireless communication system with an intelligent reflecting surface (IRS) panel installed between the transmitter and receiver is studied. The channel is considered to be the Hoyt faded and additive white Gaussian noise. Closed‐form expressions for average bit error probability (ABEP) for both coherent Gray‐coded rectangular quadrature amplitude modulation and non‐coherent modulation schemes are presented. We apply the moment‐generating function‐based method for the derivation. In addition, asymptotic ABEP expressions are also obtained. Using asymptotic ABEP expressions, we obtained diversity order which is a function of the number of IRS elements. The effect of the number of IRS elements and fading parameters on the ABEP is studied. The ABEP performance improves with an increase in the number of reflecting elements but degrades with an increase in the fading severity. The accuracy of each analytical ABEP expression is verified by the simulation of the system considered herewith.

Generalized Index Modulation for MIMO-OTFS Transmission

Recently, the combination of multiple-input multiple-output technology with orthogonal time frequency space modulation (MIMO-OTFS) has drawn extensive attention with the advantage of exploring the additional transmit diversity or spatial multiplexing of the MIMO scheme. Motivated by the potential spectral efficiency of multi-domain index modulation, in this paper, we propose a generalized index modulation based MIMO-OTFS (GIM-MIMO-OTFS) to convey extra information with the aid of the spatial and delay-Doppler indices. To reduce the supreme complexity of maximum likelihood (ML) detection with a large size of look-up table in GIM-MIMO-OTFS, a two stage index detector based on power information is presented. Furthermore, the analytical expression of average bit error probability (ABEP) is derived to evaluate the performance of the proposed scheme. Simulation results demonstrate the enhanced performance of the proposed scheme in high-mobility scenarios, and highlight the complexity and outperformance of the proposed detector compared to ML detector.

On the Exact Closed-Form ABEP Analysis of Downlink NOMA Over mmWave TWDP Fading

This paper presents the performance analysis of two users’ downlink non-orthogonal multiple access (NOMA) over a millimeter-wave two-wave with diffuse power (TWDP) fading model for successive interference cancellation errors. The new closed-form expressions of average bit error probability (ABEP) for both users are derived for quadrature phase-shift-keying and binary phase-shift-keying modulation pairs. Further, the asymptotic ABEP expressions are derived to provide better insights into the performance analysis. The diversity order of each user is also derived with the aid of asymptotic ABEP expression. The obtained expressions over TWDP fading channels are generalized ABEP expressions as it also shows ABEP expressions for both Rician and Rayleigh fading channels as special cases. Simulation results support the correctness of each analytical ABEP expression.

Joint Optimizations of Relays Locations and Decision Threshold for Multi-Hop Diffusive Mobile Molecular Communication With Drift.

In this paper, we study diffusive multi-hop mobile molecular communication (MMC) with drift in one-dimensional channel by adopting amplify-and-forward (AF) relay strategy. Multiple and single molecules type are used in each hop to transmit information, respectively. Under these two cases, the mathematical expressions of average bit error probability (BEP) of this system based on AF scheme are derived. We implement joint optimization problem whose objective is to minimize the average BEP with (Q + 2) optimization variables including (Q + 1) -hop distance ratios and decision threshold. Q is the number of relay nodes. Furthermore, considering that more optimization variables result in higher computation complexity, we use efficient algorithm which is adaptive genetic algorithm (AGA) to solve the optimization problems to search the location of each relay node and the decision threshold at destination node simultaneously. Finally, the numerical results reveal that AGA has a faster convergence speed and it is more efficient with fewer iterations compared with Bisection algorithm. The performances of average BEP with optimal distance ratio of each hop and decision threshold are evaluated. These results can be used to design multi-hop MMC system with optimal optimization variables and lower average BEP.

Theoretical and Experimental Analysis of Asymmetrically Clipped-FSK VLC System

In this article, energy efficient asymmetrically clipped frequency-shift keying (AC-FSK) based visible light communication (VLC) system is theoretically and experimentally demonstrated. In order to facilitate straightforward comparison with the experimental results, theoretical expression for bit error probability, based on the Euclidean distance analysis of AC-FSK symbols, is provided. The VLC setup is based on commercial off-the-shelf components and software defined radio. The bit error rate (BER) performance of AC-FSK is evaluated considering maximum likelihood (ML) receiver, 1-tap discrete cosine transform (DCT) based receiver and frequency-domain harmonic receiver. Simulation and experimental results reveal that the performance of harmonic and ML receivers is almost identical. On the other hand, considering harmonic receiver for both AC-FSK and state-of-the-art unipolar (U)-FSK, we also gather that the BER performance of both schemes is almost the same. However, the harmonic receiver complexity of AC-FSK is 41.6% and 33.3% less compared to that of U-FSK for modulation order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M = 16$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M = 128$</tex-math></inline-formula> , respectively. This is because unlike U-FSK, AC-FSK requires limited number of harmonics for its optimal operation.

In-Phase and Quadrature Index Modulation Aided OTFS Transmission

Recently, orthogonal time frequency space modulation with index modulation (OTFS-IM) has been proposed, which can achieve better bit error rate (BER) performance than conventional OTFS. In this letter, a new transmission scheme, OTFS with in-phase and quadrature index modulation (OTFS-I/Q-IM), is presented to increase the spectral efficiency of OTFS-IM, in which additional information bits are carried through the grid index of OTFS block in in-phase and quadrature dimensions. Furthermore, the analytical expressions of average bit error probability (ABEP) and the maximum peak to average power ratio (PAPR) are derived to evaluate the performance of the proposed scheme. Simulation results demonstrate the enhanced performance of the proposed scheme in high-mobility scenarios.

Golden codeword‐based generalized spatial modulation

SummaryConventional‐generalized spatial modulation (C‐GSM) is an multiple‐input multiple‐output (MIMO) spatial modulation (SM) scheme that transmits the same complex amplitude/phase modulation symbol from multiple active transmit antennas. By using two active transmit antennas during a transmission interval, C‐GSM is capable of achieving high spectral efficiencies. However, as the size of the signal constellation/domain increases, the minimum Euclidean distances (ED) between the symbols decrease. Hence, this leads to a degradation of the average bit error rate (ABER) performance of the scheme. Hence, motivated to improve the error performance of C‐GSM schemes, first, this study proposes a new scheme called Golden codeword‐based generalized spatial modulation (GCW‐GSM), which combines C‐GSM and the Golden code to take advantage of the benefits of both while avoiding their drawbacks. The proposed scheme uses conventional quadrature amplitude modulation (C‐QAM), and it is investigated over Rayleigh frequency‐flat fading channels with additive white Gaussian noise. Second, a closed‐form expression of the theoretical average bit error probability of the proposed GCW‐GSM scheme is formulated. Compared to simulation results, it proves to be increasingly tight at high signal‐to‐noise ratio values. Finally, the proposed scheme performance over the Rayleigh‐frequency‐flat fading channel is compared to that over the Rician channel. An improvement in the error performance of with spectral efficiency of is seen in C‐16QAM GCW‐GSM over C‐256QAM conventional‐spatial modulation and C‐256QAM C‐GSM schemes at a bit error rate (BER) of . The C‐16QAM GCW‐GSM scheme exhibits an improvement in the error performance of with spectral efficiency of over the C‐64QAM conventional quadrature spatial modulation scheme at a BER of . Finally, the 16‐QAM GCW‐GSM under Rayleigh fading has a performance gain of 3 dB over 16‐QAM GCW‐GSM under Rician fading with a Rician K factor of 3.

On the performance of digital systems in α-[formula omitted] fading and non-Gaussian noise channels

In this paper, a closed-form expression is derived for the bit error probability (BEP) under several digital modulation schemes, considering the channel subject to α-F fading and non-Gaussian noise, characterized by the additive generalized Gaussian noise (AWGGN) distribution. An asymptotic BEP analysis is carried out in this work. A closed-form and unified BEP expression is derived for a wide range of modulation schemes, under α-F fading and AWGGN for the maximal-ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) based receivers. Comments are provided on the special cases encompassed by the α-F fading and AWGGN noise, as well as on the convergence and complexity analysis of the BEP expressions derived. BEP curves are shown for different parameters that characterize the channel and are corroborated by simulations performed with the Monte-Carlo method.

Design of Multihop Communication Systems Under Hardware Manufacturing Defects and Self Interference

Most studies on multi-hop communication systems are actually based on the assumption that hardware parts are built with high quality transmit/receive radio frequency chains, which are expensive and power-hungry. In practice, low cost hardware components are employed, which are prone to hardware manufacturing defects (e.g., phase noise, nonlinear power amplifier, inphase/quadrature imbalance, nonlinear low noise amplifier and analog to digital converter impairments). This paper focuses on the design of the transmitter, relay stations (RSs) and receiver for multi-hop communication systems under hardware defects. This paper analyzes the hardware defects and their impacts on the performance of multi-hop communication system. In addition, the impact of self-interference at the RSs is considered. The effect of hardware defects is modeled using distortion noises. A closed-form expression for the signal to noise and distortion ratios (SNDRs) is mathematically derived, then the performance metrics (i.e., SNDR, outage probability (OP) and ergodic capacity) are calculated, accounting for hardware defects. In addition, exact form expression of the average bit error probability is derived. To facilitate comparison, performance metrics of the proposed multi-hop relaying system and ideal system are illustrated. We also propose a linear minimum mean square error (LMMSE) and self-interference cancellation technique to mitigate the hardware defects. The results reveal that hardware defects can degrade the system performance. In addition, SNDR ceiling is inversely proportional to the summation of the square of hardware defect lev el. Also, the proposed mitigation technique can enhance the system performance.

RIS Assisted Dual-Hop Mixed PLC/RF for Smart Grid Applications

In this letter, we analyze the performance of reconfigurable intelligent surface (RIS) assisted mixed power line communication (PLC)/radio frequency (RF) system in smart grid application. In a smart grid, the data concentrator (DC) plays an important role in communication between the home appliances through the access point (AP). The DC can communicate using the existing PLC up to the AP, and the AP interacts with the home appliances with advanced communication technology like RIS-based RF communication. The modulation scheme is considered here as binary phase-shift keying (BPSK) modulation. Based on the system model, a closed-form expression for average bit error probability (ABEP) and outage probability (OP) are derived and analyzed by varying the various parameters like the number of reflectors in the RIS, impulsive noise scenario in the PLC channel.

Analysis of SWIPT based dual-hop AF relay with SSK modulation over Nakagami-m fading channel

Space shift keying (SSK) modulation performance is analyzed with simultaneous wireless information and power transfer (SWIPT) based cooperative amplify-and-forward (AF) relaying system over the Nakagami-m fading channel. SWIPT technique can remove the need for power supply at the relays in cooperative communication. In contrast, SSK is a low complex index modulation technique that eliminates inter antenna synchronization, inter-channel interference and reduces the number of radiofrequency chains. Closed-form expression for average bit error probability (ABEP) is derived using a single AF relay with selection combining (SC) at the receiver, and an Upper bound ABEP expression is derived for multiple AF relays with the direct link (DL) from source to destination. The partial relay selection (PRS) technique has been proposed with energy harvesting (EH) to reduce the hardware complexity compared to the multiple relays. Numerical and computer simulation results are presented with the discussion. The result demonstrates that EH with SSK modulation can improve the system performance.

On the Exact Performance Analysis of Molecular Communication via Diffusion for Internet of Bio-Nano Things.

Internet of Bio-Nano Things, (IoBNT), is an ecosystem, where integration of micro and nano scale devices designed via synthetic biology communicates information. One of the communication concepts adopted in IoBNT is molecular communications via diffusion (MCvD). Inter-symbol interference (ISI) is a major cause of the performance degradation in MCvD systems. The accurate determination of the bit error probability (BEP) when ISI is present is therefore important. Most of the past literature has used the normal approximation to a binomial distribution to evaluate the approximate BEP in MCvD systems. In this paper, we derive a new expression to evaluate the exact BEP without using a normal or any other approximation when the ISI caused by a bit extends over an arbitrary number of future bit intervals. Our BEP expression applies to any receiver, full or partial absorbing, as long as its hitting probability distribution is known. In order to prove the applicability of the new expression, we present the numerical results for the BEP computed using our expression for a full absorption spherical receiver and compare them with the results obtained by particle-based simulations. Our results agree closely with the simulation results.

Space Shift Keying With Reconfigurable Intelligent Surfaces: Phase Configuration Designs and Performance Analysis

Reconfigurable intelligent surface (RIS)-assisted transmission and space shift keying (SSK) appear as promising candidates for future energy-efficient wireless systems. In this article, two RIS-based SSK schemes are proposed to efficiently improve the error and throughput performance of conventional SSK systems, respectively. The first one, termed RIS-SSK with passive beamforming (RIS-SSK-PB), employs an RIS for beamforming and targets the maximization of the minimum squared Euclidean distance between any two decision points. The second one, termed RIS-SSK with Alamouti space-time block coding (RIS-SSK-ASTBC), employs an RIS for ASTBC and enables the RIS to transmit its own Alamouti-coded information while reflecting the incident SSK signals to the destination. A low-complexity beamformer and an efficient maximum-likelihood (ML) detector are designed for RIS-SSK-PB and RIS-SSK-ASTBC, respectively. Approximate expressions for the average bit error probabilities of the source and/or the RIS are derived in closed-form assuming ML detection. Extensive computer simulations are conducted to verify the performance analysis. Results show that RIS-SSK-PB significantly outperforms the existing RIS-free and RIS-based SSK schemes, and RIS-SSK-ASTBC enables highly reliable transmission with throughput improvement.

WITHDRAWN: Reduction of FBMC/OQAM imaginary intrusion compared to OFDM

In comparison to the OFDM (Orthogonal Frequency Division), Filter Bank multicarrying function (FBMC) has superior spectral properties, which complicates operational multiple input and mixed outputs. By extending a symbol in time, we can totally remove the imaginary interference. This gives the ease of applying all MIMO strategies known in OFDM to FBMC. The approach itself is of little complexity since it is based on hadamard matrices. While FBMC spreading allows complicated orthogonality to be restored in one block of communication, interference may be seen from the neighbouring blocks. By inserting a time security slot, the signal-to - interference ratio can also be improved. Furthermore, we examine the effect on the propagation process of a time channel. The estimation of the potential for Bit Error in double selective channels has been improved. In doubly selective channels, that is, time selectivity and frequency selectivity, we study the degeneration of output between OFDM and FBMC. In order to do this, we derive closed-form Bit Error Probability (BEP) terminology for the arbitrary linear modulation methods dependent on one-tap equalizers, in which our general BEP expressions include OFDM and FBMC.

SSK modulated WPCN with Euclidean distance based selection combining receiver

In this paper, the performance of space shift keying (SSK) modulation in a wireless-powered communication network (WPCN) is analysed with selection combining based on generalized Euclidean distance at the receiver. The network considered here is with multiple number of transmitting antennas and multiple number of receiving antennas operates under Rayleigh fading. Based on the Euclidean distance between the SSK modulation constellation points, this scheme selects any number of antennas out of $$N_a$$ receiving antennas. Selecting one or $$N_r$$ ( $$N_r<N_a$$ ) number of receiving antennas with energy harvesting, the system performance will improve and the receiver complexity as well as the number of radio frequency (RF) chains can be reduced. A closed form expression for the average bit error probability (ABEP) is derived for two transmitting antennas and $$N_a$$ receiving antennas with WPCN using SSK modulation. The numerical results and simulation results are presented to illustrate the energy harvesting on system performance.