Closed-form Expressions For Bit Error Rate Research Articles

Closed-form BER expression for multi-user downlink NOMA

Massive machine-type communication (MMTC) is an essential element for realizing the Internet of Things (IoT). However, certain challenges arise because MMTC should support a massive number of users. Recently, non-orthogonal multiple access (NOMA) has been highlighted as a technology for MMTC in a limited frequency band. To design and operate a NOMA-based communication system for a massive number of users, an accurate performance analysis for an arbitrary number of users and a practical power assignment method for the channel condition of each user are required. In this study, the exact bit error rate (BER) expression for an arbitrary user number is derived in an explicit closed form for NOMA-based communication. In addition, for analytical purposes, an approximate expression with high accuracy is proposed. To achieve an extension to the fading channel, the average BER expressions for the Rayleigh and Nakagami-m fading channels are presented in closed forms. Based on the derived BER expression, a power assignment algorithm that can achieve the target performance is proposed when each user is associated with a different signal-to-noise ratio. The derived BER expressions and the power assignment algorithm were verified based on computer simulations.

Performance Analysis of a WPCN-Based Underwater Acoustic Communication System

Underwater acoustic communication (UWAC) has a wide range of applications, including marine environment monitoring, disaster warning, seabed terrain exploration, and oil extraction. It plays an indispensable and increasingly important role in marine resource exploration and marine economic development. In current UWAC systems, the terminal nodes are usually powered by energy-limited batteries. Due to the harshness of the underwater environment, especially in the ocean environment, it is very costly and difficult, even impossible, to replace the batteries for the terminal nodes in UWACs, which results in the short lifetime and unreliability of the terminal nodes and the systems. In this paper, we present the application of a wireless powered communication network (WPCN) to the UWAC systems to provide an auxiliary and convenient energy supplement for solving the energy-limited problem of the terminal nodes, where the hybrid access point (H-AP) transfers energy to the terminal nodes in the downlink. In contrast, the terminal nodes use the harvested energy to transmit the information to the H-AP in the uplink. To evaluate the proposed WPCN-based UWAC systems, we investigate the performance of the average bit error rate (BER), outage probability, and achievable information rate for the systems in a frequency-selective sparse channel and non-white noise environment. We derive the closed-form expression for the probability density function (PDF) of the received signal-to-noise ratio (SNR). Based on this, we further derive novel closed-form expressions for the average BER and the outage probability of the systems. Numerical results confirm the validity of the proposed analytical results. It is shown that there exists an optimal signal frequency and time allocation factor for the systems to achieve optimal performance, and a larger optimal time allocation factor is preferred for a smaller hybrid access point (H-AP) transmit power or a larger transmission distance, while a smaller optimal signal frequency is required for a larger transmission distance.

Analysis and Compensation of Tx and Rx IQ Imbalances in Uplink IM-OFDMA Systems

Index modulation-based orthogonal division multiple access (IM-OFDMA) has recently been proposed as a potential technique for future wireless communication systems due to its superior spectral efficiency and error performance over conventional multiple access schemes. However, its performance is still under investigation by researchers in light of a variety of scenarios and assumptions. Following this direction, in this paper, the individual and joint effects of the transmitter (Tx) and receiver (Rx) in-phase and quadrature imbalances (IQI) on the bit-error-rate (BER) performance of the uplink IM-OFDMA scheme are investigated by considering whether each user's RF front-end is identical or not. Moreover, to reduce the detrimental effect of IQI, a preamble-based estimation and compensation method is proposed for IM-OFDMA. Closed-form expressions for the average BER of IM-OFDMA are obtained by considering the physical effect of the Tx and Rx IQI. Also, using Monte Carlo simulations, the derived expressions are verified under different system configurations. Analytical and simulation results reveal that Tx and Rx IQI cause an error floor in the BER performance of IM-OFDMA schemes. However, the proposed estimation and compensation method not only reduces the impact of IQI but also leads to a better BER performance compared to the case of no IQI, which mainly refers to the frequency diversity caused by the IQI.

Performance of 5G NR-polar QAM-OFDM in nonlinear distortion plus Non-Gaussian noise over Rayleigh fading channel

The polar code readily provides rate adaptation, reaching Shannon’s capacity at low encoding and decoding complexity. It has entered the 5G New Radio (5G-NR) as a result of these alluring features to improve the bit error rate (BER) performance in Gaussian noise. In challenging environments for modern broadband communication systems, the amplitude and phase distortion caused by nonlinear distortion (NLD) of high-power amplifiers (HPAs), non-Gaussian noise or impulsive noise (IN), and multipath fading channels (H) play a significant role in BER degradation in an orthogonal frequency-division multiplexing (OFDM) system. Therefore, to improve the BER degradation of the conventional NR-polar QAM-OFDM system over such environments, different novel closed-form expressions of combined NLD-HPA and IN distributions and the log-likelihood ratios (Ls) at the OFDM demodulator output with and without Rayleigh fading channel have been derived. In addition, the novel derived closed-form BER expressions validate the derived distributions using Monte-Carlo simulation in the downlink (DL) and uplink (UL) scenarios. This system demonstrates a significant performance improvement and achieves a coding gain of 28 dB and 25.5 dB compared to the traditional coded OFDM system, which achieved only 10 dB in the case of IBO = 4 dB over the Rayleigh fading channel.

BER analysis for PAM-based UWOC-NOMA system in oceanic turbulence environment

Pulse amplitude modulation (PAM) scheme and non-orthogonal multiple access (NOMA) are attractive technologies to achieve high rate transmission and massive connectivity in the future Ocean Internet of Things (OIoT). To investigate the performance of underwater wireless optical communication (UWOC) NOMA systems based on PAM modulation, this paper develops a joint mathematical model with ocean turbulence and underwater solar noise based on the Weibull distribution. Specifically, the resolution framework on the ground of constellation multi-boundary judgments is proposed to derive the closed-form BER expressions for the wireless optical NOMA systems under ocean turbulent channels using the Laguerre approximation, which is also applicable to the other NOMA-enabled systems under higher order modulations. The accuracy of the analytical solution is demonstrated by simulation results. In addition, simulation results show that the higher-order PAM modulation can effectively reduce the bit-error rate (BER) gap between NOMA users and balance the fairness of users within the NOMA group. Furthermore, we observe that turbulence is one of the primary factors influencing the BER of the NOMA system in the marine environment, and the tilt angle of NOMA nodes has varying degrees of influence on the BER performance varying turbulence intensities. Therefore, selecting the appropriate tilt angle for the receiving nodes in a NOMA system based on the marine environment is beneficial to lowering the BER of the system.

Adaptive Transmission Based on MIMO Mode Switching Over Malaga Turbulence Channel With Pointing Error

In this paper, we propose a dynamic adaptive multiple input multiple output (MIMO) free space optical (FSO) system with spatial mode switching. Based on the channel conditions, the proposed system can select different MIMO transmission modes: diversity, multiplexing or hybrid mode that yields the maximum average channel capacity while satisfying the reliable average bit error rate (BER). Considering the combined effects of path loss, pointing error and atmospheric turbulence-induced fading modeled by Malaga distribution, we derive the closed-form expressions of average channel capacity and average BER of MIMO system for each transmission mode. From adaptive system performance evaluated results, we establish the signal-to-noise ratio (SNR) threshold look-up table (LUT) in different scenarios to select the optimal transmission mode. The extensive numerical results demonstrate that the proposed adaptive system has a significant improvement in average channel capacity compared with each stand-alone mode system. Finally, Monte Carlo simulation is also provided to verify the correctness of the proposed adaptive scheme and conclusions.

Age-Optimal Network Coding HARQ Scheme for Satellite-Based Internet of Things

Satellite-based Internet of Things (S-IoT) is viewed as an efficient solution to provide timely status updates to the terrestrial user equipment (UE), due to its ubiquitous coverage and broadband access capability inherited from high throughput satellite (HTS). However, the conventional hybrid automatic repeat request (HARQ) cannot guarantee the freshness of status update transmission, because the reliable transmission needs the retransmission of the lost packets, which deteriorates the freshness due to the nontrivial propagation delay and high bit error rate (BER) of the satellite–territory link (STL). In this article, we propose an age-optimal network coding HARQ (NC HARQ) scheme with the metric of information timeliness, i.e., Age of Information (AoI) to realize timely status updates in S-IoT. First, we model the STL as a shadowed Rician (SR) fading channel and derive the closed-form expressions of BER. Then, we propose a fixed interval NC inserted HARQ (f-NC HARQ) scheme, where the NC packets are inserted in the information packets with fixed interval to accelerate the recovery of lost information packets and derive the expressions of Peak AoI (PAoI) and average end-to-end delay. Furthermore, we propose an adaptive NC inserted HARQ (A-NC HARQ) scheme for the drastic variations in the SR fading channel, where the transmission of the status update is modeled as a partially observable Markov decision process (POMDP) problem and solved by a low complexity improved fast informed bound (iFIB) algorithm. Simulation results validate the accuracy of our theoretical derivations and show that the A-NC HARQ scheme can achieve the lowest PAoI and average end-to-end delay.

Modeling of NOMA-MIMO-Based Power Domain for 5G Network under Selective Rayleigh Fading Channels

The integration of multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) technologies is a hybrid technology that overcomes a myriad of problems in the 5G cellular system and beyond, including massive connectivity, low latency, and high dependability. The goal of this paper is to improve and reassess the bit error rate (BER), spectrum efficiency (SE) of the downlink (DL), average capacity rate, and outage probability (OP) of the uplink (UL) in a 5G network using MIMO. The proposed model utilizes QPSK modulation, four users with different power location coefficients, SNR, transmit power, and two contrasting bandwidths 80 and 200 MHz under selective frequency Rayleigh fading channels. The proposed model’s performance is evaluated using the MATLAB software program. The DL results found that the BER and SE against transmitted power showed the MIMO-NOMA enhanced the BER performance for the best user U4 from 10−1.7 to 10−5.2 at 80 MHz bandwidth (BW), and from 10−1.5 to 10−5 at 200 MHz for transmitting power of 40 dBm. In contrast, the SE performance for the best user U4 is enhanced from 24 × 10−3 to 25 × 10−3 bits/second/Hz at 80 MHz BW and from 19.8 × 10−3 to 20 × 10−3 bps/Hz at 200 MHz BW. Although the outcomes for the UL were obtained in terms of average capacity rate and OP versus SNR at 80, and 200 MHz BW, the MIMO-NOMA result showed that the average capacity rate for the best user U4 performance improves by 12 bps/Hz for 1 dB SNR and the OP is reduced by 15 × 10−3 for 80 MHz BW and by 12 × 10−3 for 200 MHz BW at an SNR of 0.17 dB. As the BW increased the BER, the average capacity rate increased while the SE and OP decreased. For both DL/UL NOMA with and without MIMO, closed-form expressions for BER, SE, average capacity rate, and OP were obtained. All users’ performance, even those whose connections were affected by interference or Rayleigh fading channels significantly improved, when MIMO-NOMA was implemented.

STAR-RIS-NOMA Networks: An Error Performance Perspective

This letter investigates the bit error rate (BER) performance of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) in non-orthogonal multiple access (NOMA) networks. In the investigated network, a STAR-RIS serves multiple non-orthogonal users located on either side of the surface by utilizing the mode switching protocol. We derive the closed-form BER expressions in perfect and imperfect successive interference cancellation cases. Furthermore, asymptotic analyses are also conducted to provide further insights into the BER behavior in the high signal-to-noise ratio region. Finally, the accuracy of our theoretical analysis is validated through Monte Carlo simulations. The obtained results reveal that the BER performance of STAR-RIS-NOMA outperforms that of the classical NOMA system, and STAR-RIS might be a promising NOMA 2.0 solution.

Evaluation of Reconfigurable Intelligent Surface-Assisted Underwater Wireless Optical Communication System

Reconfigurable intelligent surfaces (RISs) are an emerging technology aimed to enhance the energy and spectrum efficiency of wireless communication links by reconfiguring the propagation environment of radio-frequency (RF)/optical waves. Planar phased meta-material surfaces or reflect-arrays for RF RIS and multiple smart mirrors have been used for activating optical RIS. In this article, we analyze the underwater optical wireless communication (UWOC) system performance in terms of bit error rate (BER), outage probability (OP) and channel capacity (CC) under the influence of underwater turbulence, beam attenuation, pointing errors and occlusion or blockage due to obstacles. A RIS-assisted UWOC proposed to mitigate the effects obstacles, pointing errors and turbulence and improve the system performances. The probability density function and cumulative distribution functions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> RIS elements based UWOC system are evaluated over the underwater turbulence, pointing errors and blockage due to obstacles. The novel closed-form expressions for BER under binary phase shift keying and binary frequency shift keying modulation schemes using with and without coherent detection, OP, and CC for intensity modulation-direct detection and heterodyne detection cases are obtained and plotted according to the number of RIS elements with respect to the average signal-to-noise ratio. The numerical BER results are validated with the Monte-Carlo simulations.

Efficient Fast-Convolution Based Hybrid Carrier System

The weighted-type fractional Fourier transform (WFRFT)-based hybrid carrier (HC) system has been proposed to bridge the gap between orthogonal frequency division multiplexing (OFDM) system and single-carrier system with frequency domain equalization (SC-FDE). In this paper, we propose a novel HC system based on efficient fast-convolution (FC) without a cyclic prefix to meet the requirements of complex scenarios towards future communications. The proposed system can achieve flexible optimization of system performance, such as minimizing out-of-band emission (OOBE), peak to average power ratio (PAPR) and bit error rate (BER). This efficient FC based hybrid carrier (FCHC) system is among the most competitive waveforms. The closed-form BER expressions are derived and analyzed over additive white Gaussian noise (AWGN) and frequency-selective fading channels. A modified equalizer over frequency-selective channels is also provided to resist the inter-block interference (IBI). Moreover, the banded minimum mean-square error (MMSE) equalization based on FC can be embedded in the proposed system over doubly-selective channels, and then the interference caused by fading channels can be further suppressed through the combination of FC and HC. The simulation results demonstrate the superiority of the proposed system over the conventional HC system in terms of OOBE, PAPR and BER. The significant flexibility and combined performance advantages make the proposed system a potential scheme for future communications.

BER Performance of UWOC With APD Receiver in Wide Range Oceanic Turbulence

In this paper, the bit error rate (BER) performance of underwater wireless optical communication (UWOC) systems with on-off keying (OOK) modulation and an avalanche photodiode (APD) detector are analyzed in a wide range of oceanic turbulence environment, such as lognormal, Gamma, K, Weibull, and Exponentiated Weibull distributions. To achieving this goal, a new mathematical system model is established, which has not only considered the aggregated degrading phenomena, namely the absorption, scattering, and turbulence, but also been suitable for describing UWOC with APD receiver. Then the closed-form expressions of the BER performances of UWOC with APD for different turbulence distributions are derived in detail by subdividing the working situation into high and lower inter-symbol interference (ISI) scenarios. Theoretical analysis and computer simulations show that no matter what the ISI levels are, the derived closed-form expressions for system BER under various turbulences can approximate the accurate integral ones well. This is obviously helpful to the design and performance evaluation of UWOC systems.

Asymmetric Adaptive Modulation for Uplink NOMA Systems

Non-orthogonal multiple access (NOMA) as a promising technology, can achieve enhanced connectivity and spectral efficiency. However, the asymmetric channels in uplink NOMA systems can bring distinct uncertainty of the bit error rate (BER) and throughput performances to the users. To address this problem, an asymmetric adaptive modulation (AAM) framework for uplink NOMA systems is introduced in this paper. We first derive the closed-form BER expressions for uplink NOMA systems, then we propose a principle for reducing the performance uncertainty. Finally, we develop an AAM algorithm for uplink NOMA systems by studying the closed-form BER expressions. Numerical results demonstrate the correctness of the BER expressions we derived, and show that our AAM algorithm outperforms the benchmark in terms of the system sum throughput.

BER Performance Analysis for Downlink Nonorthogonal Multiple Access With Error Propagation Mitigated Method in Visible Light Communications

In order to mitigate the error propagation (EP) effect on the bit error rate (BER) performance due to the imperfect successive interference cancellation for the non-orthogonal multiple access (NOMA)-based visible light communication (VLC) downlinks, adjustable bit rate superposition coding (ABRSC) and sample-and-sum successive interference cancellation (SSSIC) decoding schemes are proposed in this paper. Based on the modified fixed-power allocation (MFPA) strategy, the closed-form expressions of BER are derived for the two-user case with on-off keying, and further extended to the multi-user scenario. The residual probability of EP is introduced and derived to theoretically assess the effectiveness of the proposed ABRSC and SSSIC schemes. Monte Carlo simulation is also conducted to validate the analytical BER results. The BER performance of the NOMA-based VLC system with multiple users is further analyzed and discussed in detail. It is found that under the total average optical transmission power constraint, the allocated average optical transmission power to current user should be higher than that to all rest of users, i.e., the power allocation factor (PAF) is supposed to be greater than 1/2, in order to avoid the error floor issue of current user, hence facilitating the successful implementation of SSSIC. Besides, increasing the bit-rate factor (BRF) could mitigate the effect of EP, and larger BRF leads to more efficient outcomes in alleviating the effect of EP.

BER analysis of NOMA with max-min relay selection

In contrast with orthogonal multiple access (OMA) technologies, non-orthogonal multiple access (NOMA) technology can achieve higher spectral efficiency and support more users simultaneously. Multiple relays can be deployed in NOMA networks, in order to combat fading and thus increase the transmission reliability. In the existing works on cooperative NOMA networks with multiple relays, the decoding error at the relays and the imperfect successive interference cancellation (SIC) are not taken into account simultaneously. In this work, we consider the bit error rate (BER) analysis of relay-aided NOMA networks, where max-min relay selection is employed. Particularly, closed-form BER expressions are derived for NOMA networks with Rayleigh fading, in the existence of the relay decoding error and imperfect SIC. The asymptotic BER performance is then obtained to provide some useful insights into the system design such as the diversity order. Finally, simulation results illustrate the correctness of the derived expressions. The presented results reveal the effects of imperfect SIC and relay decoding error on the performance of cooperative NOMA networks.

Performance analysis of dual-branch selection combining technique over the generalized Alpha-Mu fading channels

Inspired by the low-difficulty of implementing a dual-branch selection combining (SC) technique, this research paper presents approximate closed form expressions for the bit error rate (BER) of M-ary phase shift keying (M-PSK) considering the SC technique. In particular, the BER expression is derived over independent and identically distributed (i.i.d) alpha - mu fading channels and is based on the use of Meijer’s G-function. The presented mathematical formulas can be modified to study the performance of different types of fading channels including Weibull, exponential, Nakagami-m, Gamma, and Rayleigh channels. This can be achieved by updating the parameters of the propagation medium nonlinearity (alpha) and the number of multipath clusters (mu). In addition, the paper provides numerical results that demonstrate a close match in the performance of the derived expressions and the simulation findings in terms of BER. Specifically, a very close to a total BER match is achieved using a range of signal to noise ratio (SNR) levels for various selections of the alpha and mu parameters. The obtained closed form BER expression of M-PSK considering the dual-branch SC technique is novel, new, and has never been published in the literature before.

Multi-carrier Visible Light Communication System Using Enhanced Sub-carrier Index Modulation and Discrete Wavelet Transform

This work is aimed at providing a novel design of the Visible Light Communication (VLC) system that uses the Multi-Carrier Code-Division Multiple Access (MC-CDMA) technique to send and receive data through intensity-modulated/direct detected (IM/DD) VLC channel. The state-of-the-art framework of Enhanced Sub-Carrier Index Modulation (ESIM) is utilized to reduce the inherent peak-to-average power ratio (PAPR) in Orthogonal Frequency Division Multiplexing. Additionally, the use of cyclic prefix is omitted through the Discrete Wavelet Transform in the current system. Hence, the performance of the system is optimized in terms of PAPR, Bit Error Rate (BER), and data rate. The work presents the closed-form BER expressions for both conventional and proposed techniques in line-of-sight VLC channel. Correspondingly, the simulation programs are also executed to compared the proposed ESIM based WT-MC-CDMA system with both existing systems followed by an analysis of the results. Simulation results show the superior performance of the proposed system compared to existing systems.

BER performance of NOMA network with majority based JTRAS scheme in practical impairments

We investigate bit error rate (BER) performance of majority-based joint transmit and receive antenna selection (JTRAS-maj) in non-orthogonal multiple access (NOMA) networks with practical impairments including channel estimation error (CEE), feedback delay (FD) and successive interference cancellation (SIC) error. The closed-form expression of the exact BER is derived for binary phase shift keying modulation in Nakagami-m fading channels. In the high signal-to-noise ratio region, asymptotic and error floor expressions are also obtained in the absence and presence of the practical impairments, respectively. The analytical results verified by simulations reveal that non-zero and zero diversity gains are achieved in these cases, respectively. Also, the BER performance of users with worse channel gains is significantly improved as the number of receive antennas increases or channel condition enhances. In addition, the system works well up to some values of CEE, FD and SIC error.

On BER for M-User NOMA with Symmetric SC

In non-orthogonal multiple access (NOMA), the ideal perfect successive interference cancellation (SIC) is validated theoretically by the random channel coding, practically such as low-density parity-check (LDPC) codes or turbo codes. Recently, symmetric superposition coding (SSC) has been shown to achieve the ideal perfect SIC bit-error rate (BER) performance by simulations with as many as three users, while the authors of this letter derived the analytical expression for BER, only for to a two-user scenario. In this letter, the derivation of the closed-form BER expression for M users is reported. It is shown that the SSC NOMA achieves near-perfect SIC BER performance. This is possible for with two reasons; one is the power allocation of the user fairness, and the other is the optimal maximum-likelihood (ML) detection.

Performance analysis of different intensity modulation techniques over atmospheric turbulent free-space optical channels.

In this paper, we introduce a comprehensive study of the performance of intensity modulation (IM) techniques over gamma-gamma (GG) distributed free-space optical (FSO) channels. We derive closed-form expressions for the average bit error rate (BER) of thermal-noise-limited FSO systems adopting various IM techniques. The effect of atmospheric turbulence is studied. Comparisons are presented in terms of the transmitted peak power to achieve a certain BER. Results show that on-off keying, pulse amplitude modulation, and expurgated pulse-position modulation (EPPM) provide superior performance compared to other IM techniques. In addition, a proposal to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) is introduced by adding another modulation layer of EPPM. A closed-form expression for the average BER of the proposed hybrid OFDM-EPPM technique over GG turbulent FSO channel is derived. Moreover, an expression for the outage probability of the FSO system adopting the proposed OFDM-EPPM technique is presented. Results are investigated and compared to those of traditional OFDM and hybrid OFDM with PPM (OFDM-PPM). It is shown that the hybrid OFDM-EPPM technique outperforms the hybrid OFDM-PPM technique for the same data rate. Moreover, the hybrid OFDM-EPPM technique allows higher data rates with lower PAPR values compared to those of the hybrid OFDM-PPM technique for the same number of time slots.