Closed-form 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.

Nonlinear symbolic regression for bit error rate prediction of NOMA systems in 5G cellular communications

Machine learning (ML) has been suggested as a promising tool in the design of telecommunication systems to overcome the challenges of traditional methods and meet the requirements regarding future cellular networks. As an enabler of 5G communications, Non-orthogonal multiple access (NOMA) has emerged to adaptively manage the existing resources and received huge attention in terms of performance analysis to confirm its efficiency in resource management. This work addresses the applications of nonlinear symbolic regression (NLSR) techniques to evolve mapping models for bit error rate (BER) prediction in the downlink NOMA systems with perfect and imperfect successive interference cancellation (SIC) receivers. In this regard, a multi-stage structure is proposed to evaluate the BER using the related inputs as well as the output of the previous stages for imperfect SIC signal decoding. Each step consists of an NLSR block with different inputs and an output, which inputs include the effective parameters and the output of the previous stages. Experimental results confirm that the NLSR techniques are able to establish modeling expressions with good prediction accuracy compared to other benchmark methods. In particular, these ML-based techniques overcome the limitation of the classical approaches in modeling a closed-form BER formula, especially for the NOMA systems with more than two users. In addition, this BER prediction tool can be utilized by the NOMA base station as new side information for more optimal resource management.

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.

Performance Analysis of Uplink Index-Modulated NOMA for 6G Wireless Communications

In this letter, we mathematically analyze the bit-error rate (BER) performance of a generalized uplink index-modulated non-orthogonal multiple access (IM-NOMA) system consisting of a base station (BS) with multiple antennas and an arbitrary number of devices with different modulation schemes. We focus on the case that a single subcarrier is activated among S(≥2) subcarriers according to index bits to reduce computational complexity. The optimal joint maximum-likelihood (JML) algorithm is assumed to be used for detecting a super-imposed symbol from multiple devices. The closed-form BER is shown to be matched well with simulation results. We also investigate the effect of channel estimation error on the BER. To the best of our knowledge, the mathematical characterization of BER of the generalized uplink IM-NOMA system with an arbitrary number of uplink devices with different modulation schemes and multiple receive antennas at the BS does not exist in the literature. Finally, we show that our analytical framework can be applied to analyze a cell-free massive MIMO NOMA system, which is expected to be one of the most promising techniques for 6G wireless communication systems.

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.

BER performance analysis of asynchronous NOMA with arbitrary phase offset

An asynchronous transmission scenario for non-orthogonal multiple access (NOMA) user signals with arbitrary phase offset is investigated in this paper. To improve the system performance in the user power-balanced conditions, we adopt a synthetic detection method at the receiver, i.e., the jointly optimal maximal likelihood detection aided triangular successive interference cancellation (JO ML-TSIC) method. Analytical bit error rate (BER) solutions are obtained for a two-user case with the optimal, intentional one-half symbol period time delay implemented between the user signals. Furthermore, closed-form BER solutions for the case using the triangular successive interference cancellation (TSIC) detection method are also derived for comparisons. Numerical results show that the JO ML-TSIC receiver for the asynchronous system outperforms the TSIC receiver as well as the synchronous successive interference cancellation (SIC) receiver in all the conditions concerned. The results also show that the superiority of the JO ML-TSIC receiver is strengthened when the signals experience flat Rayleigh fading channels compared to the TSIC and the synchronous SIC receivers.

A Closed-Form Minimum BER Precoder for Orthogonal Time Frequency Space Systems

This letter devises a closed-form precoder for Orthogonal Time Frequency Space (OTFS) systems with linear equalization to minimize the bit error rate (BER). The precoder is developed by optimally allocating the power to adapt to the equivalent channel in the delay-Doppler domain. To achieve the minimum BER precoder design, we convert the minimization of the average BER into the minimization of its lower bound subject to a transmission power constraint. By exploiting the convexity, a closed-form minimum BER precoder is designed, which actually achieves the lower bound. As such, the unified bit error probability function for both the zero-forcing (ZF) and minimum mean square error (MMSE) equalizations is derived and verified with their numerical counterparts. Simulation results demonstrate that the designed precoders can provide lower BER than the existing linear equalizations without precoding.

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.

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.

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 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.

Exact BER Performance for Symbol-Asynchronous Two-User Non-Orthogonal Multiple Access

Two-user non-orthogonal multiple access systems with quadrature phase-shift keying modulation are studied. A time asynchronous scheme for successive interference cancellation receivers that maximally suppresses the inter-user interference compared to any other time asynchronous schemes is proposed. Exact bit error rate (BER) solutions for the two users operating in the additive white Gaussian noise channel using the proposed scheme are derived. A simpler closed-form BER approximation for the weaker user is also presented. Compared to the symbol-synchronous scheme, numerical results show the proposed asynchronous scheme reduces the BER for the stronger signal by a factor of one-half.

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 Uplink Massive Multiuser SM-MIMO System With Imperfect Channel State Information

In this paper, the error performance and spectrum efficiency (SE) of uplink massive multiuser spatial modulation (SM) MIMO systems with zero-forcing detection for perfect and imperfect channel state information (CSI) are investigated over composite Rayleigh fading channels. We firstly derive the error probabilities of transmit antenna index detection and transmitted symbol detection of each user. Using these results, the bit error rate (BER) performance of the system under perfect CSI is analyzed. Furthermore, a closed-form average BER of the system is derived. We generalize the analytical results of perfect CSI to those of imperfect CSI for practicality, and derive a closed-form BER for the system with imperfect CSI. Based on this, two asymptotic BER expressions are developed to characterize the error performance of the system for large-scale receive antennas and high SNR. By means of the asymptotic expressions, the diversity order of the system is attained. Besides, we derive a lower bound on the achievable SE of the system with imperfect CSI. With this lower bound, an approximate expression of the achievable SE is obtained in closed form. Simulation results indicate that our theoretical analysis is valid, and agrees with simulation results well.

A Theoretical and Experimental Evaluation on the Performance of LoRa Technology

A theoretical study and an experimental evaluation on the performance of the long-range (LoRa) technology are presented in this paper. After an instructive mathematical review of important concepts, we assess the LoRa performance in additive white Gaussian noise (AWGN) channels through a numerical model, to elucidate its communication capabilities in negative signal-to-noise ratio (SNR) conditions and, as consequence, in the long distances promised by such low power and narrowband technology. Because of the significance of forward error correction codes in the performance of modern systems, we propose an analytical bit-error-rate (BER) expression that considers the influence of LoRa code rate ( $\textit {CR}$ ) parameter. The agreement between the theoretical and the numerical results of a Hamming coded system validated the closed-form BER, evaluated in terms of SNR in AWGN channels. Moreover, an experimental setup with off-the-shelf LoRa wide area network (LoRaWAN) equipment was prepared to demonstrate the feasibility of this promising technology, as well the impact of the $\textit {CR}$ parameter on the packet error rate (PER), in a link with a single end-device. As expected, communication in urban and open areas with distances up to ≈ 3 and ≈ 10 km, respectively, were achieved, according to measurements of the average received signal indicators around −100 dBm for an average SNR ≈ 5 dB. The usefulness of the practical analysis was confirmed by the agreement between the theoretical and the measured noise floors, and by the verification of the substantial impact of the parameter $\textit {CR}$ on the system PER.

BER Analysis for Uplink NOMA in Asymmetric Channels

The bit error rate (BER) analysis has been recognized as an effective approach to investigate the problems in non-orthogonal multiple access (NOMA) systems, such as inter-user interference (IUI) and error propagation. However, the impact of asymmetric channels on adaptive modulation and coding (AMC) will bring great challenges to the BER analysis of NOMA systems. In this letter, by exploiting the scaling characteristics of Euclidean distance, we disclose the boundary effect of asymmetric channels and derive the boundary value for paired users. In addition, we provide closed-form BER expressions for uplink NOMA users on both sides of the boundary value. Numerical results verify the existence of the boundary value and conform to our derivations.

Closed-Form BER Expressions of M-Ary DCSK Systems Over Multipath Rayleigh Fading Channels

In this letter, we derive a closed-form bit error rate (BER) of $M$ -ary differential chaos shift keying ( $M$ -DCSK) systems over multipath Rayleigh fading channels via approximating Gaussian $Q$ -function by polynomials. The approximation is made piecewisely using polynomials of different degrees and Remez algorithm is applied to achieve the minimax approximation. Our method can be extended into the existing non-coherent transmit-reference chaos-based modulation systems, e.g., short-reference DCSK and multi-carrier DCSK systems. The derived closed-form BERs are compared with the simulated ones in order to verify the efficiency of proposed approximation scheme.

Optimal Detection for Ambient Backscatter Communication Systems With Multiantenna Reader Under Complex Gaussian Illuminator

This article addresses the issue of symbol detection in ambient backscatter communication systems with the multiantenna reader. Focusing on the ON-OFF keying modulation, the optimal detector minimizing the bit error rate (BER) is devised based on the maximum a posteriori principle. We then analyze the exact closed-form BER expression for the optimal detector. Moreover, simple approximate BER expressions are derived in certain asymptotic regimes. Furthermore, a simple energy detector is analyzed as a benchmark scheme, and the asymptotic BER is devised in a closed form. The findings of this article suggest that implementing multiple antennas at the reader is an effective means to enhance the BER performance and extend the tag-reader communication range. Also, the optimal detector always outperforms the energy detector. In particular, the optimal detector can avoid the error floor phenomenon, which is inevitable for the energy detector in the high SNR regime.