Bit Error Rate Expressions Research Articles

A New Frequency-Bin-Index LoRa System for High-Data-Rate Transmission: Design and Performance Analysis

As an attempt to tackle the low-data-rate issue of the conventional LoRa systems, we propose two novel frequency-bin-index (FBI) LoRa schemes. In scheme I, the indices of starting frequency bins (SFBs) are utilized to carry the information bits. To facilitate the actual implementation, the SFBs of each LoRa signal are divided into several groups prior to the modulation process in the proposed FBI-LoRa system. To further improve the system flexibility, we formulate a generalized modulation scheme and propose scheme II by treating the SFB groups as an additional type of transmission entity. In scheme II, the combination of SFB indices and that of SFB group indices are both exploited to carry the information bits. We derive the theoretical expressions for bit error rate (BER) and throughput of the proposed FBI-LoRa system with two modulation schemes over AWGN and Rayleigh fading channels. Simulation results not only verify the accuracy of theoretical BER and throughput analyses but also show that the proposed FBI-LoRa schemes can significantly increase the transmission throughput compared with the existing LoRa systems at the expense of a slight loss in BER performance. The proposed FBI-LoRa system is a promising alternative for high-data-rate Internet of Things (IoT) applications.

Performance of NOMA‐assisted MRC receivers in presence of imperfect SIC and CSI errors

SummaryIn this paper, we analyze the performance of maximum‐ratio combining (MRC) receivers for single‐input multiple‐output (SIMO) non‐orthogonal multiple access (NOMA) system. We explore the aforesaid system performance in presence of impairments like imperfect channel state information (CSI) and successive interference cancellation (SIC) errors. In general, receive diversity provides diversity gain and helps to maintain quality of service (QoS), while the NOMA system achieves higher spectral efficiency compared to orthogonal multiple access (OMA). Power‐domain NOMA system transmits superimposed‐coded signal, which utilize SIC detection method at the receiving users. Here, we derive the closed‐form expression of the average bit error rate (BER) for the MRC‐based NOMA system. We also analyze the performance of the system in high signal‐to‐noise ratio (SNR) regime through derived asymptotic expression. Furthermore, the outage probability, diversity order, and sum rate comparison between NOMA and OMA system are also presented. Simulation results also validate the derived theoretical expressions and confirm the diversity gain achieved for the considered system.

BER analysis of tightly packed planar RIS system using the level of spatial correlation and discrete phase shifter

AbstractIn this article, the bit error rate (BER) performance of a tightly packed reconfigurable intelligent surface (RIS) assisted communication system is analyzed in terms of the level of spatial correlation. In conventional models, channels are assumed to be independent and identically distributed and continuous phase shifts are available for phase compensation. However, in practice, as RIS reflecting units are arranged in more compact form (less than 0.5) due to space constraints, correlation effects among the reflecting elements are to be considered. Further, discrete phase shifters are widely used to meet practical deployment limitations. These practical constraints severely affect the error performance of the system. It necessitates that the impact of spatial correlation and discrete phase shifts on the BER performance of the system is to be analyzed. The instantaneous signal to noise ratio is the square of the sum of correlated random variables. In order to analyze the BER performance accurately, the exact statistical distribution for the sum of spatially correlated random variables is to be chosen. In this work, appropriate distribution fitting is chosen based on the level of spatial correlation. Numerical BER expressions are derived with the chosen statistical distributions. The analysis on the impact of spatial correlation and discrete phase shifter on BER performance would be more beneficial for design and practicing engineers in the field of 6G wireless communications.

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.

A Novel Differential Chaos Shift Keying Scheme With Transmit Diversity

A novel differential chaos shift keying scheme with transmit diversity, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TD-DCSK scheme</i> , is proposed in this letter. The proposed TD-DCSK scheme can achieve full diversity and high data rate by advisably designing the space-time (ST) block of the transmitted signal. With the designed ST block, the transmitter with multiple transmit antennas in the TD-DCSK scheme requires only one radio frequency chain, which is particularly important for keeping low hardware complexity. We derive the theoretical expression of bit-error rate (BER) and diversity order of the TD-DCSK scheme over multipath Rayleigh fading channels, and analyze its hardware complexity. Simulation results illustrate the superiority of the proposed scheme and validate the accuracy of the theoretical derivation. The proposed TD-DCSK scheme stands out as a promising solution for low-power and low-cost short-range wireless communications.

Analysis of Scintillation Effects on Free Space Optical Communication Links in South Africa

The performance of free space optical communication (FSOC) systems is severely degraded by certain atmospheric conditions prevalent in places where they are deployed, in spite of their numerous advantages. In clear weather conditions, the random fluctuation in the atmosphere’s refractive index causes substantial scintillation losses to transmitted optical signals. It is therefore imperative to estimate the potential losses due to atmospheric turbulence in locations where FSOC links are to be deployed. This will provide the necessary fade margin for FSOC systems so that designed links withstand such atmospheric disturbances. In this paper, statistical analysis of wind speed data collected for various cities of South Africa is used for calculating the corresponding refractive index structure parameter (Cn2). These Cn2 values, as well as the zero inner scale and infinite outer scale model and finite inner and finite outer scale model, are used in computing the scintillation indices not exceeding 50%, 99%, 99.9%, and 99.99% of the time for the investigated locations. The Lognormal and Gamma–gamma distribution models are then employed for the computational analysis of the irradiance fluctuations and channel characteristics while considering the effect of pointing errors for weak and moderate to strong turbulence regimes. Finally, derived mathematical expressions for outage probabilities and bit error rate (BER) performances for FSOC links, employing various intensity modulation and direct detection (IM/DD) schemes, are presented.

Performance analysis of atmospheric optical communication systems with spatial diversity affected by correlated turbulence

This paper presents a complete analytical framework for obtaining the performance associated with a free-space optical (FSO) communication system with a spatial diversity and equal gain-combining technique. The system is affected by gamma–gamma scintillations with different realistic degrees of channel correlation depending only on the physical parameters of the link. We derive new analytical closed-form expressions for the average bit error rate (ABER) considering different scenarios to provide very realistic behavior of the system including different numbers of FSO receivers in several geometric configurations, with different receiving areas, different path lengths, and a variety of turbulence conditions. Furthermore, a very accurate approximate closed-form expression is also derived for the ABER of any generic coding scheme with either a very complex or, directly, no closed-form expression for its associated conditional BER that is first obtained in the ideal case of absence of turbulence. Numerical results via Monte Carlo simulation are provided to corroborate the validity of all the derived analytical expressions.

Pulse Jamming in Aperture-Averaged FSO Receiver Over Exponentiated Weibull Fading Channel

In this paper, we study the pulse jamming effect thoroughly in aperture-averaged free space optical (FSO) systems. The FSO fading channels are considered to be Exponentiated Weibull (EW) distributed due to its excellent fit for all aperture sizes over the ranges of atmospheric turbulence conditions. It is inferred from the theoretical analysis that random jamming behaviour is impulsive and it reveals a destructive property over aperture-averaged FSO receivers. Analytical expressions of the average bit error rate (ABER) and outage probability (OP) are formulated for the considered FSO system in the presence of random jammer. The effects of pulse jamming on ABER and OP performances are shown. Additionally, the asymptotic ABER analysis is performed in order to investigate the response of the considered FSO system in high transmit power region and to analyze the diversity order under the pulse jamming effect. Pointing error impairments, being another important performance degrading parameter of the FSO communication system, are studied along with the pulse jamming effect. Also, asynchronous jamming effect over the ABER performances is described by both analytically and graphically.

BER performance of nonzero dead time SPAD-based UWOC with signal accumulation over generalized gamma turbulence channels

Underwater wireless optical communication (UWOC) becomes a hot topic in current researches. It suffers from severe absorption, scattering and turbulence, which result in a low reception power even in a short communication distance. To address this challenge, a single-photon avalanche diode (SPAD) based UWOC with signal accumulation method is proposed in this paper. Bit error rate (BER) performance of above method considering nonzero SPAD dead time over generalized gamma turbulence channels is investigated. For this goal, we first derive the expression for the instantaneous BER of above UWOC system. Then we obtain the optimal decision threshold corresponding to the minimum average BER. Based on those obtain expressions, we construct a useful closed form expression for the average BER corresponding to the minimum BER. With those expressions, the effects of the system parameters on the BER performance under turbulence channels are studied. The simulations show that a poor BER performance of 0.0094 for the system without using the signal accumulation under turbulence σ2 = 0.31 can be improved to 7.5 × 10−7 by using 10 accumulation times, which indicates that the signal accumulation can overcome the adverse turbulence effect. Besides, we also find that even with quiet low receive power of 1 photon/bit, the UWOC system can still obtain a good BER performance of smaller than 10−6.

Performance Analysis of Massive Hybrid Directional Modulation With Mixed Phase Shifters

To reduce the signal-to-interference-plus-noise ratio (SINR) loss of analog directional modulation (DM) with finite radio frequency (RF) phase shifters (PSs), a hybrid analog and digital (HAD) DM with mixed PSs is proposed. Using the law of large numbers, the closed-form expressions of SINR performance loss (PL), secrecy rate (SR), and bit error rate (BER) are derived. In accordance with the closed-form expression of SINR loss, it is clear that the SINR PL at desired receiver (Bob) gradually decreases as the fraction <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> of the low-resolution phase shifter decreases, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> is defined as the ratio of the number of low-resolution shifters to the total number of shifters. The simulation results show that the SINR PL, SR PL, and BER gradually decrease as the number of quantization bits increases. When the fraction of low-resolution shifters is equal to 50%, 2 bits is sufficient for low-resolution shifters to achieve a SINR PL less than 0.5 dB and a negligible BER degradation. Also, when the number of quantization bits of low-resolution shifters is equal to 2, the SR PL is about 0.3 bits/s/Hz. Thus, compared with analog DM, the HAD DM structure strikes a good balance between PL and circuit cost.

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.

Bit error rate and outage probability analysis for multi-hop decode-and-forward relay-aided NOMA with imperfect SIC and imperfect CSI

This paper investigates a multi-hop decode-and-forward (DF) relay-aided non-orthogonal multiple access (MH-DF-R-NOMA) scheme. The model overcomes the problems associated with poor channel quality and disconnection communication with the broadcast station for the users through the path from the intermediate relay nodes to deliver the signal to the users. We assume that we have multiple intermediate relay nodes that constitute the path to transmit the signal to two users who have different channel qualities. Consequently, the closed-form expressions for bit error rate (BER) and outage probability (OP) at all intermediate relay nodes and users are derived. In the analysis, the imperfect channel state information (CSI) and imperfect successive interference cancellation (SIC) are taken into account. Computer simulation are presented to validate theoretical analyzes. The results indicate that the degradation of BER and OP performances for the near user is higher than the far user. We also show the superiority of our model over the single relay scheme. Furthermore, the OP of MH-DF-R-NOMA outperforms its counterpart in OMA.

Performance enhancement for differential energy signal detection of ambient backscatter communications

AbstractAmbient backscatter communications are a critical enabling technology of radio frequency identification in Internet of Things due to its full usage of ambient signals with low cost to transmit tag signals. However, the signal detection of tag signals is a challenging task as tag signals are usually superposed on the ambient radio frequency signals and the channel state information is unavailable due to its huge and unacceptable computation complexity at tags. To solve this, we in this article proposed an enhanced signal detection scheme for the differential energy detection in ambient backscatter communications. We discovered that the single detection threshold in classic detection will not provide desirable results in smart storage scenarios. We proposed a double‐threshold detection method which subtly integrates differential energy detection with maximum likelihood method to improve the detection accuracy while reducing the complexity of the reader. In addition, we derived the closed‐form expressions for bit error rate (BER), miss detection, and false alarm probabilities of the data bits sent by the tag. Simulation results are presented to show that our proposed detector can offer lower BER and computational complexity compared with single threshold detection schemes in low‐power and low‐storage scenarios, especially when the system is in a poor channel status environment.

Infrastructure-to-Vehicle Visible Light Communications: Channel Modelling and Performance Analysis

Visible light communication (VLC) has emerged as a potential wireless connectivity solution for infrastructure-to-vehicle (I2V) communications. In this paper, we investigate the performance of I2V VLC systems with access points in the form of streetlights. Particularly, we consider a typical two-lane highway road where the light poles are located at both roadsides and uniformly separated from each other. Based on non-sequential ray tracing simulations, we first propose a closed-form path loss expression as a function of transceiver and infrastructure parameters. Then, we statistically analyze the path loss and derive a closed-form expression for its probability distribution function (PDF). Utilizing the derived PDF, we derive an approximate closed-form bit error rate (BER) expression. We confirm the accuracy of derived BER expression through comparison with Monte Carlo simulation results and demonstrate the effect of transceiver and infrastructure parameters such as receiver aperture, pole height, car height, lateral shift, and spacing between light poles on the BER performance.

On the Error Rate Performance of Full-Duplex Cooperative NOMA in Wireless Networks

Error rate analyses of cooperative non-orthogonal multiple access (CNOMA) systems are of paramount importance to investigate the communication reliability for each user and facilitate the development of enhancement algorithms. Although CNOMA has recently attracted great attention, its error performance, particularly that of full-duplex cooperative NOMA (FD-CNOMA), is still underexplored in the literature. In this paper, we investigated the error performance of FD-CNOMA systems under imperfect successive interference cancellation (SIC) and residual self-interference (RSI), where new closed-form expressions of the exact bit error rates (BER) are derived for both users. Through the derived BER expressions, high-SNR analyses are conducted to show that FD-CNOMA has an error floor. Based on the derived expressions, we proposed a novel SINR-based selective FD-relaying, which minimizes the end-to-end (e2e) BER and improves the overall system performance. The analyses are extended to cover pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM) with arbitrary modulation orders. Monte Carlo simulations and numerical results are presented to corroborate the derived analytical expressions and give valuable insights into the error performance of FD-CNOMA systems.

A Novel SR-DCSK-Based Ambient Backscatter Communication System

In order to expand the application of differential chaos shift keying (DCSK) technology in Internet of Things, a novel ambient backscatter communication system is proposed. In this system, the ambient short reference DCSK (SR-DCSK) signal is ultilized as radio frequency (RF) source, and the modulation waveform design can be easily generated by the state transition of the SR-DCSK modulation symbol according to the transmitted information bit, so as to eliminate strong direct-link interference. Furthermore, a noise reduction method based on averaging operation at the detector is designed for enhancing the bit error rate (BER) performance. Theoretical BER expression over Rayleigh fading channel is derived and validated via simulation. Moreover, the performance of the proposed system is compared with those of other DCSK-based systems.

Performance Analysis and Resource Allocation for a Relaying LoRa System Considering Random Nodal Distances

In conventional star-topology LoRa networks, the gateways are expected to collect the data from all the nodes nearby. However, a major challenge for the conventional LoRa system is the performance degradation due to the long-range communication over fading channels. To resolve the challenging issue, this paper investigates a two-hop amplify-and-forward relaying LoRa network in a two-dimension plane, where random nodal distances are considered. Moreover, a relay-selection mechanism is developed for the proposed system. Based on the best relay-selection protocol, the analytical bit-error-rate (BER) and asymptotic BER expressions, achievable diversity order, coverage probability, and throughput of the proposed system are derived over the Nakagami-<inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading channel. Furthermore, to maximize the throughput of the proposed system, a two-dimensional resource allocation optimization problem (i.e., the spread factor selection and power allocation optimization) is formulated and investigated. The proposed optimal spread factor selection and power allocation scheme is verified to outperform the two baseline schemes. Simulation and numerical results show that although the proposed system reduces the throughput compared to the conventional LoRa system, it significantly improves the BER and coverage probability. Hence, the proposed system can be considered as a promising technique for low-power, long-range and highly reliable Internet-of-Things applications.

Cascaded double fading channels: A case of [formula omitted] – [formula omitted] shadowing

In this study, the cascaded double κ−μ shadowed fading model is mathematically introduced. A novel expression is obtained for the cumulative distribution function (CDF) of the cascaded double κ−μ shadowed fading channels by using Meijer’s G function and Laplace transform. Based on the obtained CDF expression, the exact and asymptotic expressions are derived for the outage probability (OP), the average bit error rate (BER) for various modulations of the considered channel model. The OP and the average BER curves with exact simulations obtained by the proposed expressions are presented for different parameters and modulation schemes of the considered channel model. Finally, the accuracy of the derived OP and the average BER expressions is confirmed with exact simulations.

BER Expression of QAM for Symbol-Level Jamming

In wireless communication systems, quadrature amplitude modulation (QAM) schemes are widely used for high-speed data transmission, and recently, symbol-level jamming (SLJ) is being studied as an effective jamming technique. However, bit error rate (BER) expressions of QAM for SLJ have not been presented in previous studies. In this paper, we derive the exact BER expressions of QAM considering phase coherent and noncoherent scenarios under SLJ. Using the derived expressions, we investigate the SLJ order that maximizes BER of QAM for jamming-to-signal ratio (JSR). Further, we present BER of QAM with tone jamming and show that tone jamming is a special case of noncoherent SLJ. In addition, we use a probability density function of the SLJ amplitude to show that the high order noncoherent SLJ is similar to noise jamming. To increase BER in a low JSR region, we present a BER expression of QAM when SLJ exists in a pulse form. Using the derived expression, we investigate the order and pulse duration ratio to maximize BER for JSR. The derived expressions are verified using computer simulations.

Performance of FSO Communication Systems Employing Alamouti-Type Space-Time Encoding Over Málaga Channels With Pointing Errors

In this work, spatial diversity techniques have been proposed for free-space optical (FSO) communication systems to combat the deteriorating effects, such as atmospheric turbulence effects and pointing errors, and the performance of FSO communication systems with Alamouti encoding scheme over Málaga <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {M})$</tex-math></inline-formula> turbulence channel is investigated. We first derive the probability distribution function (PDF) of end-to-end channel gain under atmospheric turbulence and pointing error circumstances. Then, by capitalizing on this PDF, closed-form expressions of the average bit error rate (BER) and the outage probability (OP) for the proposed system are obtained. Additionally, to provide more insights, the asymptotic expressions for the average BER and the OP are also derived. In the analysis, intensity modulation/direct detection and heterodyne detection techniques are considered so that the obtained results can cover both cases. Furthermore, analytic results are successfully validated through Monte Carlo simulations. Our results highlight the gains in performance that can be achieved when Alamouti encoding scheme is employed in FSO communication systems.