Analytical Bit Error Rate Expressions Research Articles

DHT-based GFDM and STC-GFDM systems for beyond 5G wireless networks

This manuscript endeavours an exploration of Generalized Frequency Division Multiplexing (GFDM) as a promising alternative to the Orthogonal Frequency Division Multiplexing (OFDM) in next-generation cellular networks. GFDM’s exceptional performance in minimizing out-of-band emissions (OOBE) and maximizing spectral efficiency (SE) makes it a compelling candidate, especially when integrated with Multi-Input Multi-Output (MIMO) technology to enhance reliability through spatial diversity. However, ensuring GFDM’s resilience against frequency-selective channels (FSCs), especially in low-latency scenarios, is crucial.This research investigates Discrete Hartley Transform (DHT) based GFDM and Space-Time Coded GFDM (STC-GFDM) systems, proposing a comprehensive framework to enhance performance metrics such as Bit Error Rate (BER) and Achievable Rate (AR). Further enhancements are achieved through a Minimum BER-Power Allocation (MBER-PA) strategy, optimizing BER and AR in QAM-based GFDM and STC-GFDM systems employing a DHT precoding scheme. Analytical expressions for BER and AR are derived and validated via Monte Carlo simulations. Additionally, a comparative analysis against traditional GFDM systems is conducted, evaluating metrics including Peak-to-Average Power Ratio (PAPR), BER, and AR.

Performance analytics of adaptive subcarrier intensity modulated free-space optical communications over general Málaga turbulence links

In this paper, we study the performance analysis of free-space optical (FSO) system employing a constant-power variable-rate adaptive subcarrier intensity modulation (SIM) and utilizing phase-shift keying (PSK) over the Málaga atmospheric turbulence with pointing errors. According to a target bit-error rate (BER) and the instantaneous signal-to-noise ratio (SNR), the adaptive strategy adopts the subcarrier PSK modulation order. More precisely, we develop new analytical expressions for the average BER, the upper bound on ergodic channel capacity for non-adaptive modulation, and the attainable spectral efficiency (SE) of an adaptive SIM-FSO communication system. According to the simulation results, it is possible to achieve an increase in SE under weak-to-strong turbulence conditions without the need to increase the average optical power transmitted or compromise the BER requirements.

BER analysis on exposure effect for optical camera communication.

The exposure effect of cameras in optical camera communication (OCC) distorts the received light pulses and generates inter-symbol interference (ISI), which adversely affects the bit error rate (BER) performance. In this Letter, we derive an analytical expression of BER based on the pulse response model of the camera-based OCC channel and analyze the impact of exposure time on BER performance considering asynchronous transmission characteristics. Numerical simulations and experimental results demonstrate that a long exposure time is beneficial in a noise-dominant communication scenario, while a short exposure time is preferable when ISI is dominant. This Letter provides a comprehensive analysis of the influence of exposure time on BER performance, offering a theoretical foundation for the design and optimization of OCC systems.

A Power-Domain MST Scheme With BPPM in NLOS Ultraviolet Communications

Due to the high path loss of non-line-of-sight (NLOS) ultraviolet communications (UVC) channel, pulse modulation schemes, such as on-off keying (OOK) and M-ary pulse-position modulation (PPM), and photon-counting receivers are commonly adopted. Although M-ary PPM can be demodulated and decoded without the channel state information, its spectral efficiency is lower than OOK's. To improve the spectral efficiency of M-ary PPM in NLOS UVC, a power-domain multilayer-superposed transmission (MST) scheme with binary PPM (BPPM) is proposed in this work. Based on this scheme, the signal in each layer can be directly decoded without successive interference cancellation, which is necessary for other MST schemes in the power domain. Hence, a low complexity receiver in the NLOS UVC system can be realized. Additionally, the bit-error rate (BER) and achievable data rate (ADR) expressions of the proposed MST scheme are derived. Monte-Carlo simulations are performed to verify the analytical BER expression. The NLOS UVC system performance employing the proposed MST scheme is further demonstrated and compared with pure BPPM. The results indicate that with the optimal power allocation factor for each layer, the overall ADR of the NLOS UVC system with the proposed power-domain MST scheme can surpass that with pure BPPM.

Low-Complexity Codebook Design for SCMA-Based Visible Light Communication

Sparse code multiple access (SCMA), as a code-domain non-orthogonal multiple access (NOMA) scheme, has received considerable research attention for enabling massive connectivity in future wireless communication systems. In this paper, we present a novel codebook (CB) design for SCMA based visible light communication (VLC) system, which suffers from shot noise. In particular, we introduce an iterative algorithm for designing and optimizing CB by considering the impact of shot noise at the VLC receiver. Based on the proposed CB, we derive and analyze the theoretical bit error rate (BER) expression for the resultant SCMA-VLC system. The simulation results show that our proposed CBs outperform CBs in the existing literature for different loading factors with much less complexity. Further, the derived analytical BER expression well aligns with simulated results, especially in high signal power regions.

Symbol Error-Rate Analytical Expressions for a Two-User PD-NOMA System with Square QAM

Power domain non-orthogonal multiple access (PD-NOMA) is one of the most perspective multiplexing technologies that allows improving the capacity of actual networks. Unlike orthogonal multiple access (OMA), the PD-NOMA non-orthogonally schedules multiple users in the power domain in the same orthogonal time-spectrum resource segment. Thus, a non-orthogonal multiplexed signal is a combination of several user signals (usually, modulation and coding schemes (MCS) based on quadrature amplitude modulation) with different power weights. The symbol error rate (SER) and bit error rate (BER) performances are one of the main quality characteristics of any commutation channel. The issue is that a known analytical expression for BER and SER calculation for conventional OMA cannot be applied in terms of the PD-NOMA. In the following work, we have derived the SER and BER analytical expressions for gray-coded square quadrature amplitude modulation (QAM) user channels that are transmitted in two-user PD-NOMA channel under additive white Gaussian noise (AWGN). Through the simulation, the verification of the provided expressions is presented for four multiplexing configurations with various user power weights and QAM order combinations.

An exact BER analysis of NOMA-VLC system with imperfect SIC and CSI

Visible Light Communication (VLC) has emerged as a promising technology for 5G and beyond networks by offering a wide license free spectrum. In order to develop a high data-rate and error-free network, in this paper, non-orthogonal multiple access (NOMA) technique is combined with VLC technology. In particular, a two user downlink NOMA based VLC system is considered in which the transmitter uses on–off keying (OOK) and L-ary pulse position modulation (L-PPM). The closed form mathematical expressions for bit-error-rate (BER) of OOK and L-PPM modulated NOMA-VLC system is derived in the presence of perfect and imperfect channel state information (CSI). Moreover, imperfect successive interference cancellation (SIC), which is a more practical scenario, is considered for this analysis. The analysis shows that the error performance of L-PPM modulated NOMA-VLC system is superior to OOK modulated NOMA-VLC system for (L > 2). Further, with the far user power allocation coefficient greater than 0.5, the far user completely outperforms the near user. Furthermore, the channel estimation error has an adverse effect on BER performance of the system under consideration. The performance of the considered system is investigated for the parameters of interest, i.e., location of the far user, field of view (FOV) and channel estimation error. The derived analytical BER expressions are verified with the simulation results.

Generic BER Analysis of VLC Channels Impaired by 3D User-Mobility and Imperfect CSI

Visible light communications (VLC) has emerged as a high-speed, low-cost, and green supplement for the existing radio frequency (RF) based infrastructures. However, the performance of VLC based systems is found to degrade significantly due to detrimental outages caused by non-negligible variations in the VLC channel-gain, that are jointly induced by radial user-mobility and random photodetector-orientation (together designated as 3D mobility in this letter). In addition to the 3D user-mobility mentioned above, the performance of VLC based systems is further limited by imperfect channel-state information (CSI). Such degradations in the VLC-link caused by the aforementioned factors necessitate the quantification of performance-metrics for further benchmarking/receiver-design. In this work, an analytical expression for bit-error rate (BER) is derived for a single LED indoor VLC system considering the radial user-mobility, random receiver orientation, and imperfect CSI altogether. Further, the derived BER expressions are validated using computer-simulations using typical VLC channel models from the literature. A close agreement between the analytical and the simulated BER is observed, which verifies the accuracy of the presented analysis.

Analysis of M-QAM Modulated Underwater Wireless Optical Communication System for Reconfigurable UOWSNs Employed in River Meets Ocean Scenario

In this paper, the bit error rate (BER) performance of underwater wireless optical communication system employing with M-ary quadrature amplitude modulation is proposed for underwater optical wireless sensor networks (UOWSN) in river meets ocean scenario. The underwater channel degradation effects such as absorption, scattering and oceanic turbulence is taken into account. The oceanic turbulence is modelled by the Gamma-Gamma distribution. The first time, we proposed re-configurable UOWSN for the real time scenario of the river meets the ocean and derived the novel closed form analytical BER expressions of the proposed system over Gamma-Gamma turbulence with attenuation effects. The impact of oceanic turbulence parameters such as the variations of temperature, kinetic energy, viscosity, salinity, link range and the water type of system performance is investigated for river water, mixed water (river and ocean water) and ocean water. The proposed system and the related analysis will be highly useful in UOWSN and the Internet of underwater thing (IoUT) applications.

On BER analysis of nonlinear VLC systems under ambient light and imperfect/outdated CSI

Visible light communication (VLC) has emerged as a promising supplement to the existing radio frequency (RF) technology, which facilitates high speed communication for next generation communication systems. Although promising, the performance in a practical VLC system is severely impaired by ambient light interference. Furthermore, nonlinearity of light emitting diodes (LEDs) and imperfect/oudated channel state information (CSI) are other factors that degrade the achievable bit error rate (BER) performance. In this work, an analytical framework for analyzing the expression for BER of a wide class of modulation techniques is derived for an impaired VLC system considering: (a) ambient light interference, (b) LED nonlinearity, and (c) imperfect and outdated CSI. The derived analytical expressions for BER are validated through extensive computer simulations performed over typical VLC channels. Lastly, the utility of the derived analytical framework is demonstrated in the context of high data-rate VLC systems, wherein the performance of DC biased optical orthogonal frequency division multiplexing (DCO-OFDM) is quantified for VLC links impaired by the aforementioned degradations.

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.

Error probability performance of chirp modulation in uncoded and coded LoRa systems

This paper focuses on the error probability performance of LoRa, a long-range low-power wireless communication technology suited for the Internet of Things (IoT). We propose accurate approximations for the bit error probability of the uncoded LoRa chirp modulation in additive white Gaussian noise (AWGN) channel. Our approach, which is based on a smart modification of a union bound on the error probability, is applied to both coherent and noncoherent detection. Simulation results show that the proposed theoretical bit error rate (BER) expressions are more accurate than the existing BER approximations that use similar complexity. We show that the proposed BER expressions are valid for both orthogonal and quasi-orthogonal LoRa, and are easier to compute than the exact BER for orthogonal signaling. Moreover, we extend the theoretical performance analysis to coded LoRa systems and we propose analytical BER expressions for Hamming-coded LoRa signals with hard-decision decoding. In addition, we analyze by simulation the error probability of coded LoRa systems with soft-decision decoding in multipath channels. The obtained results (both theoretical and simulated) quantify the performance gains of channel coding with respect to uncoded transmissions, in both AWGN and multipath channels, for coded LoRa systems that use the same bandwidth (with lower bit rate) of the uncoded LoRa system.

Bit error probability analysis of IR-UWB ED-OOK system using cooperative dual-hop DTF strategy

The Bit Error Rate (BER) of a single user cooperative Impulse Radio (IR)-Ultrawideband (UWB) communication system employing Energy Detector (ED) receiver with On-Off Keying (OOK) in IEEE 802.15.4a UWB multipath environment is investigated in this paper. Analytical evaluation based on Energy detection principle is performed to derive approximate BER Expressions for various diversity combining cases, namely optimum combining, linear combining and selective combining using cooperative dual-hop Detect and Forward (DTF) relay protocol in presence and absence of Inter-symbol interference (ISI). Numerical results reveal that there is a significant improvement in BER, with increase in number of relay diversity paths and decrease in number of frames Nf. The accuracy and perfection in approximation used in investigation of BER is confirmed with the validation of the analytical BER expressions with that of the simulation results. The analytical and simulation results confirm that among the diversity combining schemes, the performance of optimum combining is better compared with linear combining, which in turn performs better than selective combining.

A novel chaotic modulation approach of packaged antenna for secured wireless medical sensor network in E‐healthcare applications

AbstractThis article first time reports the chaotic modulation approach toward RF signal processing for secured wireless medical sensor network (WMSN) in E‐healthcare applications. A Lorenz based chaotic modulation approach is implemented which provides lowest bit error rate (BER). The definite analytical expressions for BER in a differential chaos‐shift keying (DCSK) modulation scheme is derived and it predicted good correlation between simulated and theoretical. It is observed that proposed Lorenz chaos‐based DCSK modulation scheme is a potential candidate to provide high security in the patient data for WMSN. An off‐body UWB slotted antenna is designed which could avoid limitation of short‐range distance like implanted ones. The entire work includes numerical, simulated and experimental data in three phases. In first phase, Lorenz chaotic oscillator with electronics compatibility is executed which acts as data acquisition unit and demonstrates two‐dimensional and three‐dimensional chaos attractors. While in the second phase, analysis of BER achieves value of less than 10−4 by providing pseudorandom bit sequence at 5 Gb/s. A chaos modulated envelope using Lorenz based DCSK modulation is obtained by delay element γ. Finally, the third phase is designed on‐wafer off‐body antenna and demonstrates 3.1 to 10.6 GHz UWB toward RF signal processing in E‐healthcare applications.

Closed-form and analytical BER expression for OFDM system with μ-law companding operation

The μ-law companding function has been applied widely in orthogonal frequency division multiplexing (OFDM) to reduce the peak-to-average power ratio (PAPR). However, nonlinear distortion caused by the μ-law companding function is considered a key impairment in OFDM communication systems. Few studies have addressed theoretical nonlinear distortion caused by μ-law companding function for OFDM systems. In this paper, we derive a closed-form expression of signal distortion as well as the closed-form bit error rate (BER) of OFDM system caused by the μ-law companding function. Based on the theoretical signal distortion and BER expression, the theoretical BER value and signal distortion value can also be calculated, which can guide us to choose appropriate μ value for different BER condition and bit-to-noise (Eb/No) condition efficiently. Then the PAPR performance can also be predicted. The results show good agreement on the Monte-Carlo simulation results and the obtained theoretical BER results. Furthermore, based on theoretical signal distortion and theoretical BER expression, the figure of the relationship among BER value, Eb/N0 and μ is also given. Based on this figure, we can find the appropriate μ law for different BER and Eb/N0 condition. And then the PAPR performance can also be predicted.

Performance analysis of a parameter‐tuned bistable parallel array system for binary pulse amplitude modulation signal processing

In order to improve the signal-to-noise ratio (SNR) gain and lower the bit error rate (BER) when a weak signal is buried in the noise, the parameter-tuned stochastic resonator (PSR) is studied in more detail. In this study, the authors explore the impact of the number of branches on performance. Hence, they build the parameter-tuned bistable parallel array system, which consists of a group of PSRs and propose a novel method to derive the probability density function (PDF) of the output signal, which combines the conventional PDF based on the approximation theory with Gaussian distribution. Based on this method, an analytical expression for BER of the system is derived. It is of interest to note that for an input binary pulse amplitude modulation signal buried in noise, the weak signal can be detected by using the parameter-tuned bistable parallel array system. It is found that via the array PSR effect, the system output SNR gain can be improved. Moreover, the BER can also be reduced with the increase of the array size as the array size increases.

Performance evaluation of T‐COFDM under combined noise in PLC with log‐normal channel gain using exact derived noise distributions

In this study, the performance analyses of the proposed turbo-coded orthogonal frequency division multiplexing (T-COFDM) are investigated over the power-line communication with lognormal channel gain based on derived effective complex-valued ratio distributions of the individual and combined noise samples at the zero-forcing equaliser output. The effective noise samples are derived in the presence of Nakagami-m background interference (BI) noise, Middleton class A impulsive noise (MCAIN) and their combination. The performance of the turbo code has been improved by computing the exact log-likelihood ratio using derived distributions, with the derivation of pairwise error probability and the average upper-bounds (AUBs). Moreover, the bit error rate (BER) degradation in the conventional T-COFDM system has been improved by deriving two clipping thresholds to combat the effect of the non-Gaussian noise, the first one has been derived in the presence of the impulsive noise only modelled by MCAIN model and the second one in the presence of combined Nakagami-m BI noise and MCAIN model. Monte Carlo simulations demonstrate the significant BER improvements of the proposed T-COFDM system compared to the improved conventional T-COFDM system with a close agreement to the AUBs derivation and analytical BER expression.

THE EVALUATION OF PERFORMANCE FOR A MASS-MIMO SYSTEM WITH THE STSK SCHEME OVER 3-D FADING CHANNEL

The evaluation to the performance of bit error rate (BER) for an massive multi-input multi-output (M-MIMO) system with spatial time shift keying (STSK) scheme over three-dimensions (3-D) fading model is proposed in this article. The long-term evaluation advanced (LTE-A) or 5th generation (5G) M-MIMO radio system is deployed with beamforming techniques over 3-D environment that contains the correlation phenomenon between angle of arrival (AoA) and angle of departure (AoD). Moreover, the determination of moment generating function (MGF) and characteristic function (CF) approaches is applied to derive analytical expression of BER for 3-D M-MIMO in order to avoid some difficult steps. Besides, the channel capacity is presented by using of mutual information to confirm the accuracy of the theoretically derived formulas. Furthermore, the work of performance evaluation is with different numbers of transmitter and receiver antennas. The correlation parameter between AoA and AoD definitely generates impact on the performance of BER when consider an M-MIMO system over the fading model and beamforming transmission.

Performance of nonorthogonal FSK for the Internet of Things

IEEE 802.15.4 is a popular standard for low-rate wireless communications used for the Internet of Things (IoT). This IEEE standard contains a variety of physical layers (such as SUN, TVWS, RCC LMR, and LECIM) that make use of different modulations, such as nonorthogonal frequency-shift keying (FSK) and position-based FSK. This paper proposes simple closed-form expressions to evaluate the bit-error rate (BER) performance of nonorthogonal FSK schemes used for the IoT. Both coherent and noncoherent detection cases are investigated in additive white Gaussian noise (AWGN) and frequency-nonselective fading channels. In case of AWGN channels, the proposed BER expressions are obtained by selecting and modifying two terms of a union bound on the error probability. In case of fading channels, the proposed BER expressions are obtained by integration of the conditional BER over the fading statistics. Simulation results confirm the good accuracy of the proposed analytical BER expressions for different channel models (such as AWGN, Nakagami-m, Rice, lognormal) and for different detection techniques (such as noncoherent, coherent, and coherent with a residual phase error). Experimental results with wireless transmission and reception confirm the accuracy of the proposed approach. In addition, this paper also presents a BER expression for coherent detection of position-based FSK. Simulation results demonstrate that the presented BER expression for position-based FSK is more accurate than the BER expressions proposed in the literature.

BER Analysis of WFRFT Precoded OFDM and GFDM Waveforms With an Integer Time Offset

In this paper, we investigate bit error rate (BER) performances of weighted-type fractional Fourier transform (WFRFT) precoded orthogonal frequency-division multiplexing (OFDM) and generalized frequency-division multiplexing (GFDM) waveforms with an integer time offset (TO) over additive white Gaussian noise and fading channels. First of all, theoretical BER expressions of hybrid carrier systems with TO are derived according to the linear combination characteristic of WFRFT. In addition, the fusion mechanism is also employed to calculate noise enhancement factor (NEF) of WFRFT precoded GFDM waveforms, and then analytical BER expressions are derived, including the cases with TO. Basically, analytical BER expressions of WFRFT precoded OFDM and GFDM waveforms are under the same framework, and BER of the latter could be simplified to the former when GFDM systems are reduced to OFDM systems. Through WFRFT precoding, the BER performance of GFDM waveforms could be improved by about 2 dB over fading channels with timing errors. Furthermore, using derived NEF of WFRFT precoded GFDM waveforms, theoretical BER expressions could be easily extended to space-time coded systems. Finally, when interblock interference and intercarrier interference are generated due to insufficient cyclic prefix and timing errors, BER performances of WFRFT precoded OFDM and GFDM waveforms also surpass their two special cases, i.e., nonprecoded and discrete Fourier transform precoded ones.