Bit Error Probability Analysis Research Articles

A New Perspective on Polar Codes: Analysis of Bit Error Probability

A New Perspective on Polar Codes: Analysis of Bit Error Probability

Reconfigurable intelligent surface assisted downlink INOMA system

AbstractNonorthogonal multiple access (NOMA) and reconfigurable intelligent surface (RIS) methods are explored to enhance spectral and energy efficiency of a wireless network. In this article, we have proposed a downlink RIS‐assisted index modulation NOMA for next‐generation wireless systems, and it is referred to as R‐INOMA. In the proposed R‐INOMA system, a base station transmits information through RIS to three users, the first user is assigned in the spatial domain and the remaining two users are multiplexed using power domain NOMA. We provide an analytical analysis of bit error probability (BEP) for the proposed R‐INOMA system. Impact of number of surfaces, transmit antennas, modulation order, diversity order, and imperfect channel estimation is analyzed for the R‐INOMA. Simulation results show that the proposed R‐INOMA achieved better BEP and sum‐rate over existing NOMA techniques. In the R‐INOMA, doubling of the reflecting surfaces provides a 4 dB gain for a fixed error probability, and the sum‐rate improves as the number of transmitting antennas and reflecting surfaces increases.

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

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

A Lightweight Machine Learning Assisted Power Optimization for Minimum Error in NOMA-CRS Over Nakagami-$m$ Channels

Non-orthogonal multiple access based cooperative relaying system (NOMA-CRS) has been proposed to alleviate the decay in spectral efficiency of the conventional CRS. However, existing NOMA-CRS studies assume perfect successive interference canceler at the relay and mostly investigate sum rate whereas the error performance has not been taken into consideration. In this paper, we analyze error performance of the NOMA-CRS and the closed-form bit error probability (BEP) expression is derived over Nakagami-m fading channels. Then, thanks to the high performance of machine learning (ML) in challenging optimization problems, a joint power sharing-power allocation (PS-PA) scheme is proposed to minimize the bit error rate (BER) of the NOMA-CRS. The proposed ML-assisted optimization has a very low online implementation complexity. Based on provided extensive simulations, theoretical BEP analysis is validated. Besides, the proposed ML-aided PS-PA provides minimum BER (MBER) and outperforms previous PA strategies for the NOMA-CRS notably.

ICI and BEP analysis of hyperbolic FRFT based systems for satellite internet of things

In this paper, calculations of intercarrier interference (ICI) and bit error probability (BEP) of hyperbolic fractional Fourier transform (FRFT) based systems for the satellite internet of things applications, has been considered. Analysis of ICI power and BEP in Rician flat fading channels has been done, mathematically. Simulations approve that the systems based on the hyperbolic FRFT are resistant against carrier frequency offset in high-speed moving conditions. Also, in severely deep fade conditions, the hyperbolic FRFT based systems have an acceptable performance in the achieved bit error probability.

On the BEP analysis of M-QAM and R-QAM under cascaded double η-μ, κ-μ or α-μ fading channels

This article presents new expressions for the bit error probability (BEP) of the M-ary quadrature amplitude modulation (M-QAM) and rectangular QAM (R-QAM) scheme in a frequency non-selective channel model with cascaded double fading, characterized in the links by the distributions η-μ, κ-μ or α-μ. In this paper, the probability density function (PDF) of the signal-to-noise ratio (SNR) of the double link is written in terms of an integral of the product of the PDF of the envelope of the first link by the PDF of the SNR of the second link. With this procedure, expressions for the BEP of the M-QAM and R-QAM scheme, with and without a maximum ratio combiner (MRC) associated, are obtained by means of the general expressions of Cho and Yoon, calculated with the help of the Gauss-Laguerre quadrature. The new expressions are written in terms of the integral of the moment generating function (MGF) of the instantaneous SNR from the second link, which are simpler than using expressions involving infinite series in terms of special functions like hypergeometric functions and the Meijer G-function. In addition, insights regarding the expressions obtained and comments about their complexity are provided. Several curves for the BEP are presented, for different parameters that characterize the channel and different numbers of branches of the MRC. All analytical expressions obtained in this paper are corroborated by computer simulations performed with the Monte Carlo method.

Cooperative AF relaying with energy harvesting in Nakagami-[formula omitted] fading channel

In this paper, the bit error performance of an energy harvesting (EH) cooperative amplify-and-forward (AF) relaying system, in which the relay harvests energy from radio frequency source signal and then uses this energy to transmit its signal to the destination in the presence of a direct link between the source and the destination, is investigated in Nakagami- m fading channel. A unified approach to the analysis of bit error probability (BEP) is presented for the cases where the relay harvests energy based on power splitting (PS), time switching (TS) and ideal operational modes. Simulation results validate the theoretical analysis performed for coherent M-PSK and M-QAM and different system parameters. Dual-hop EH and conventional non-EH cooperative AF relaying systems are considered for comparison purposes. The obtained results show that the system bit error rate performance is mostly dependent on the channel parameter m and the energy harvesting parameters.

Spatially Modulated Bidirectional Cognitive Cross Network Design With Physical-Layer Coding

In this paper, a bidirectional cognitive cross network using spatial modulation (SM) along with physical-layer network coding (PLNC) is proposed. In our model, a primary user pair located far from each other, exchanges information in the lack of a direct link so that a relay is required for a reliable communication. A secondary user pair shares their relay with the primary user in return for access to the licensed spectrum. Both users exploit SM while the relay also applies PLNC. It is assumed that each user pair can eavesdrop the signal of the other user pair to use these signals as side information and cancel them from the PLNC mapped signal broadcasted by the relay. Optimum power allocation, in which two scenarios are considered, is proposed for sources and the relay. In Scenario 1 , the optimization is performed by minimizing the bit error probability (BEP) of the primary user due to its priority in the licensed band. Scenario 2 , which minimizes BEP of both users, provides the optimum results for the whole system. A theoretical BEP analysis is performed and the results are supported via computer simulation results, which are in perfect match with theoretical findings.

Design and analysis of a spread‐spectrum communication system with chaos‐based variation of both phase‐coded carrier and spreading factor

This study designs and analyses a new phase-coded spread-spectrum communication system where both phase-coded carrier and spreading factor are varied based on a chaotic behaviour in the communication process. This design aims to reduce the probability of interception of the considered system. Discrete values generated by a chaotic map are exploited to create a non-return-to-zero (NRZ)-chaos sequence and simultaneously make bit duration variable. The NRZ-chaos sequence is then modulated by binary phase-shift keying technique to produce the phased-coded carrier. Owing to chip duration being constant, the variation of bit duration also leads to the variation of spreading factor. Spectrum spreading in the transmitter is performed by multiplying directly the variable-duration bits with the phase-coded carrier. A coherent receiver relying on a direct correlator is used for recovering the data. Design of the transmitter and receiver as well as analysis of bit error probability for the proposed system in cases of single-user and multi-user under additive white Gaussian noise channel is presented. Simulation results are shown to confirm the operation of the designed structures and the obtained analytical performance.

Predictive relay-selection cooperative diversity in land mobile satellite systems

Cooperative diversity protocols promise a new dimension of diversity that provides better communication by engaging nearby relays in forming a ‘virtual’ array of antennas for combined signal transmission. The current incremental cooperative diversity algorithms incrementally select best relay(s) to cooperate based on the channel quality reported by the relays. However, the algorithms do not take into consideration the fact that the chosen best relay(s) at estimation may not always be the best at the time of communication. This is due to the time delay between the relay selection and its transmission of signal (problem of outdated channel quality information (CQI)). To solve this problem, the concept of channel prediction is introduced and employed whereby each relay determines a predicted value of its CQI based on its past measurements. The paper therefore develops a novel predictive relay-selection (PRS) cooperative diversity model that seeks to improve land mobile satellite communication through prediction protocols. In the model, the chosen best relay is the one with the best predicted CQI value instead of the traditional outdated one. Performance analysis of outage probability and average bit error probability for the newly developed PRS cooperation shows that the PRS cooperation is better than direct and outdated CQI relay communication. Copyright © 2015 John Wiley & Sons, Ltd.

SEP of Decode-and-Forward Cooperative Systems With Relay Selection in Nakagami- <inline-formula> <tex-math notation="TeX">$m$</tex-math></inline-formula> Fading Channels

The exact average bit error probability (BEP) of decode-and-forward (DF) cooperative systems with relay selection for binary phase-shift keying (BPSK) signals in Nakagami-m fading channels is derived. Two types of relay selection schemes, i.e., signal-to-noise ratio (SNR)-based relay selection and log-likelihood-ratio-based relay selection, are investigated, assuming that there are no feedback channels from the destination to the relays. Two types of receivers, i.e., a λ-maximal ratio combining receiver and a piecewise linear receiver, are examined. The BEP analysis for DF cooperative systems employing BPSK signals is used to derive symbol error probability upper bounds of DF cooperative systems with SNR-based relay selection for quadrature phase-shift keying and 16-quadrature amplitude modulation (16-QAM) signals.

Simple, Unified, and Accurate Prediction of Error Probability for Higher Order MPSK/MDPSK With Phase Noise in Optical Communications

Higher order $M$ -ary phase shift keying (MPSK) and differential phase shift keying (MDPSK) ( $M\ge 4$ ) are used in optical communications for increased spectral efficiency. This paper proposes a unified and systematic approach to predicting the error probability of MPSK with phase reference error (PRE) and MDPSK with residual phase noise (RPN) in additive white Gaussian noise (AWGN) channel. It is shown that AWGN leads to an equivalent additive observation phase noise (AOPN), whose probability density function (pdf) conditioned on knowing the received signal magnitude is Tikhonov. For high signal-to-noise ratio (SNR), the Tikhonov pdf can be accurately approximated by a Gaussian pdf. This AOPN can be combined with the PRE/RPN, and the distribution of the combined phase noise (AOPN + PRE/RPN) facilitates the computation of the probability of the received signal phasor falling in any sector in the complex plane. It thus enables us to express the symbol error probability of MPSK/MDPSK with phase noise as one Gaussian $Q$ -function. Moreover, it facilitates the analysis of bit error probability (BEP) with Gray code mapping for MPSK/MDPSK. All the new BEP expressions obtained are linear combinations of single Gaussian $Q$ -functions, and do not involve the product of Gaussian $Q$ -functions. It is shown that our Gaussian AOPN $+$ PRE/RPN model provides a simpler and quicker way to accurately estimate the error performance as a function of the phase error variance. Our unified approach is increasingly more accurate as $M$ increases.

Bit error probability of decode‐and‐forward relaying with efficient partial relay selection in non‐identical Rayleigh fading channels

Efficient partial relay selection (EPRS) is an advanced technique to improve the performance of partial relay selection (PRS) at the cost of a small additional feedback overhead. However, EPRS has the worst performance but lower feedback overhead when compared with best relay selection. In this study, the authors present a bit error probability (BEP) analysis of EPRS in decode-and-forward relaying systems over independent and non-identical Rayleigh fading channels, where the direct link between the source and the destination is available. In particular, they provide an exact and closed-form expression of the BEP of M-ary square quadrature amplitude modulation for EPRS. The BEP analysis is verified through simulations. The numerical results show that EPRS significantly outperforms PRS for a large gap between the average channel powers for the first and the second hops except when all the average channel powers for the first hop are smaller than those for the second hop.

BEP Analysis for DF Cooperative Systems Combined with Signal Space Diversity

In fading channels, increasing diversity gains can effectively improve the reliability of transmissions. This letter considers high-order diversity acquisition by incorporating signal space diversity (SSD) into a decode-and-forward (DF) cooperative system. Our focus is on the bit error probability (BEP) analysis for this cooperative system. In particular, a tight closed-form upper bound on the end-to-end BEP is derived. Moreover, an asymptotic approximation for the BEP is presented which reveals that both the signal space diversity and the spatial diversity gains are achieved when all channels are available. Simulation results validate the theoretical analysis and show that a significant BEP gain over the traditional DF-based system is obtained at no additional power or bandwidth expense.

Bit-Error Probability of Asynchronous Multicode DS-CDMA Systems in Rayleigh Fading

A precise bit-error probability analysis method for multicode DS-CDMA systems in Rayleigh fading is derived. The proposed method applies to a multicode DS-CDMA system with an arbitrary number of multiple code sequences and any selection of multiple code sequences. The method gives accurate results for Rayleigh fading while requiring only a single numerical integration of an integrand involving the well-known Q-function. The solution discriminates the effect of the selection of different multiple code sequences on the bit-error probability, whereas Gaussian approximations do not. Numerical examples show that the differences between exact and approximate methods for a multicode DS-CDMA system operating over Rayleigh fading channels may be more significant than for a single code system in Rayleigh fading channels or for a multicode system in AWGN channels when the spreading factor is not significantly large compared to the number of multiple code sequences.

Theoretical Analysis of Bit Error Probability for 4-State Convolutional Code with Max-Log MAP Decoding

In this letter, a theoretical analysis of bit error probability for 4-state convolutional code with Max-Log-maximum a posteriori probability (MAP) decoding is presented. This technique employs an iterative calculation of probability density function of the state metric per one transition, and gives the exact bit error probability for all signal-to-noise power ratio.

Performance of RS coded M-ary modulation with and without symbol overlapping

In this paper, we present analytical bit error probability results for M-ary modulation concatenated with Reed Solomon (RS) codes. The analysis of bit error probability is nontrivial as the number of bits per symbol for the RS codes may not be an integer multiple of the number of bits per symbol for a modulation symbol. We propose a Markov chain technique which allows analytical evaluation of the bit error probability for such cases. The performance of RS coding with coherent biorthogonal, coherent/non-coherent orthogonal modulation over an additive white Gaussian noise (AWGN) channel is evaluated. Simulation of the bit error probability of RS code concatenated with a Nordstrom Robinson (NR) code as an inner code is performed and compared with the case of biorthogonal modulation. From the results, we notice that a stronger inner code gives better bit error probability. In addition, the throughput of the coded system with biorthogonal modulation over an AWGN channel is discussed. For a Rayleigh flat fading and block fading channel, we analyze the bit error probability of RS codes concatenated with biorthogonal modulation. From the result, we notice that a stronger outer code gives a better bit error probability for the case of Rayleigh flat fading channel.

Interference Robust Transmission for the Downlink of an OFDM-Based Mobile Communications System

Radio networks for future mobile communications systems, for example, 3GPP Long-Term Evolution (LTE), are likely to use an orthogonal frequency division multiplexing- (OFDM-) based air interface in the downlink with a frequency reuse factor of one to avoid frequency planning. Therefore, system capacity is limited by interference, which is particularly crucial for mobile terminals with a single receive antenna. Nevertheless, next generation mobile communications systems aim at increasing downlink throughput. In this paper, a single antenna interference cancellation (SAIC) algorithm is introduced for amplitude-shift keying (ASK) modulation schemes in combination with bit-interleaved coded OFDM. By using such a transmission strategy, high gains in comparison to a conventional OFDM transmission with quadrature amplitude modulation (QAM) can be achieved. The superior performance of the novel scheme is confirmed by an analytical bit-error probability (BEP) analysis of the SAIC receiver for a single interferer, Rayleigh fading, and uncoded transmission. For the practically more relevant multiple interferer case we present an adaptive least-mean-square (LMS) and an adaptive recursive least-squares (RLS) SAIC algorithm. We show that in particular the RLS approach enables a good tradeoff between performance and complexity and is robust even to multiple interferers.

Unified Analysis of UWB Transmitted-Reference Schemes in the Presence of Narrowband Interference

Transmitted-Reference (TR) signaling, in conjunction with an autocorrelation receiver (AcR), offers a low- complexity alternative to Rake reception in ultrawide bandwidth systems. This paper provides a unified performance analysis of various TR schemes by developing an analytical framework based on the sampling expansion approach. Specifically, we derive the uncoded bit error probability (BEP) of different TR signaling schemes, including TR and differential TR (DTR) signaling valid for a broad class of fading channels. We consider both AcRs and modified AcRs with noise averaging. We further develop a quasi-analytical method as well as an approximate analytical method to extend the BEP analysis to include the effect of narrowband interference (NBI). We show that the approximate analytical method is particularly useful in obtaining BEP expressions that provide insight into the effect of NBI. We quantify the effects of NBI and channel power dispersion profile on the optimum integration interval of an AcR. Finally, we compare TR and DTR signaling in terms of their sensitivity to NBI.

Performance Study of Asynchronous FFH/MFSK Communications using Various Diversity Combining Techniques with MAI Modeled as Alpha-Stable Process

In this paper, we present analytical bit-error probability expressions of an asynchronous fast frequency-hopped multiple-access system over fading channels with multiple-access interference modeled as alpha-stable noise. Various diversity-combining receivers over both Rician fading and Rayleigh fading channels are analyzed based on the Fourier-Bessel series. Numerical results under various environments show that the two non-linear diversity-combining methods significantly outperform the linear-combining receiver