Expression For Average Bit Error Probability Research Articles

Joint Code Index Modulation Aided Enhanced Spatial Modulation for High-Rate MIMO Systems

In this paper, a novel scheme, which introduces the technology of the code index modulation (CIM) into the realm of enhanced spatial modulation (ESM), named CIM-ESM, is proposed to achieve high spectral efficiency and high energy efficiency in multiple-input multiple-output (MIMO) systems. In the CIM-ESM scheme, information bits are conveyed not only by modulated symbols and spreading code indices, but also by the indices of the active antenna and constellation combinations. Meanwhile, the mathematical expressions for the average bit error probability (ABEP) in the presence of channel estimation errors, data rate, energy efficiency, and complexity of the CIM-ESM scheme are deduced. To achieve a higher transmission rate and code utilization, we further propose an enhanced scheme, named joint CIM-ESM (JCIM-ESM) scheme. In the JCIM-ESM scheme, spreading codes are jointly selected to form spreading code pairs and the matching indices of the spreading code pairs are utilized to convey extra information bits. Finally, Monte Carlo simulation results corroborate the tightness of the derived ABEP expression in the high signal-to-noise ratio region and reveal that both the CIM-ESM and JCIM-ESM schemes can provide better performance than CIM spread spectrum (CIM-SS), generalized CIM-aided spatial modulation (GCIM-SM), generalized space CIM (GSCIM), and CIM-aided QSM (CIM-QSM) schemes.

Average bit error probability performance of intelligent reflecting surface‐aided wireless communications over Hoyt fading

SummaryIn this article, the performance of a wireless communication system with an intelligent reflecting surface (IRS) panel installed between the transmitter and receiver is studied. The channel is considered to be the Hoyt faded and additive white Gaussian noise. Closed‐form expressions for average bit error probability (ABEP) for both coherent Gray‐coded rectangular quadrature amplitude modulation and non‐coherent modulation schemes are presented. We apply the moment‐generating function‐based method for the derivation. In addition, asymptotic ABEP expressions are also obtained. Using asymptotic ABEP expressions, we obtained diversity order which is a function of the number of IRS elements. The effect of the number of IRS elements and fading parameters on the ABEP is studied. The ABEP performance improves with an increase in the number of reflecting elements but degrades with an increase in the fading severity. The accuracy of each analytical ABEP expression is verified by the simulation of the system considered herewith.

Quadrature Spatial Scattering Modulation for mmWave Transmission

In this letter, we investigate a novel quadrature spatial scattering modulation (QSSM) transmission technique based on millimeter wave (mmWave) systems, in which the transmitter generates two orthogonal beams targeting candidate scatterers in the channel to carry the real and imaginary parts of the conventional signal, respectively. Meanwhile, the maximum likelihood (ML) detector is adopted at the receiver to recover the received beams and signals. Based on the ML detector, we derive the closed-form average bit error probability (ABEP) expression of the QSSM scheme. Furthermore, we evaluate the asymptotic ABEP expression of the proposed scheme. Monte Carlo simulations verify the exactness and tightness of the derivation results. It is shown that the ABEP performance of QSSM is better than that of traditional spatial scattering modulation.

On the Exact Closed-Form ABEP Analysis of Downlink NOMA Over mmWave TWDP Fading

This paper presents the performance analysis of two users’ downlink non-orthogonal multiple access (NOMA) over a millimeter-wave two-wave with diffuse power (TWDP) fading model for successive interference cancellation errors. The new closed-form expressions of average bit error probability (ABEP) for both users are derived for quadrature phase-shift-keying and binary phase-shift-keying modulation pairs. Further, the asymptotic ABEP expressions are derived to provide better insights into the performance analysis. The diversity order of each user is also derived with the aid of asymptotic ABEP expression. The obtained expressions over TWDP fading channels are generalized ABEP expressions as it also shows ABEP expressions for both Rician and Rayleigh fading channels as special cases. Simulation results support the correctness of each analytical ABEP expression.

Analysis of SWIPT based dual-hop AF relay with SSK modulation over Nakagami-m fading channel

Space shift keying (SSK) modulation performance is analyzed with simultaneous wireless information and power transfer (SWIPT) based cooperative amplify-and-forward (AF) relaying system over the Nakagami-m fading channel. SWIPT technique can remove the need for power supply at the relays in cooperative communication. In contrast, SSK is a low complex index modulation technique that eliminates inter antenna synchronization, inter-channel interference and reduces the number of radiofrequency chains. Closed-form expression for average bit error probability (ABEP) is derived using a single AF relay with selection combining (SC) at the receiver, and an Upper bound ABEP expression is derived for multiple AF relays with the direct link (DL) from source to destination. The partial relay selection (PRS) technique has been proposed with energy harvesting (EH) to reduce the hardware complexity compared to the multiple relays. Numerical and computer simulation results are presented with the discussion. The result demonstrates that EH with SSK modulation can improve the system performance.

BP neural network-based ABEP performance prediction for mobile Internet of Things communication systems

Wireless communications play an important role in the mobile Internet of Things (IoT). For practical mobile communication systems, N-Nakagami fading channels are a better characterization than N-Rayleigh and 2-Rayleigh fading channels. The average bit error probability (ABEP) is an important factor in the performance evaluation of mobile IoT systems. In this paper, cooperative communications is used to enhance the ABEP performance of mobile IoT systems using selection combining. To compute the ABEP, the signal-to-noise ratios (SNRs) of the direct link and end-to-end link are considered. The probability density function (PDF) of these SNRs is derived, and this is used to derive the cumulative distribution function, which is used to derive closed-form ABEP expressions. The theoretical results are confirmed by Monte-Carlo simulation. The impact of fading and other parameters on the ABEP performance is examined. These results can be used to evaluate the performance of complex environments such as mobile IoT and other communication systems. To support active complex event processing in mobile IoT, it is important to predict the ABEP performance. Thus, a back-propagation (BP) neural network-based ABEP performance prediction algorithm is proposed. We use the theoretical results to generate training data. We test the extreme learning machine (ELM), linear regression (LR), support vector machine (SVM), and BP neural network methods. Compared to LR, SVM, and ELM methods, the simulation results verify that our method can consistently achieve higher ABEP performance prediction results.

Sum of Squared Fluctuating Two-Ray Random Variables With Wireless Applications

The fluctuating two-ray (FTR) channel fading offers good fit for small-scale experimental data in millimeter wave communications. We first investigate the statistical characterizations of the sum of independent nonidentically distributed squared FTR random variables. More specifically, the exact and approximate analytical expressions for moment generating function, probability density function, and cumulative distribution function are derived. Then, the performance of the maximal-ratio combining system over FTR fading channels is assessed in terms of the outage probability (OP) and the average bit error probability (ABEP). Moreover, asymptotic OP and ABEP expressions are obtained to obtain physical insights into the impact of the system and channel parameters on the overall performance. Finally, the correctness of our results is verified by simulation results.

Performance analysis of dual-hop AF relaying over [formula omitted]-[formula omitted] fading channels

This letter investigates the error performance of dual-hop amplify-and-forward (AF) relaying over α-μ fading channels. Specifically, making use of the Fox’s H-function, closed-form exact expressions for the n-th moment of the received signal-to-noise ratio (SNR) and average bit error probability (ABEP) are derived for arbitrary parameter values of the α-μ distribution. To gain insights into the error performance, a closed-form ABEP expression for the case of asymptotically high SNR at the second hop is also derived. The analytical expressions are validated through simulations.

ABEP Performance of AF System Employing QSSK over IoT Network

Quadrature space shift keying (QSSK) modulation in cooperative communication, combined with cooperative relaying, improves the reliability in communication and enhances the overall spectral efficiency. Here, QSSK scheme is analyzed for complete uplink and downlink transmission system between a base station and a connected device for Internet-of-Things (IoT) application with dual-hop amplify-and-forward (AF) relaying systems using a single relay, multiple relays and relay selection techniques. Analytical expressions for cumulative distribution function (CDF) of the end-to-end signal-to-noise ratio are derived and used to evaluate the average bit error probability (ABEP) of QSSK modulation in mixed Rayleigh-Rician fading channel. The obtained ABEP expressions are in the form of Whittaker function which can be numerically evaluated using its numerical or series representation. Numerical and simulation results are presented to illustrate the impact of fading parameters on the system performance.

Quadrature space shift keying performance with dual‐hop AF relay over mixed fading

SummaryQuadrature space shift keying (QSSK) modulation combined with cooperative relaying improves the reliability in communication and enhances the overall spectral efficiency. Here, QSSK scheme is analyzed for multiple‐input multiple‐output (MIMO) wireless communication system with dual‐hop amplify‐and‐forward (AF) relaying systems over asymmetric mixed Rayleigh/Rician and symmetric Nakagami‐m/Nakagami‐m fading channels. Analytical expressions for cumulative distribution function (CDF) of the end‐to‐end signal‐to‐noise ratio are derived and used to evaluate the average bit error probability (ABEP) of QSSK modulation in mixed asymmetric and symmetric fading channels. The obtained ABEP expression is in the form of Whittaker function, which can be numerically evaluated using its numerical or series representation. Numerical and simulation results are presented to illustrate the impact of fading parameters on the system performance.

Impact of symmetric and asymmetric fading channels on dual-hop AF relay system with SSK modulation

Performance of dual-hop amplify-and-forward relaying system is analyzed over asymmetrical Nakagami-m/Rcian and symmetrical Nakagami-m/Nakagami-m fading channel with space shift keying (SSK) modulation. Expressions for average bit error probability (ABEP) of SSK modulation scheme over the line-of-sight and non-line of sight fading channels have been obtained. Analytical expressions for cumulative distribution function of the end-to-end signal-to-noise ratio are derived and a mathematical expression for the ABEP of SSK modulation is obtained for both in presence of the direct link between source to destination and in absence of the direct link. The derived expressions are given in terms of the Whittaker functions and Gamma functions. ABEP expressions are also derived which provide useful insights into the factors governing the performance of the considered system. The numerical results have been verified with Monte-Carlo simulation results.

Impact of Pointing Errors on the Error Performance of Intersatellite Laser Communications

The effect of pointing errors on the average bit error probability (ABEP) of an intersatellite laser communication link is studied. A closed-form expression in terms of the Marcum $Q$ -function is given for calculating the instantaneous channel gain. This expression provides great potential in further performance analysis and system optimization. In addition, tight, closed-form upper and lower bounds on the ABEP are derived, by using bounds on the Gaussian $Q$ -function. These bounds are in simpler form than existing results and are much more efficient in numerical evaluations. Further simplifications of these bounds are performed and invertible ABEP expressions are given. Via numerical comparisons, these invertible ABEP expressions are shown to be accurate approximations within a wide range of transmit power of interest and thus provide efficient error prediction methods. The diversity gain is easily obtained using the invertible ABEP expressions, which is related to the ratio of the equivalent beam radius to the pointing error displacement standard jitter at the receiver. Moreover, we show explicitly how the ABEP depends on different system parameters.

Antenna selection for N R‐STAR‐ M QAM spatial modulation

A new multiple-ring star- M -ary quadrature amplitude modulation-aided spatial modulation ( N R-STAR- M QAM-SM) scheme is proposed. The aim is to minimise the average bit error probability (ABEP) of the system. Then in the interest of further minimising the ABEP, the authors formulate a low-complexity algorithm to achieve the optimum radii of N R-STAR- M QAM-SM. This algorithm is based on a specific multiple-input multiple-output configuration and the pairwise error probability function. To validate the results of the proposed scheme, a closed-form union-bound theoretical ABEP expression is derived. Finally, to improve the error performance of N R-STAR- M QAM-SM, the authors propose a low-complexity Euclidean distance-based antenna selection (EDAS) algorithm for N R-STAR- M QAM-SM (EDAS- N R-STAR- M QAM-SM). Since all amplitude/phase modulation schemes are considered to have rotational symmetry and symmetric constellation points have the same EDAS solution, the authors achieve EDAS- N R-STAR- M QAM-SM by searching only one constellation point per symmetric constellation set. The EDAS- N R-STAR- M QAM-SM solution exhibits a significant reduction in the computational complexity compared with the conventional EDAS solution.

Analytical Framework for Space Shift Keying MIMO Systems With Hardware Impairments and Co-Channel Interference

This letter provides a general analytical framework for multiple-input multiple-output space shift keying systems considering hardware impairments, at the transmitter and receiver sides, and co-channel interference. Specifically, a closed-form expression for the average bit error probability (ABEP) in the case of two transmit antennas and arbitrary number of receive antennas is derived. As well, a tight upper bound ABEP expression in the general case of arbitrary number of transmit and receive antennas is obtained. Besides, an asymptotic simple expression is found over Rayleigh fading channels. Analytical results, which are validated via simulation ones, explicitly demonstrate that non-zero bounds of the ABEP exist in the high power region, which is in contrast to the case of ideal hardware, where the ABEP asymptotically goes to zero.

ABEP Performance of ISDF Relaying M2M Cooperative Networks

In this paper, the average bit error probability (ABEP) performance of the incremental-selective decode-and-forward (ISDF) relaying mobile-to-mobile (M2M) cooperative networks over N-Nakagami fading channels is investigated. The exact ABEP expressions are derived, and the power allocation problem is formulated.The derived ABEP expressions are verified by Monte Carlo simulations. The simulation results showed that the propagation parameters, such as the fading coefficient, and the power-allocation parameter, have a significant influence on the ABEP performance.

On the Performance of Full-Duplex Two-Way Relay Channels With Spatial Modulation

In this paper, the spatial modulation (SM) technique is employed at the source and relay nodes in a full-duplex two-way relay channel (FD-TWRC) to support spectral-efficient bi-directional communications while guaranteeing a low cost implementation. Maximum likelihood detectors are employed at each node that is subject to an intrinsic self-loop interference. We first propose a tight upper bound on the average bit error probability (ABEP). Then, based on the ABEP upper bound, an asymptotic ABEP expression is derived in the high signal-to-noise ratio (SNR) regime. Exploiting the asymptotic ABEP, an exact SNR threshold for the selection between FD-TWRC-SM and half-duplex (HD)-TWRC-SM is derived in a closed form, which sheds light on when it is beneficial to select the FD (or HD) mode. In addition, the power allocation (PA) among sources and relay is investigated, through which an optimal PA factor in terms of ABEP is obtained. All analytical results derived in this paper are verified by Monte Carlo simulations, from which some new insights are obtained on the performance of FD-TWRC-SM.

Performance Analysis of Coherent FSO-OFDM Systems With Frequency Offset

In this letter, we investigate the performance of coherent free-space optical (FSO)—orthogonal frequency division multiplexing (OFDM) systems with multiple receivers over an atmospheric turbulence channel considering the frequency offset effect. In particular, we derive an exact average bit error probability (ABEP) of coherent FSO-OFDM systems in a turbulence-induced fading channel. To mitigate the atmospheric turbulence-induced amplitude fluctuations and phase aberrations, a modal compensation technique is assumed to be employed at the receivers. Numerical results confirm the validity of the derived ABEP expression.

Effect of Timing Error on the Performance of BPSK Modulation over a Fading Channel

In this letter, a closed form expression for the conditional bit error probability (BEP) with static timing errors of binary phase shift keying (BPSK) modulation over a Rayleigh fading channel is presented. The expressions for average BEP are then given for dynamic timing errors assuming the normalized timing error has either a Gaussian probability density function (pdf) or a Tikhonov pdf. Numerical results to corroborate the derived analytic expressions are presented for average BEP obtained by averaging the conditional error probability over the pdf of normalized timing errors.

MGF for gamma‐shadowed ricean fading channel

AbstractThe moment‐generating function (MGF) of the received signal‐to‐noise ratio (SNR) is a convenient tool in the performance analysis of modulation schemes in fading channels. In this letter, we derive the MGF for gamma‐shadowed Ricean fading channels under the assumption that the average power of the Ricean fading is characterised by a gamma distribution. The MGF is expressed in a series form. An application of the derived MGF for evaluating the average bit error probability (ABEP) for binary differential phase‐shift keying (DPSK) is given. The exact expression for ABEP and the corresponding asymptotic expression (assuming large SNR) are derived and mutually compared. The computational efficiency is elaborated on. Special cases of the exact expression for ABEP agree with corresponding known results. Copyright © 2007 John Wiley & Sons, Ltd.