Average Bit Error Probability Performance Research Articles

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.

Generalized Quadrature Space-Frequency Index Modulation System With Low-Complexity Detection

In this article, we propose a generalized quadrature space-frequency index modulation (GQSFIM) system that maps the information bits to the subcarrier activation pattern (SAP), the two antenna activation patterns (AAPs), and the modulated symbols. Specifically, two independent AAPs are utilized for the modulated symbols in a GQSFIM subblock to get higher spectral efficiency. With the help of the union bounding technique, the closed-form average bit error probability (ABEP) expression of the GQSFIM system with the maximum-likelihood (ML) detection is derived. Additionally, two low-complexity step-by-step signal detection algorithms, local ML based minimum mean-squared error (MMSE) and local ordered block based MMSE, are provided to reduce the high computational complexity of the ML detection, where the SAP, the two AAPs, and the modulated symbols are detected separately. Numerical results verify the correctness and accuracy of the theoretical ABEP of the GQSFIM system, especially in the high signal-to-noise ratio region. Moreover, the proposed GQSFIM system achieves better spectral efficiency and ABEP performance compared with the typical space-frequency index modulation systems.

Generalized 3-D Spatial Scattering Modulation

Three-dimensional (3-D) massive multiple-input-and-multiple-output (MIMO) systems, which explore degrees of freedom in both the vertical and the horizontal dimensions, are a promising technology to enhance spectral efficiency in the next-generation communication systems. As an emerging modulation technology with millimetre wave (mm-wave) communication in massive MIMO systems with limited radio-frequency (RF) chains, the spatial scattering modulation (SSM) makes use of beamspace domain resources to further improve the spectral efficiency. However, most published works on the SSM only focus on two-dimensional (2-D) MIMO systems. In this paper, we generalize the SSM system to 3-D space. First, we design a novel generalized 3-D SSM system by considering both vertical and horizontal angles to determine scattering paths, which are selected to convey information bits. Then, we propose a whitening filter based optimal detection algorithm to detect the received symbols with correlated noise, where the correlation is generated by the combination of the received signals from the large-scale planar receiving antenna array. Next, we design a 2-D fast Fourier transform (FFT) based transceiving approach to improve the hardware friendliness. After that, we propose a low-complexity detector based on the linear minimum mean square error (MMSE) detection algorithm. Moreover, we derive the union upper bound on average bit error probability (ABEP) in a closed form and the asymptotic performance expression for the generalized 3-D SSM system. Finally, we analyse the impact of transmission environment on the ABEP performance. Numerical results show that the generalized 3-D SSM system outperforms the conventional 2-D SSM system, which reduces the ABEP by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10\times $ </tex-math></inline-formula> with the same signal-to-noise ratio (SNR) level under the typical indoor environment.

On the Performance of 3-D Spatial Modulation Over Measured Indoor Channels

In this paper, a measurement-based three-dimensional (3-D) spatial modulation (SM) system is first proposed in the existing literature. The major contributions of this work include: 1) a 3-D SM measurement system with a <inline-formula><tex-math notation="LaTeX">$\boldsymbol{16 \times 16}$</tex-math></inline-formula> virtual uniform rectangle array (URA) at the transmitter and a virtual uniform line array (ULA) with 16 elements at the receiver, 2) a comprehensive measurement activity indoors taking both line-of-sight (LOS) and none-LOS (NLOS) scenarios into account, and 3) the first measurement-based average bit error probability (ABEP) evaluation for 3-D SM system. Numerical results reveal that the widely used independent and identically distributed (i.i.d.) Rayleigh channel model significantly overestimates the performance of the SM system. Moreover, we find that the ABEP performance of 3-D SM is worse than that of the 2-D SM under the same spacing among the antenna array, while 3-D SM outperforms 2-D SM under the same size of the antenna array.

Generalized Polarization-Space Modulation

A novel generalized polarization-space modulation (GPSM) is proposed for polarized multiple-input multiple-output (MIMO) systems with a limit number of radio frequency (RF) chains. In the spatial domain, multiple dual-polarized (DP) transmit antennas are activated, and then combinations of those indices are used to convey information. While in the polarization domain, depending on the random input bits, only one polarization state is selected for each active DP transmit antenna to transmit information following the rule of the polarized shift keying. At the receiver, the maximum likelihood detector is employed as a benchmark to detect information bits being used to select the polarization state and activated DP antennas. In the detector, imperfect channel state information (CSI) is taken into account. Two less computationally complex detectors, i.e., a linear detector and a sphere decoding (SD) detector are proposed to relieve the computational burden. Sacrificing the average bit error probability (ABEP) performance, the proposed linear detector can reduce the computational complexity significantly. The proposed SD detector can achieve the optimum ABEP performance, while reducing computational complexity by reducing the search space. A closed-form union upper bound (UUB) on the ABEP of the GPSM system with imperfect CSI at the receiver is analytically derived and validated through simulations. From the UUB, a loose asymptotic bound on the ABEP, which sheds light on deriving the diversity gain and the coding gain, is derived. Numerical results show that the signal-to-noise ratio loss caused by increasing the number of transmit antennas is less than 3 dB while the spectral efficiency is increased by 7 b/z/Hz. Therefore, the GPSM can be a promising candidate of down link massive MIMO systems to achieve a high spectral efficiency with a limit number of RF chains.

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.

ABEP Evaluation of Spatial Modulation Communication Systems: Improved Analytical Framework

Average bit error probability (ABEP) performance evaluation of spatial modulation (SM) over wireless fading channels has attracted huge interest in the literature. In general, the core step to analytically evaluate such ABEP performance is to theoretically derive the associated average pairwise error probabilities (average-PEPs). However, these average-PEPs have been derived so far in exact and closed-form expressions only for two cases: 1) SM systems with real-valued modulation regardless of the fading channel type, 2) SM systems with complex-valued modulation but only for Rayleigh fading channel type. In case of complex-valued modulation with non Rayleigh fading, such average-PEPs were derived either in exact but integral-form expressions or in closed-form but non-simplified and non-tight approximate expressions. Thus, here, we introduce a new analytical framework to fill this literature gap by deriving new exact and closed-form formulas for the SM system's average-PEPs. We first apply the proposed framework on SM system with perfect channel-state-information (CSI) considering Rayleigh and Rician fading environments as two separate scenarios. Then, in order to show the effectiveness of the proposed approach, we reapply it for the imperfect CSI estimation scenario, where more generic exact average-PEPs are derived. Numerical and simulation results are provided, which show that, as compared to the widely adopted conventional literature approximate method, the proposed framework offers much better accuracy over the whole signal-to-noise-ratio (SNR) region.

Performance analysis of a wireless energy‐harvesting cooperative system with precoding spatial modulation

An energy-harvesting decode-and-forward cooperative system over correlated Rayleigh fading channels is investigated. Simultaneous wireless information and power transfer (SWIPT) technology is employed at the relay to improve energy efficiency. To overcome the spatial correlation among the transmit antennas, precoding spatial modulation (PSM) is formulated. The average bit-error probability (ABEP) upper bound is derived and it matches closely with the Monte Carlo simulation results. The influence of the parameters, such as the power-splitting factor and transmit correlation coefficient, on system performance is studied. The results show that the proposed PSM-SWIPT system can achieve better ABEP performance than SM-SWIPT, space shift keying-SWIPT and multiple-input–multiple-output-SWIPT systems under the same spectral efficiency.

SSK modulation performance with relay selection and selection combining

In this letter, the performance of space shift keying (SSK) modulation is analyzed with partial amplify and forward (AF) relay selection (RS) from multiple numbers of relays and selection combining (SC) at the receiver. This scheme selects a single radio frequency (RF) chain from the transmitter to the relay using the RS as well as relay to the receiver using the SC technique. Closed‐form expression for average bit error probability (ABEP) is derived and Numerical and computer simulation results are presented with the discussion. The result derived is compared with the best RS where the best link between the transmitter to the receiver is selected with SC at the receiver. It is revealed that there is an interesting trade‐off between partial RS and best RS with SC at the receiver. However, it is shown that partial RS with SC has almost equal ABEP performance in comparison to best RS with SC with low hardware complexity.

Performance Analysis of Spatial Modulation Under Rapidly Time-Varying Rayleigh Fading Channels

Due to the problem of inter-channel interference, the average bit error probability (ABEP) performance of the traditional multiple transmit and multiple receive antenna systems obviously deteriorates. A promising scheme to address this issue is the spatial modulation (SM) which activates only one transmit antenna at each signaling period. In addition, the demand to provide data services for high mobility users is ever increasing, where fading channels are more likely to be rapidly time-varying. Therefore, in this paper, we investigate the ABEP performance of SM under the assumption that system’s fading channels are Rayleigh and varying from one signaling period to another within the same transmitted data block. Further, to simplify the decoding complexity at the receiver, the channel is assumed to be estimated at the first location of each data block and then used to detect the received symbols at the remaining locations of the block. For such a system, and unlike other literature works, we derive novel, exact and closed-form reduced enough expressions for the average pairwise error probabilities (average-PEPs), which are then used to compute the system’s overall per-block ABEP efficiently. The derived expressions are generic and valid for both time-varying and slow fading environments. Furthermore, the obtained analytical results are exploited to quantitatively show that the time-varying fading environment degrades the SM system’s performance through irreducible error floors. Numerical and simulation results of various examples are provided to validate the theoretical analyses and also to get some insights into the effect of the different system parameters (such as the speed of the mobile, the carrier frequency, and the block size of the channel variations) on the overall SM error performance.

Error Analysis of SSK With Euclidean Distance Based Selection Combining

In this paper, we analyze the performance of space shift keying (SSK) modulation scheme with Euclidean distance based selection combining (ED-SC) at the receiver. This scheme utilizes a single radio frequency (RF) chain receiver that selects one out of $N_{r}$ receiver antennas based on the Euclidean distance between the SSK constellation points. In addition to this, the performance of generalized ED based SC (GED-SC) is also analyzed by utilizing two or more RF chains at the receiver. The closed form expressions for the average bit error probability (ABEP) of ED-SC and GED-SC schemes are derived for two transmit and $N_{r}$ receive antennas. Further, the theoretical ABEP analysis of ED-SC is derived for $N_{t} > 2$ . In addition to this, we also derive the diversity order analysis of ED-SC SSK system for $N_{t} = 2$ . From the diversity order analysis, it can be inferred that the diversity order obtained by the ED-SC SSK system is $N_{r}$ . It is observed from the simulation results that the performance of $2\times 4$ GED-SC SSK system with two and three RF chains is only slightly worse than the optimal detection with $N_{r}=4$ . Since only a single RF chain is utilized for signal reception in ED-SC, the receiver complexity of employing $N_{{RF}}$ RF chains in GED-SC and $N_{r}$ RF chains in optimal detection is greatly reduced. Moreover, the simulation results of the ABEP performance of ED-SC SSK system in imperfect channel state information at the receiver is shown.

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.

Spatial Modulation via 3-D Mapping

This letter proposes a jointly mapped spatial modulation (JM-SM) scheme to break through the constraint on the number of transmit antennas in traditional SM systems. It is realized via jointly mapping the transmit information bits to 3-D constellation points. A 3-D constellation design scheme for a JM-SM is analyzed and established by minimizing the system average bit error probability (ABEP). In addition, the extension of the joint 3-D mapping to generalized spatial modulation is discussed. The simulation results show that the proposed schemes can be adapted to multiple-input multiple-output systems with an arbitrary number of transmit antennas and offer better ABEP performance than those existing schemes.

Performance Analysis of IDF Relaying M2M Cooperative Networks over N-Nakagami Fading Channels

Exact average bit error probability (BEP) expressions for mobile-relay-based mobile-to-mobile (M2M) cooperative networks with incremental decode-and-forward (IDF) relaying over N-Nakagami fading channels are derived in this paper. The average BEP performance under different conditions is evaluated numerically to confirm the accuracy of the analysis. Results are presented which show that the fading coefficient, the number of cascaded components, the relative geometrical gain, and the power allocation parameter have a significant influence on the average BEP performance.

Performance analysis of threshold digital relaying M2M cooperative networks

Exact average bit error probability (BEP) expressions for mobile-to-mobile cooperative networks employing threshold digital relaying over N-Nakagami fading channels are derived. The power allocation problem is formulated for performance optimization. The average BEP performance is evaluated via numerical simulation to verify the accuracy of the analysis with binary phase shift keying (BPSK) modulation. The simulation results showed that the fading coefficient, number of cascaded components, relative geometrical gain, and power-allocation parameter have a significant influence on the performance.

Performance of Two-Hop Relay Assisted Decode-and-Forward Transmission under Mixed Fading Environments

This study analyses the performance of two-hop decode-and-forward (DF) relaying protocol under mixed faded channels by evaluating outage probability ( ) and average bit-error probability (ABEP). It is assumed that the channel between source and relay is Rayleigh fading, whereas the relay-destination link is subject to Weibull fading. First, a closed-form expression is formulated for and then it is used to obtain ABEP for the considered system model. The ABEP performance of two-hop DF relaying is presented for M-ary phase shift keying (M-PSK) signaling with different constellation sizes. Moreover, the proposed analytical expressions are verified by simulations that present the correctness of the derived formulas.DOI: http://dx.doi.org/10.5755/j01.eee.21.1.9806

Performance Analysis of Dual-Hop AF Relaying Systems over Mixed $\eta{-}\mu$ and $\kappa{-} \mu$ Fading Channels

This paper investigates the end-to-end performance of a dual-hop amplify-and-forward (AF) relaying communication system where the source-to-relay and the relay-to-destination channels are subject to different fading conditions. The relay is assumed to either possess perfect channel state information (CSI) or have a fixed gain. We consider the case where the one hop's channel is subject to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\eta$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> fading, whereas the other hop's channel is subject to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\kappa$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex> </formula> fading. This mixed fading propagation channel is capable of accurately modeling various practical dual-hop transmissions. Examples of such environments are encountered in micro-/macrocellular systems and/or hybrid satellite/terrestrial wireless communication systems, where typically, only the one hop's channel has a line-of-sight (LOS) component. For both CSI-assisted and fixed-gain relaying and for integer-valued fading parameters, exact analytical expressions in the form of rapidly convergent infinite series for the outage probability (OP) and average bit error probability (ABEP) of several modulation schemes are derived. Moreover, for CSI-assisted relaying and arbitrary-valued fading parameters, closed-form lower bounds [tight for high values of the signal-to-noise ratio (SNR)] for the OP and ABEP performance are obtained. The analysis is also substantiated by obtaining previously published equivalent performance expressions as special cases of our generic fading models, namely, those available for Nakagami- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> and Rice fading channels. In addition, the derived analytical expressions have been numerically evaluated, and the performance evaluation results have been further validated by comparing them with equivalent results that have been obtained by means of Monte Carlo computer simulations.

Feedback Power Control with Bit Error Outage Probability QoS Measure on the Rayleigh Fading Channel

We propose to use the probability of instantaneous bit error outage (IBEO) as a new performance measure in the design of an actual feedback power control system. It is defined as the probability that the instantaneous bit error probability (IBEP) exceeds an IBEP threshold. We propose the IBEO-based power control law where the transmitted power is adjusted according to the variations of the channel such that the IBEO probability is kept within some quality of service (QoS)-specified threshold. It ensures that in the long term, no more than a certain fraction of received bits would have IBEP exceeding some IBEP threshold. Therefore, the instantaneous QoS is guaranteed. Based on a practical system model with channel estimation and prediction, we develop the traditional average bit error probability (ABEP)-based power control law and the new IBEO-based power control law. For both laws, we derive explicit ABEP and IBEO probability results. The IBEO-based law shows a remarkable gain over the ABEP-based law in terms of IBEO probability, and sacrifices only a little in the ABEP performance.

A New Approach to Bivariate Hoyt Distribution and its Application in Performance Analysis of Dual-Diversity Receivers

Novel infinite series based expressions for the bivariate Hoyt distribution are derived. More specifically, expressions for the joint probability density function (JPDF) and the joint cumulative distribution function (JCDF) of two Hoyt fading envelopes are derived, and proposed for use in performance analyses of dual-branch diversity receivers operating over correlated Hoyt fading channels. Using these reasonably simple and mathematically tractable expressions, we evaluate the performance of a dual-branch selection combining (SC) diversity receiver in terms of the outage probability (P out ) and the average bit error probability (ABEP) criteria. The ABEP performance is evaluated for binary differential phase-shift-keying (BDPSK) and binary non-coherent frequency-shift keying (BNFSK) modulation schemes.