Expressions For Average Symbol Error Probability Research Articles

Analyzing ASEP with imperfect‐phase error and various modulation schemes on IRS‐aided wireless network over κ–μ fading channel

AbstractNext‐generation wireless systems constitute a promising technology, and intelligent reflecting surface (IRS)‐aided mobile communications can be used to design and simulate a smart and flexible radio environment. We examine the average symbol error probability (ASEP) on an IRS‐aided wireless network over a κ–μ fading channel with imperfect phase error. In addition, the ASEP for non‐coherent M‐ary frequency shift keying, M‐ary phase shift keying, and M‐ary differential phase shift keying on an IRS‐aided wireless network over a κ–μ fading channel are analyzed. Furthermore, exact closed‐form mathematical expressions for ASEP across different modulation schemes including ASEP with imperfect phase error are derived. The accuracy of the derived expressions is validated through simulations. The system effectiveness is comprehensively examined, uncovering valuable insights into channel fading values and the number of reflecting components.

Performance analysis of RIS-Assisted wireless networks in the presence of imperfect phase errors

In this article, an analysis of the average symbol error probability (ASEP) for a reconfigurable intelligent surface (RIS)-assisted wireless network with imperfect phase noise errors is proposed. In particular, we focus on a RIS-assisted wireless transmission in which imperfect phase errors are modeled by the Tikhonov distribution. The source (S) and destination (D) nodes are equipped with a single antenna, and the channels between the S-RIS and RIS-D nodes exhibit Rayleigh fading which is a good fit for the non-line-of-sight instances. For this system, we derive novel and exact analytical and asymptotic expressions for the ASEP, and the obtained ASEP expressions are then exploited to evaluate the error performance of under different network configurations. The proposed theoretical analysis is confirmed through the exact simulation results.

Mobile Performance Intelligent Evaluation of IoT Networks Based on DNN

The rapid development of the sensor equipment has promoted the rapid growth of the Internet of Things (IoT). The IoT has been widely employed in the multidimensional signal processing and gradually formed the IoT networks. Mobile communication promotes the wide application of the IoT networks. In this study, the transmit antenna selection (TAS) scheme is employed to investigate the average symbol error probability (ASEP) performance of mobile IoT networks over the 2-Rayleigh channels. We first employ moment-generating function (MGF) approach to derive the exact ASEP expressions. We also investigate the outage probability (OP) performance and derive OP expressions. Employing the deep neural network (DNN), an OP intelligent prediction algorithm is proposed. Then, the numerical simulations are conducted to confirm the ASEP and OP performance analysis. The effect of different channel parameters is also analyzed. Compared with Nakagami and Rayleigh channel models, the 2-Rayleigh model has 83.6% and 59.1% increase in ASEP values, respectively. Compared with ELM and RBF models, the DNN model has 31.7% and 22.5% increase in OP prediction accuracy, respectively.

SIMO subcarrier PSK FSO links with phase noise and non‐zero boresight pointing errors over turbulence channels

Terrestrial free-space optical (FSO) communication systems with subcarrier intensity modulation have experienced a particular research attention in the recent past. However, their performance strongly degrades in the presence of atmospheric turbulence, pointing errors, and phase noise impairments. In order to overcome these limitations, the authors consider a receiver diversity scheme of a typical subcarrier phase-shift keying (PSK) system and investigate the performance by means of the average symbol error probability (ASEP). They assume a wide range of turbulence conditions, non-zero boresight pointing errors, and phase noise strengths described through the gamma-gamma, Beckmann, and Tikhonov distributions, respectively. Novel approximate ASEP expressions are derived for single-input single-output and single-input multiple-output (SIMO) configurations. Appropriate numerical results are depicted and validated by Monte Carlo simulations.

Performance analysis of one- and two-way relays for underwater optical wireless communications

In this paper, the amplify and forward (AF) cooperative technique for one- and two-way relays has been implemented for underwater optical wireless communication (UOWC). UOWC suffers from scattering, absorption, and turbulence effects. The distance of communication between UOWC devices is typically within the range of 100 m. So relay-based UWOC has been proposed to improve the performance of device-to-device (D2D) based UWOC by increasing the effective link range. Performance analysis of unidirectional and bidirectional relay-based systems has been carried out in terms of outage probability and average symbol error probability (ASEP) for log-normal underwater fading channels. The analytical results have been validated by means of Monte Carlo simulations. Closed form expressions for ASEP have been obtained by using a mixture of gamma distributions, which was not possible using log-normal distributions. It has been observed that bidirectional relays, even though they have a better data rate than unidirectional relays, suffer in terms of outage probability.

A Study of Single Transmit Antenna Selection with Modulation

Multiple-input multiple-output (MIMO) systems have attracted a vast amount of interest, due to improvements offered in capacity and diversity. However, several challenges still remain. Single transmit antenna selection with modulation (STASM) is an important closed-loop variant of MIMO, and addresses several of its challenges, while achieving full-diversity. On this note, the average symbol error probability (ASEP) of STASM with M-ary quadrature amplitude modulation (M-QAM) and M-ary phase shift keying (M-PSK) is formulated and validates the Monte Carlo simulation results. The formulated ASEP expressions are relatively easy to evaluate. Euclidean distance-based antenna selection for spatial modulation (EDAS-SM) is an innovative closed-loop MIMO scheme that provides many advantages. However, since STASM achieves a full-diversity compared to EDAS-SM, there exists a cross-over point after which its error performance is superior to the latter. For multiple receive antennas, the cross-over point only occurs in the moderate-to-high signal-to-noise ratio region, which may be difficult to achieve in practice. Hence, an adaptive transmit mode switching system based on STASM and EDAS-SM as transmission candidates is proposed. A selection criterion for the transmission candidate is based on minimizing the instantaneous symbol error probability in every transmission interval. By switching between STASM and EDAS-SM, the proposed scheme minimizes the ASEP.

New Analytical Expressions for ASEP of Modulation Techniques with Diversity Over Lognormal Fading Channels with Application to Interference-Limited Environment

In this paper, the analytical expressions of the average symbol error probability (ASEP) for both coherent and non-coherent modulation formats with diversity schemes such as maximal ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC) over the lognormal (LN) distribution assuming independent and identically distributed (i.i.d.) channels have been derived. The functions involving LN distribution are simplified using the Gauss–Hermit and Gaussian Quadrature integration. Furthermore, the effect of the diversity order and constellation size on the error probability has been examined extensively under various shadowing conditions such as infrequent light, average, and frequent heavy shadowing. As an application, the derived results are used to analyze the performance of the communication systems over the interference-limited environment. The impact of the number of interferers on important performance metrics such as the outage probability, the ASEP, and the channel capacity has been examined. The accuracy of the analytical results are validated by comparing them with the exact numerical results and Monte Carlo simulations. The analytical expressions are simple and easily implementable in software package such as MATLAB. The proposed analytical expressions are supposed to be a vital tool in areas such as IEEE 802.15.3a wireless communication system, indoor environment, radio channel effect by body worn devices, ultra-wideband indoor channel.

Performance Analysis of M2M Sensor Networks

The average symbol error probability (ASEP) and outage probability (OP) performance of mobile-to-mobile (M2M) senor networks employing transmit antenna selection (TAS) and selection combining (SC) over N-Nakagami fading channels are investigated in this paper. Based on the moment generating function (MGF) approach, the exact ASEP expressions are derived for several modulation schemes. The exact closed-form OP expressions are also presented. Then, the ASEP and OP performance under different conditions are evaluated through numerical simulations to confirm the accuracy of the analysis. The simulation results show that the number of antennas, the fading coefficient, and the number of cascaded components have an important influence on the ASEP and OP performance.

Performance Analysis of Switched Diversity Combining System

The average symbol error probability (ASEP) and outage probability (OP) performance of the switched diversity combining (SDC) system over N-Nakagami fading channels is investigated in this paper. The probability density function (PDF) of the signal-to-noise ratio (SNR) is used to derive exact and approximate ASEP expressions for phase shift keying (PSK) and pulse amplitude modulation (PAM). Exact closed-form expressions for OP of the SDC system are also presented. The ASEP and OP performance under different conditions is evaluated through numerical simulation to verify the analysis. Results are presented which show that the performance of the SDC system is improved when the number of diversity branches and the fading coefficient is increased, but is degraded as the number of cascaded components is increased.

Performance Analysis of SEC-SC System

In order to achieve the balance between implementation complexity and system performance, a new hybrid combining technique named SEC-SC is proposed in this paper, which is composed of switch-and-examine combining (SEC) and selection combining(SC).The average symbol error probability (ASEP) and outage probability (OP) of the SEC-SC system over N-Nakagami fading channels is investigated. The exact ASEP expressions are derived for several modulation schemes, including phase shift keying (PSK), quadrature amplitude modulation (QAM), and pulse amplitude modulation (PAM). The exact closed-form OP expressions are also presented. Then the ASEP and OP performance under different conditions is evaluated through numerical simulations to verify the analysis. The simulation results showed that the performance of the SEC-SC system is improved with the diversity branches and the fading coefficient increased, but the level of improvement is declined as the number of cascaded components increased.

Performance Analysis of the MRC M2M System

The average symbol error probability (ASEP) of a mobile-to-mobile (M2M) system employing maximal ratio combining (MRC) over N-Nakagami fading channels is investigated in this paper. The characteristic function (CF) of the signal-to-noise ratio (SNR) at the MRC output is used to derive exact ASEP expressions for several q-ary modulation schemes, including phase shift keying (PSK) modulation, quadrature amplitude modulation (QAM), and pulse amplitude modulation (PAM). Then the ASEP performance under different channel conditions is evaluated through numerical simulation to verify the analysis. These results show that the performance of the MRC M2M system is improved as the number of diversity branches or the fading coefficient is increased. Conversely, performance is degraded as the number of cascaded components is increased.

On the ASEP of Decode-and-Forward Dual-Hop Networks with Pilot-Symbol Assisted M-PSK

We develop an analytical framework for the end-to-end (e2e) average symbol error probability (ASEP) of dual-hop relaying networks with pilot-symbol assisted M-ary phase-shift keying (M-PSK) modulation. The relays use the selective decode-and-forward protocol and are equipped with multiple receive antennas. The channels are estimated per antenna branch based on the least-squares estimation (LSE) technique by means of pilot symbols. Also, maximal-ratio combining and coherent detection are performed per receiving end. Exact e2e analytical ASEP expressions are derived for binary and quadrature phase-shift keying (BPSK and QPSK), while simple approximate expressions and bounds are obtained for high signal-to-noise ratio (SNR) when M ≥ 2. Our analysis is generic enough to account for any frequency-flat, time-selective, and/or arbitrarily correlated fading channel model per hop. As a case study, we further provide e2e ASEP expressions considering arbitrarily correlated Nakagami fading channels. For high SNR, closed-form expressions are derived, while the cooperation-gain and diversity-order are also extracted. In addition, two power allocation strategies are investigated and analytical solutions are provided. Comparisons between numerical and computer simulation results are finally presented to verify the validity of the proposed approach and the accuracy of the high-SNR approximate expressions.

Distribution of Inner Product of Complex Gaussian Random Vectors and its Applications

Let X and Y be two independent L x 1 complex Gaussian random vectors distributed as CN (m×, σ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> × I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> ) and CN (m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</sub> , σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> ), respectively, where I_L denotes the L x L identity matrix. The joint characteristic function (c.f.) of the real and imaginary parts of the inner product Y <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> X is derived in closed form, with (·) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sup> denoting the conjugate transpose. Based on this joint c.f., a unified analytical framework for the derivation of the average symbol error probability (ASEP) of a multibranch diversity reception system over flat correlated fading using M-ary phase-shift keying is developed. The receiver employs maximal-ratio combining with least squares channel estimation by means of pilot symbols. The optimal average pilot-to-noise power ratio is obtained in closed form, and the analytical framework is applied to Nakagami and Rice fading. For Nakagami fading, closed form ASEP expressions are obtained for the cases of high signal-to-noise (SNR) and binary phase-shift keying, while for Rice fading, high SNR approximate expressions are obtained in terms of a single integral under the constant correlation model and for independent and identically distributed channels. Both analytical and computer simulation results are presented and compared in order to verify the validity of the proposed analysis.

Error performance of digital modulation schemes with MRC diversity reception over η-μ fading channels

This paper provides exact-form expressions for the average symbol error probability (ASEP) of various digital modulation schemes with maximal ratio combining (MRC) diversity over L independent, not necessarily identically distributed (n.i.d.) eta-mu fading channels. The derived expressions are given in terms of the Lauricella and Appell hypergeometric functions and include several others available in the literature such as those for Nakagami-m and Hoyt. General asymptotic ASEP expressions are also derived for all the considered modulation schemes which provide useful insights regarding the factors affecting the performance of the considered system.