Average Symbol Error Rate Research Articles

Performance analysis of dual‐hop variable‐gain relaying with beamforming over κ – μ fading channels

In this study, the performance of a dual-hop amplify-and-forward relaying system with beamforming is analysed, where only the source and destination are equipped with multiple antennas and both hops are subject to κ - μ fading channels. The κ - μ fading model is a general fading model that can accurately model practical small scale fading in line-of-sight environments and accommodates Rician, Nakagami- m , and Rayleigh as special cases. New exact analytical expressions on the outage probability (OP), average symbol error rate (SER), and average capacity are derived. Moreover, asymptotic results for the OP, SER, and average capacity are also derived in simpler forms in terms of basic elementary functions which make it easy to understand the system behaviour and the impact of the channel parameters. These analytical results are general and can emulate different symmetric and asymmetric fading scenarios as special cases such as Rician/Rician, Nakagami- m /Nakagami- m , Rayleigh/Rayleigh, and mixed κ - μ , Rician, Nakagami- m , and Rayleigh fading links.

Performance study of multi‐hop communication systems with decode‐and‐forward relays over fading channels

In this study, we investigate the performance of multi-hop systems with decode-and-forward relaying over fading channels. Specifically, the authors derive closed-form expressions for the probability density function, cumulative distribution function, and moment generating function of the end-to-end signal-to-noise ratio. In addition, they derive closed-form expressions for the end-to-end capacity (ergodic and outage) and average symbol error rate (coherent and non-coherent) of the system. The derived expressions can be transformed to study the performance of multi-hop communication systems over other well-known fading channel models by using the proper values for the and parameters. Finally, the performance of multi-hop scenario is analysed and investigated using numerical evaluation. Results are provided to illustrate the system's performance and the impact of number of hops and fading parameters on network performance. The derived expressions, in this study, are very important for the prediction of the performance metrics and statistics such that efficient designs of multi-hop wireless systems can be realised.

Performance Evaluation of Wireless Communication Systems over Composite $${\varvec{\alpha}}{-}{\varvec{\mu}}/$$ α - μ / Gamma Fading Channels

The composite $$\alpha {-}\mu /$$ gamma distribution is considered in this paper. Specifically, we derived closed-form expressions for the power probability density function (PDF) and the cumulative density function (CDF). We then use the PDF and the CDF to derive novel closed-form expressions for the outage probability, the average symbol error rate, and the average channel capacity over the composite $$\alpha {-}\mu /$$ gamma fading channels. All derived expressions are valid for integer and non-integer values of the fading parameters. Some representative numerical examples are provided to study the impact of the fading and shadowing parameters on the system performance. Furthermore, the numerical results are compared with Monte-Carlo simulations. Both results demonstrate excellent agreement which validates our analysis.

X-Duplex Relaying: Adaptive Antenna Configuration

In this letter, we propose a joint transmission mode and transmit/receive (Tx/Rx) antenna configuration scheme referred to as X-duplex in the relay network with one source, one amplify-and-forward (AF) relay and one destination. The relay is equipped with two antennas, each of which is capable of reception and transmission. In the proposed scheme, the relay adaptively selects its Tx and Rx antenna, operating in either full-duplex (FD) or half-duplex (HD) mode. The proposed scheme is based on minimizing the symbol error rate (SER) of the relay system. The asymptotic expressions of the cumulative distribution function (CDF) for the end-to-end signal to interference plus noise ratio (SINR), average SER and diversity order are derived and validated by simulations. Results show that the X-duplex scheme achieves additional spatial diversity, significantly reduces the performance floor at high SNR and improves the system performance.

Performance of dual‐hop DF relaying systems with QAM schemes over mixed η‐μ and κ‐μ fading channels

AbstractPerformance of a dual‐hop decode‐and‐forward relaying system that uses quadrature amplitude modulation (QAM) scheme is analyzed over mixed η‐μ and κ‐μ fading channels. Closed‐form expressions are derived for the average symbol error rate (ASER) for rectangular QAM and cross QAM schemes using moment‐generating function‐based approach. The obtained ASER expressions accommodate other mixed fading channels addressed in the literature, as special cases. Further, a simple expression for the asymptotic ASER has been obtained, useful to determine the system performance at high signal‐to‐noise‐ratio values. The obtained asymptotic ASER results reveal that the diversity order is determined by the most severely faded link while the coding gain is affected by the total power of the system. Additionally, we analyze the optimal power allocation method, which provides a practical design rule to optimally distribute the total transmission power between the source and the relay to minimize the ASER. Extensive numerical and computer simulation results are presented that confirm the accuracy of presented mathematical analysis.

Performance analysis of orthogonal frequency division multiplexing‐based cooperative amplify‐and‐forward networks with non‐linear power amplifier over independently but not necessarily identically distributed Nakagami‐ m fading channels

In this study, performance analysis of variable-gain amplify-and-forward relaying orthogonal frequency division multiplexing-based systems over independently but not necessarily identically distributed Nakagami-m fading channels using non-linear power amplifier (PA) at the relay and maximal ratio combining scheme at destination. Specifically, novel closed-form expressions of outage probability and asymptotic outage probability are investigated for the considered system model. Further, an average symbol error rate (ASER) expression is derived for general-order rectangular quadrature amplitude modulation (RQAM) scheme using cumulative distribution function-based approach, which is also the novel contribution of the work. Since the transfer function of PA used at relay is nonlinear, this introduces non-linear distortion (NLD) in the considered system model. Thus, the impact of NLD and fading parameters on outage probability, diversity gain of the system and ASER performances are analysed. Further, the impact of NLD on constellation order for RQAM scheme is also discussed. The theoretical results are compared with computer simulations to verify the accuracy of the derivations. The derived expressions are generalised over variety of fading environments for integer-valued fading parameter.

A Tight Lower Bound for the Symbol Error Performance of the Uplink Sparse Code Multiple Access

We derive a tight lower bound for symbol error rate (SER) performance of the sparse code multiple access (SCMA) uplink operated over Rayleigh fading channels. In particular, based on the working principle of message passing algorithm receiver and the special structure of the sparse binary matrix, which is used to control the collisions of SCMA system, the system can be simplified to a single user single input multiple output (SU-SIMO) system employing maximal ratio combining (MRC) reception. In this way, the average SER lower bound of SCMA is obtained by calculating the average SER of SU-SIMO system employing MRC reception. Our results show that the derived lower bound is not only an efficient means of analyzing the SER performance, but also is tight, especially in the high signal-to-noise ratio regime.

Downlink Error Rates of Half-Duplex Users in Full-Duplex Networks Over a Laplacian Inter-User Interference Limited and EGK Fading

This paper develops a mathematical framework to study downlink error rates and throughput for half-duplex (HD) terminals served by a full-duplex (FD) base station. The developed model is used to motivate long term pairing for users that have a non-line of sight (NLOS) interfering link. Consequently, we study the interferer limited problem that appears between NLOS HD users-pair that are scheduled on the same FD-channel. The distribution of the interference is first characterized via its distribution function, which is derived in closed form. Then, a comprehensive performance assessment for the proposed pairing scheme is provided by assuming Extended Generalized- $\mathcal {K}$ fading for the downlink and studying different modulation schemes. To this end, a unified closed-form expression for the average symbol error rate is derived. Furthermore, we show the effective downlink throughput gain harvested by the pairing NLOS users as a function of the average signal-to-interference-ratio when compared with an idealized HD scenario with neither interference nor noise. Finally, we show the minimum required channel gain pairing threshold to harvest downlink throughput via the FD operation when compared with the HD case for each modulation scheme.

Timing jitter’s influence on the symbol error rate performance of the L -ary pulse position modulation free-space optical link in atmospheric turbulent channels with pointing errors

An analytical approach is proposed to evaluate the impact of timing jitter on the error performance of the L-ary pulse position modulation (L-PPM) free-space optical (FSO) link, under the gamma–gamma (ΓΓ) turbulence with pointing errors. The expression of the conditional symbol error rate (SER) for a certain timing jitter is developed while the Gaussian–Hermite polynomial approximation is utilized to derive the closed-form expression of the average SER by the jitter’s variance. It is discovered that the timing jitter contributes to an error floor on the SER in both Monte–Carlo simulations and the theoretical results. Also, the jitter with small variance could be tolerable. What is more, the PPM system with lower order is more sensitive to the timing jitter than the higher ones.

Average symbol error rate and outage probability of DS-CDMA systems with AF relaying over asymmetric fading channels

In this paper, approximate outage probability (OP) and average symbol error rate (SER) of cooperative direct-sequence code-division multiple access (DS-CDMA) systems with amplify-and-forward (AF) relaying are evaluated over asymmetric fading channels. Practically, the channels between source (S), relay (R) and destination (D) nodes in a DS-CDMA system can be subject to different fading due to the nature of wireless medium. Motivated by this reality, the S–D path is assumed to be Nakagami-m distributed which is a general fading model for different types of channel conditions while S–R and R–D paths are considered to experience Rician fading in order to include line of sight conditions. First, closed-form solutions are obtained for both the cumulative distribution function and the probability density function of S–R–D paths. Then, a closed-form total moment generating function (MGF) of the considered system is derived. The lower bound of the OP is calculated with the help of the inverse Laplace transform of the derived MGF expression while average SER is analyzed by evaluating the integral over the derived MGF. Finally, an asymptotic MGF expression is proposed for high signal-to-noise ratio (SNR) analysis of AF DS-CDMA systems. The simulation results are provided to verify the correctness of the analytical derivations. It is shown that the approximate OP and average SER results are in well agreement with the simulations and the asymptotic results are tight from medium to high SNR regime.

Performance Analysis of Cooperative Systems With Unreliable Backhauls and Selection Combining

In this paper, a cooperative wireless system with unreliable wireless backhaul connections is investigated. To increase the throughput and maximize the receiver signal-to-noise ratio (SNR), a selection combining (SC) protocol is employed. Cooperative transmitters are connected to the control unit (CU) via independent but unreliable wireless backhaul connections. Simultaneously taking into account the reliability of each backhaul and different fading conditions of Nakagami- $m$ fading channels, the statistical properties of the effective SNR (e-SNR) at the receiver are investigated. Closed-form expressions are derived for several performance metrics, including the outage probability, average spectral efficiency (ASE), and average symbol error rate (ASER). The effects of backhaul reliability on these performance metrics are also investigated. The scaling relationship between the convergence behavior of these performance metrics and the conventional diversity gain is also analytically investigated in the asymptotic high-SNR regime. Monte Carlo simulations are conducted to verify the derived impact of backhaul reliability on the performance.

On the Performance of X-Duplex Relaying

In this paper, we study an X-duplex relay system with one source, one amplify-and-forward relay, and one destination, where the relay is equipped with a shared antenna and two radio frequency (RF) chains used for transmission or reception. X-duplex relay can adaptively configure the connection between its RF chains and antenna to operate in either half-duplex (HD) or full-duplex (FD) mode, according to the instantaneous channel conditions. We first derive the distribution of the signal to interference plus noise ratio, based on which we then analyze the outage probability, average symbol error rate (SER), and average sum rate. We also investigate the X-duplex relay with power allocation and derive the lower bound and upper bound of the corresponding outage probability. Both analytical and simulated results show that the X-duplex relay achieves a better performance over pure FD and HD schemes in terms of SER, outage probability and average sum rate, and the performance floor caused by the residual self interference can be eliminated using flexible RF chain configurations.

A Novel Low-Complex Antenna Selection Scheme for Beyond 4G (B4G) Systems

Multi input multi output (MIMO) based transmission modes are very popular in 4G and beyond wireless standards. It offers high quality services at the cost of increased hardware and signal processing complexity. Antenna selection is one of the suitable solutions to overcome the limitations of MIMO scheme. Antenna selection schemes are becoming very popular in the recent wireless techniques like massive MIMO, cognitive radio, multi-hop relay networks (MHR) and wireless local area networks. Instead of using all the available antennas for transmission and reception, antenna selection schemes select good antennas based on the channel state information (CSI). To attain the full benefits of transmitter and joint antenna selection schemes, accurate CSI is required at the transmitter side. The non-zero feedback delay and time varying channel conditions, make the CSI available at the transmitter outdated, which also affects the antenna selection process. In this work, we have derived the closed form average symbol error rate (SER) expression of M-ary phase shift keying (PSK) modulation, for three different antenna selection schemes, by considering the effect of delayed CSI. All these derived expressions are the function of correlation between CSI at the receiver and delayed CSI at the transmitter. The simulation results show that the antenna selection gain decreases with the decrease in correlation. It is also observed that scheme 1 based antenna selection is optimal under delayed CSI conditions, for different constellations and more suited for future wireless standards.

Approximation of Multi-Hop Relay to Dual-Hop Relay and Its Error Performance Analysis

In this letter, we develop a novel analytical framework in order to derive average symbol error rate (ASER) as a tractable form in multi-hop amplify-and-forward (AF) relay systems with cooperative diversity. In the proposed analytical approach, we modify multi-hop relay systems to dual-hop schemes over Rayleigh fading channels. The received signal in the $l$ th relay can be expressed as a single signal from the source, and the probability density function (pdf) of its signal-to-noise ratio (SNR) can be equivalently modeled as a summation of the pdfs of the SNRs among the source and $(l-1)$ relays. Based on this, the ASERs are then analyzed as approximated bounds, which are verified by comparison with simulation results. The derived ASER expressions show that the diversity order of multi-hop AF relay systems with $L$ relays is $(L+1)$ , which is identical to that of dual-hop systems.

Performance analysis of AF relaying based on water-filling power allocation over Nakagami-m fading

This paper investigates exact performance of an amplify-and-forward (AF) relay system based on water-filling power allocation in Nakagami-m fading environment, where m is a nonnegative integer plus one half. We first offer the cumulative distribution function (CDF) and probability density function (PDF) of the received signal-to-noise ratio (SNR) at a destination. Then outage probability, moments of SNR, higher-order statistics of the capacity are explicitly conducted. Especially, average symbol error rate (SER) under an additive white generalized Gaussian noise (AWGGN) is developed for water-filling power allocation scheme. While the average SER subjected by an additive white Gaussian noise (AWGN) can be regarded as a special case. Finally, all theoretical formulas are truly attested by various simulation results.

Performance Analysis of Space Information Networks with Backbone Satellite Relaying for Vehicular Networks

Space Information Network (SIN) with backbone satellites relaying for vehicular network (VN) communications is regarded as an effective strategy to provide diverse vehicular services in a seamless, efficient, and cost-effective manner in rural areas and highways. In this paper, we investigate the performance of SIN return channel cooperative communications via an amplify-and-forward (AF) backbone satellite relaying for VN communications, where we assume that both of the source-destination and relay-destination links undergo Shadowed-Rician fading and the source-relay link follows Rician fading, respectively. In this SIN-assisted VN communication scenario, we first obtain the approximate statistical distributions of the equivalent end-to-end signal-to-noise ratio (SNR) of the system. Then, we derive the closed-form expressions to efficiently evaluate the average symbol error rate (ASER) of the system. Furthermore, the ASER expressions are taking into account the effect of satellite perturbation of the backbone relaying satellite, which reveal the accumulated error of the antenna pointing error. Finally, simulation results are provided to verify the accuracy of our theoretical analysis and show the impact of various parameters on the system performance.

Combined Constellation Rotation With Weighted FRFT for Secure Transmission in Polarization Modulation Based Dual-Polarized Satellite Communications

In this paper, a novel transmission scheme based on constellation rotation and weighted fractional Fourier transform (WFRFT) is proposed to enhance the physical-layer security in polarization modulation (PM)-based dual-polarized satellite communications. Typically, by appropriately selecting the WFRFT order, the distribution of the signals processed by WFRFT can be close to Gaussian, which makes them difficult to be detected by eavesdroppers. However, once the signals are captured, it is possible for eavesdroppers to recover the information through the WFRFT order scanning method. To overcome this problem, in the proposed scheme, the constellation points are randomly rotated before the WFRFT operation, making it almost impossible to crack the WFRFT order. In this manner, the constellations are distorted, which is difficult for the eavesdropper to demodulate the signals accurately. Furthermore, a robust nonzero secrecy capacity is guaranteed. In addition, the impairment to the PM from the polarization-dependent loss effect is discussed, and a zero-forcing prefilter is applied at the receiver side to mitigate this adverse effect. Finally, the security performance of the proposed scheme is evaluated in terms of the average secrecy capacity and symbol error rate by numerical simulations in dual-polarized satellite communications.

Analysis of Uplink ICI and IBI in Heterogeneous Cellular Networks With Multiple Macrocells

This letter analyzes the effects of inter-carrier interference (ICI) and inter-block interference (IBI) on uplink reception of small cells (SCs) in orthogonal frequency division multiple access heterogeneous cellular networks. Tight upper and lower bounds of the power of ICI and IBI plus co-channel interference from nearby SCs, average rate, and symbol error rate (SER) per SC subcarrier are derived. Results show that the theoretical analysis is close to simulation. Importantly, the average rate and SER are seriously degraded by the interference at high signal-to-noise ratio.

Beamforming for Dual-Hop MIMO AF Relay Networks With Channel Estimation Error and Feedback Delay

This paper concerns the beamforming (BF) design for a dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay network. Both a general antenna configuration and imperfect channel state information are taking into consideration, where multiple antennas are deployed at the source, relay, and destination, channel impairments exist at the source-relay and relay-destination hops. The BF scheme is optimized to maximize the received signal-to-noise ratio (SNR). In order to evaluate the performance of the relay network, asymptotic average symbol error rate (ASER) at high SNR is derived. Computer simulations are conducted to show the superiority of the designed BF scheme and the impacts of channel impairments and antenna configurations on the performance of the MIMO AF relay systems. It is shown that the diversity order of the relay network can be reduced to one due to the channel impairments.

Relayed FSO communication with aperture averaging receivers and misalignment errors

In this paper, the performance of decode-and-forward relay-assisted free-space-optical (FSO) communication systems under atmospheric turbulence induced fading and misalignment errors is investigated. To mitigate the adverse effects of the atmospheric turbulence, the aperture averaging receivers are considered both at the relay and destination sides. The atmospheric turbulence induced fading is modeled via the exponentiated-Weibull distribution, which has recently been proposed to characterize an FSO link in the presence of finite-sized receiver aperture. The expression for the moment generating function (MGF) of the instantaneous signal-to-noise ratio is derived. Further, new closed form expression for the outage probability is obtained. Moreover, the new expression for the average symbol error rate of the subcarrier intensity modulated M-ary phase shift keying is obtained using the MGF-based approach. Finally, numerical examples are discussed and all the derived analytical results are corroborated by Monte-Carlo simulations. Relayed FSO Communication with Aperture Averaging Receivers and Misalignment Errors. Available from: https://www.researchgate.net/publication/307931308_Relayed_FSO_Communication_with_Aperture_Averaging_Receivers_and_Misalignment_Errors [accessed Nov 10, 2016].