Average Symbol Error Rate Performance Research Articles

Performance Analysis of NOMA-Based Hybrid Satellite-Terrestrial Relay Networks With CCI

Hybrid satellite-terrestrial relay networks (HSTRNs) which exploit relay cooperative technology in the integrated system of satellites and terrestrial base stations (BSs) are expected to offer enhanced transmission performance benefited from the spatial gain of independent fading paths. To enable multi-user accessing and resource sharing among users, non-orthogonal multiple access (NOMA) technique can be applied in HSTRNs. In this paper, we consider a NOMA-based HSTRN where a satellite transmits signals to a relay base station (RBS) and a destination ground station (DGS), and RBS also serves a cellular user (CU) and DGS simultaneously by leveraging NOMA scheme. We assume that the satellite shares spectrum with a number of cellular small BSs (SBSs), hence SBSs will cause co-channel interference (CCI) to DGS, RBS and CU. We examine the transmission characteristics of the satellite and terrestrial links, and derive the closed-form expressions of the outage probability (OP) and average symbol error rate (ASER) of DGS and CU, respectively. Specially, we consider the effect of perfect and imperfect successive interference cancellation (SIC) on the ASER performance of CU. Then, considering the stochastic characteristics of satellite links and CCI, we analyze the mean energy efficiency (MEE) of the satellite and propose an optimal power allocation scheme which maximizes the MEE of the satellite and achieves system performance optimization. Simulation results demonstrate the effectiveness of the theoretical analysis and the proposed power allocation scheme.

Performance analysis of multihop wireless systems with decode and forward relays over Fisher– Snedecor F fading channels

ABSTRACT By reducing the transmitting power at the base station and expanding the coverage range of wireless communication, cooperative communication has turned into a higher imperative. This article evaluates the outage probability, average symbol error rate (ASER) for coherent as well as noncoherent modulation pattern, ergodic capacity and throughput of a multihop communication technique over the Fisher–Snedecor F fading channels. The multihop transmission scheme utilises a source, a set of relays and the destination node. The intervening relays of the system are regenerative with decode and forward type. Each hop of the system undergoes Fisher–Snedecor F fading channels. The MGF-based approach is used to derive the ASER of the system. The outage probability and ASER performance upgrade with the advancement of fading parameter as well as shadowing parameter of the channel. The ergodic capacity decreases with the improvement in shadowing parameter and the number of hops. The throughput of the system rises in connection with the reduction of total hops. Simulations validate the correctness of the numerically appraised results.

On the ASER performance of RF energy harvesting multiple relay networks

We present the average symbol error rate (ASER) of quadrature amplitude modulation (QAM) for radio frequency energy harvesting assisted dual-hop multiple amplify-and-forward (AF) relay network. In this relaying network, partial relay selection scheme is employed to select best relay among multiple relays, while selection combining is considered at destination to combine the signals coming from the direct path and the relaying path. In particular, we derive the exact ASER expressions of rectangular QAM (RQAM), hexagonal QAM and cross QAM schemes for the considered systems over independent and non-identically distributed Nakagami-m fading channels using cumulative distribution function method. Moreover, the asymptotic ASER expression of RQAM is determined to examine the system’s diversity order. Further, to verify the correctness of derived expressions, numerically evaluated results are compared with Monte Carlo simulations. Furthermore, the effects of fading parameter, number of relay, time switching ratio, and large scale fading are studied on the ASER performance.

Performance analysis of space time coded generalized frequency division multiplexing system over generalized fading channels

AbstractDue to its low out‐of‐band emission and high spectral efficiency, the generalized frequency division multiplexing (GFDM) has been adopted as one of the most prominent waveform techniques for the 5G networks. To further combat the deep fading, the space time coding (STC) can be integrated with the GFDM system which provide high diversity gain that results into low symbol error rate at the receiver. In this article, a generalized model of space time coded GFDM system (STC‐GFDM) has been proposed. More precisely, a comprehensive analytical framework to compute the average symbol error rate (ASER) is introduced, which can be used for any MIMO configuration, code rate, and arbitrary fading channel. The proposed framework has wider applicability over generalized fading channels and having more accurate exact solution along with easy to evaluate approximate solution. Thus, the proposed framework extends the horizon of performance analysis of STC‐GFDM system over any fading scenario, that is not covered so far in the literature. In general, the closed from expressions of exact and approximate along with asymptotic ASER are derived for different fading channels using moment generating function (MGF) approach. Particularly, the ASER analysis has been performed analytically using derived expression over Rayleigh, TWDP, Nakagami‐q, and Nakagami‐m fading channels for ‐ary quadrature amplitude modulation (‐QAM). This analysis confirms that with the increase in transmit and receive antenna and decrease in modulation order, the ASER performance improves for all fading channels. Also, the improvement in ASER is observed as the power of specular components (ie, LOS paths) increases. Furthermore, these analytical results are validated using Monte‐Carlo simulation.

On the ASER performance of SC receiver with RQAM and HQAM over [formula omitted]-[formula omitted] fading

In this paper, we consider a multi-branch selection combining receiver over independent and non-identically distributed κ-μ fading channels. We derive new exact expressions for moment generating function of output signal-to-noise-ratio (SNR), average symbol error rate (ASER) of coherent rectangular and hexagonal quadrature amplitude modulations, and ASER of non-coherent frequency shift-keying modulation schemes. Further, an asymptotic ASER expression is also derived to determine the diversity order of the system. The analytical results are validated using Monte-Carlo simulations for a wide range of SNRs and fading parameters. Finally, the impact of channel parameters and the number of branches on the ASER performance is also studied.

On the ASER Performance of UAV-Based Communication Systems for QAM Schemes

In this letter, we derive an average symbol error rate (ASER) expression of rectangular quadrature amplitude modulation (RQAM) scheme for unmanned aerial vehicle-enabled communication systems operating over double-shadowing and double-scattering composite fading channel. A moment generating function for the receiver output signal-to-noise ratio is obtained to analyze the ASER expression of non-coherent modulation schemes. An asymptotic expression of ASER for RQAM scheme is also derived to examine diversity order of the considered system. Further, the impact of composite fading parameters and path loss on ASER performance is highlighted. Finally, we validate all the theoretical results through Monte Carlo simulations.

Approximate ASER analysis of MIMO TAS/MRC networks over Weibull fading channels

In this paper, the average symbol error rate (ASER) evaluation of multiple-input-multiple-output (MIMO) systems with transmit antenna selection (TAS) and maximal ratio combining (MRC) are analysed under Weibull fading conditions. The impact of additive white Gaussian noise (AWGN) and additive white generalized Gaussian noise (AWGGN) on the ASER evaluation of the MIMO TAS/MRC networks are considered. Closed form approximate and asymptotic ASER expressions of the considered network with AWGN for different quadrature amplitude modulation techniques are derived based on the probability density function approach. The closed-form approximate and asymptotic ASER expressions for the AWGGN case are also obtained. In addition, a comprehensive analysis of the ASER performance for the MIMO TAS/MRC networks is demonstrated by varying the fading parameter values, numbers of transmitter-receiver antennas and constellation size. Finally, the obtained theoretical results are confirmed through the exact simulation results.

Different QAM schemes analyses for ARS fading channels

AbstractQuadrature amplitude modulation (QAM) techniques are employed for various communication systems due to its advantages such as efficient bandwidth and high rate. In this paper, the average symbol error rate (ASER) performances of single‐input single‐output networks are investigated to address the different QAM schemes combined use. The link in the network experiences the alternate Rician shadowed (ARS) fading which has the benefit of contributing left or right‐sided bimodality. Four different QAM schemes such as rectangular QAM, cross‐QAM, hexagonal QAM, and square QAM are used for the considered network. Under these assumptions, new closed‐form expressions for the ASER in terms of elementary functions and Meijer's G functions are derived. The derived ASER expressions are obtained by employing the Prony approximation with two terms which has fractional coefficients to provide precise results. Based on the second‐order exponential function approximation for Gaussian Q‐function, the ASER expressions of the considered system are also proposed. Additionally, we provide other important engineering insights based on the high signal‐to‐noise‐ratio analysis of the ASER performance over ARS fading channels. Finally, all our theoretical results are confirmed with simulations.

On ASER performance of higher order QAM schemes in two‐way multiple‐relay networks under imperfect CSI

In this study, the authors present an analytical approach to evaluate the performance of a two-way multi-relay system with direct link using a three-phase analogue network coding and opportunistic relay selection scheme. Herein, the imperfect channel state information is considered over independent and non-identically distributed Nakagami-m fading channels with integer-valued fading parameter. For analysis, initially, the closed-form expressions of cumulative distribution function and moment generating function (MGF) for the considered system are derived. Further, by using the MGF-based approach, generalised expressions of average symbol error rate (ASER) for higher-order quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived. They then analyse the asymptotic behaviour of ASER expression to evaluate the system's diversity order. Furthermore, a comparative analysis of the ASER performance for various QAM constellations is illustrated and impact of the number of relays, fading parameter, relay location, and channel estimation error are highlighted on the system's performance. Finally, all the analytical results are validated through Monte-Carlo simulations.

On the ASER performance of amplify-and-forward relaying MIMO/FSO systems using SC-QAM signals over log-normal and gamma-gamma atmospheric turbulence channels and pointing error impairments

ABSTRACT In this work, we analyse pointing error effects on the performance of amplify-and-forward (AF) relaying multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing sub-carrier quadrature amplitude modulation (SC-QAM) signal over log-normal and gamma-gamma distributed atmospheric turbulence channels. We study the pointing error effects by taking into account the influence of beam-width, aperture size and jitter variance on the average symbol error rate (ASER), which is derived in closed-form expressions of MIMO/FSO and SISO/FSO systems. In addition, the number of relaying stations is taken into account in the statistical model of the combined channel including atmospheric loss, atmospheric turbulence and pointing error impairments. The numerical results show that by combining AF relaying stations and MIMO/FSO configurations, the link length can be extended because the transmitted power is reduced according to the amplifier gain. Moreover, the performance of AF relaying MIMO/FSO systems is better than that of AF relaying SISO/FSO systems at the same link length.

Error performance of digital modulations over Fisher-Snedecor F fading channels

In this paper, symbol error probability (SEP) and the average symbol error rate (ASER) of digital modulation schemes are derived in the presence of Fisher-Snedecor F fading. First, an analytical SEP expression is proposed based on complementary cumulative distribution function (CDF) for M-ary phase shift keying (M-PSK) and M-ary pulse amplitude modulation (M-PAM). Then, an asymptotic solution is also presented for the SEP of M-PSK and M-PAM modulations in order to get more insights on the performance at high signal-to-noise ratio (SNR) regime. Finally, an exact ASER expression for rectangular quadrature amplitude modulation (RQAM) is derived and then, the ASER performance is analyzed based on two different upper bound approximations of Gaussian Q-function in Fisher-Snedecor F fading channels. The proposed expressions are not only valid for integer values of fading and shadowing parameters but also valid for non-integer values. The performance results which are in good agreement with the exact simulations are illustrated for different modulation schemes and various configurations of fading and shadowing parameters.

An Approximate Error Expression for RQAM Scheme under α-η-µ Fading Conditions

In this paper, average symbol error rate (ASER) performance of rectangular quadrature amplitude modulation (RQAM) scheme is analyzed over α-η-µ fading channels. First, an ASER expression is derived based on Chernoff approximation of Gaussian Q-function. Then, an asymptotic ASER formula is obtained for analyzing system behavior at high signal-to-noise ratio (SNR) regime. The ASER performance is presented for different modulation levels and fading parameter values. In addition, relative truncation error (RTE) is illustrated in order to determine how many terms are needed for the computation of proposed expression. It is shown that analytical results are in close agreement with exact results.

Impact of Fast Fading CCI on Performance of Optimum Combining in DF Relaying

We present the effect of fast fading co-channel interference (CCI) on the performance of decode-and-forward (DF) relaying. This paper derives closed-form expressions for the average symbol error rate (SER) with optimum combining (OC) in the presence of fast fading CCI. It is shown that the average SER performance of fast fading CCI is worse than that of slow fading CCI, which is the previous research assumption. In result, DF relaying systems should be designed with consideration of fast fading CCI.

Symbol Error Rate Minimization Precoding for Interference Exploitation

This paper investigates a new beamforming approach for interference exploitation, which has recently attracted interest as an alternative to conventional interference-avoidance beamforming for the downlink of multiple-input multiple-output systems. Contrary to existing interference exploitation approaches that focus on signal-to-noise ratio performance, we adopt an approach based on the detection region of the signal constellation. Focusing on quality of service, we then formulate the optimization for minimizing the error probability (EP) for the worst user, subject to power constraints. We do this by employing the knowledge of channel state information at the transmitter, along with all downlink users’ data that are readily available at the base station during downlink transmission. In this context, we also show that the detection-region-based beamforming and the worst user EP downlink beamforming are equivalent problems. Finally, we further propose a sum EPs approach and provide an analytic bound of average symbol error rate performance. Our simulations verify that the proposed techniques provide significantly improved performance over conventional downlink beamforming techniques.

Impact of Imperfect CSI on ASER of Hexagonal and Rectangular QAM for AF Relaying Network

In this letter, we derive the closed-form expression of outage probability for a dual-hop variable-gain amplify-and-forward relay network. The maximal ratio combining receiver over independent and non-identically distributed frequency flat Nakagami-m fading channels with integer-valued fading parameter and imperfect channel state information (CSI) is considered. Asymptotic analysis on outage probability is also performed. Average symbol error rate (ASER) expressions are derived for general-order hexagonal and rectangular QAM schemes using the cumulative distribution function-based approach. The impact of the fading parameter and imperfect CSI are highlighted on the system performance. Comparative analysis of ASER performance for different QAM constellations is also illustrated. Monte Carlo simulations are performed to validate the derived analytical results for both perfect and imperfect CSI.

Performance analysis of QAM in amplify-and-forward cooperative communication networks over Rayleigh fading channels

Performance analysis of quadrature amplitude modulation (QAM) schemes for cooperative amplify-and-forward (AF) dual-hop relaying system over independent and identically distributed (i.i.d.) Rayleigh fading channels are presented in this paper. Specifically, we derive closed-form lower-bound expressions of average symbol error rate (ASER) for general order rectangular QAM (RQAM) and cross QAM (XQAM) using well-known moment generating function (MGF) based approach with maximal ratio combining (MRC) scheme. Further, using best relay selection scheme (BRS), we also derive an ASER expression for XQAM. Numerical and simulated results are compared to validate the correctness of derived expressions. Furthermore, comparative analysis of RQAM and XQAM schemes is discussed which confirms that XQAM is better alternative over RQAM for transmission of odd number of bits per symbol for the considered system model. We also compare the ASER performance for MRC and BRS schemes in terms of SNR gain using different XQAM constellations. Moreover, the impact of system parameters on ASER is also highlighted.

Average SER Performance of Distributed Antenna Systems Over Shadowed Generalized-Gamma Channels for Different Modulation Schemes

Recently, much attention has been drawn to distributed antenna systems (DAS), which are proposed to improve the performance of mobile communication systems. This paper focuses on the analysis of the average symbol error rate (SER) of DAS over a generic composite channel. Initially, a new composite channel model is considered for DAS, which is a mixture of path loss, lognormal shadowing and generalized-Gamma fast fading. This composite channel model is a generic model, which includes many well-known composite channel models as special cases. Based on the channel model, the cumulative distribution function of the output signal-to-noise ratio is obtained by employing selective transmission scheme. Moreover, by averaging the channel conditions and the positions of the MS in the cell, an approximate expression of the average SER is derived, which is a unified form of expression for many commonly used modulation schemes. Numerical results show that the derived expression of the average SER can provide sufficient precision for evaluating the SER performance of DAS under different modulation schemes.

Invertible Exponential-Type Approximations for the Gaussian Probability Integral Q(x) with Applications

In this article, we present very tight exponential-type approximations for the Gaussian probability integral Q(.) and/or the complementary error function erfc(.) which are subsequently used to devise the conditional symbol error probability (CEP) formulas for several classes of digital modulation schemes that are both invertible and in a desirable exponential form. These invertible CEP formulas are of interest in the optimization of discrete-rate adaptive modulation designs and for computation of the symbol/bit error outage performance metric. Our framework also facilitates the derivation of simple and tight closed-form approximation formulas for the average symbol error rate performance metric for a wide range of digital modulation schemes over generalized fading channels via the moment generating function approach. The accuracies of our new closed-form approximations have been validated with that of the exact expressions in an integral form.

Performance of L-Branch MRC Receiver in η-μ and κ-μ Fading Channels for QAM Signals

Error performance of a L-branch maximal ratio combining (MRC) receiver in η-μ and κ-μ fading channels is analyzed. A simple and highly accurate approximation to the average symbol error rate (ASER) expression of quadrature amplitude modulation (QAM) scheme is derived. Steps to extend the approach to analyze ASER performance of coherent, differentially encoded quadri-phase shift-keying (DE-QPSK) and π/4-QPSK schemes are also stated. Numerically evaluated results are plotted and compared with Monte Carlo simulation to verify the accuracy of the derivation.

Performance of Beamforming in Correlated MISO Systems with Estimation Error and Feedback Delay

This paper analyzes the exact average symbol error rate (SER), outage probability and ergodic capacity performance of beamforming in spatially correlated multiple-input single output systems with channel estimation error and feedback delay. We derive the joint distribution function of two correlated quadratic forms and employ the result to obtain expressions for the cumulative distribution function, probability density function, moment generating function and moments of the signal-to-noise ratio. Using these expressions, we investigate the exact SER applicable for a large number of modulation schemes, outage probability and the ergodic capacity of the system. The results show that the average SER performance is sensitive to both feedback delay, channel estimation and spatial correlation at the transmitter. Furthermore, feedback delay causes an error floor and has the most degrading impact on performance. We also present Monte Carlo simulation results as verification of our analytical results.