Asymptotic Average Symbol Error Rate Research Articles

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.

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.

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.

QAM signaling over [formula omitted] shadowed fading channels

In this study, average symbol error rate (ASER) expressions for rectangular quadrature amplitude modulation (RQAM) and cross quadrature amplitude modulation (XQAM) over κ−μ shadowed fading are proposed by considering two different system models. In the first system model, a single-input–single-output (SISO) scheme is considered while a multiple-input–multiple-output (MIMO) with single transmit antenna selection and maximal ratio combining (TAS/MRC) is investigated as a second system model. First, the exact, approximate and asymptotic ASER expressions of RQAM and XQAM for a SISO system model are proposed based on probability density function (PDF) of instantaneous signal-to-noise ratio (SNR). Second, ASER expressions of RQAM and XQAM schemes for a MIMO system with TAS/MRC are obtained by using the PDF of instantaneous SNR at the receiver side. Then, ASER performances of RQAM and XQAM for the considered two system models are compared in the presence of different fading configurations. Finally, our numerical results illustrate that the analytical ASER expressions proposed in this study are well agreement with their simulations.

Average Symbol Error Rate Analysis of QAM Schemes Over Millimeter Wave Fluctuating Two-Ray Fading Channels

In this study, analytical expressions are derived by using probability density function approach over millimeter wave fluctuating two-ray (FTR) fading channels for average symbol error rate (ASER) of rectangular quadrature amplitude modulation (RQAM) and cross quadrature amplitude modulation (XQAM) schemes. First, an exact ASER expression for RQAM over millimeter wave FTR fading channels is derived. Second, two different upper bound ASER expressions of RQAM scheme under millimeter wave FTR fading conditions are obtained by using Chernoff and Chiani approximations of Gaussian Q-function. In addition to this, an asymptotic ASER expression for RQAM is also proposed. Then, an analytical formulation is presented for XQAM signaling over millimeter wave FTR fading channels in terms of infinite series representations which rapidly converge. Finally, the numerical results of the proposed analytical expressions are compared with the simulation results in order to validate the analytical findings in this work.

Performance assessment of correlated Rayleigh‐inverse Gaussian fading channel over distributed MIMO systems with ZF detectors

Composite fading channel modelling of terrestrial wireless propagation is crucial for the design of communication system and its performance analysis. In this study, a systematic characterisation of Rayleigh-inverse Gaussian (RIG) distribution is provided for modelling the channel of distributed multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receiver in the presence of transmit antenna correlation. At the outset, the closed-form expression for probability density function of instantaneous signal-to-noise ratio (SNR) is derived followed by its associated moments and cumulative density function. In the subsequent analysis, exact closed-form analytical expression of ergodic capacity with its bounds are derived and their asymptotic expressions are obtained in high and low SNR regime. Then the closed-form expressions are deduced for average symbol error rate (ASER) and outage probability (OP). Additionally, the authors propose to formulate simplified expressions for asymptotic ASER as well as OP and assess their approximation accuracy. Numerical results are presented to compare the performance of RIG model with the existing generic models and illustrate that RIG is superior in terms of ergodic capacity, ASER and OP. Finally, the derived analytical expressions are validated through Monte Carlo simulations which demonstrate the effectiveness of RIG model in the diverse environmental scenario for various system and channel parameters.

ASER Analysis of Hexagonal and Rectangular QAM Schemes in Multiple-Relay Networks

In this paper, analytical lower bound expressions of average symbol error rate (ASER) for general-order hexagonal quadrature amplitude modulation (QAM) and rectangular QAM (RQAM) schemes are derived for multiple amplify-and-forward relay networks over independent and nonidentically distributed Nakagami-m fading channels with an integer-valued fading parameter using a well-known cumulative distribution-function-based approach. Furthermore, ASER expressions for 32-cross QAM, differentially encoded quadriphase shift keying (QPSK), and π/4-QPSK modulation schemes are derived for the considered systems. The asymptotic ASER expression is also derived for the RQAM scheme, which is useful to examine system's diversity order. Numerically evaluated results are verified by Monte Carlo simulation.

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.

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.

A novel user pairing scheme for functional decode-and-forward multi-way relay network

In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain. This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M-ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.

Performance of a Free-Space-Optical Relay-Assisted Hybrid RF/FSO System in Generalized <inline-formula> <tex-math notation="LaTeX">$M$</tex-math> </inline-formula>-Distributed Channels

This paper investigates the average symbol error rate (ASER) performance of a dual-hop hybrid relaying system relying on both radio frequency (RF) and free space optical (FSO) links. Specifically, the RF link is used for supporting mobile communication, while the FSO link is adopted as the backhaul of the cellular infrastructure. Considering non-line-of-sight (NLoS) RF transmissions and a generalized atmospheric turbulence (AT) channel, the associated statistical features constituted of both the exact and the asymptotic moment generating functions (MGF) are derived in closed form. They are then used for calculating the ASER of M-ary phase shift keying (PSK), differentially encoded non-coherent PSK (DPSK) and non-coherent frequency-shift keying (FSK). A range of additional asymptotic expressions are also derived for all the modulation schemes under high signal-to-noise ratios (SNR). It is observed from the asymptotic analysis that the ASERs of all the modulation schemes are dominated by the average SNR of the RF link in the hybrid relaying system using a fixed relay gain, while in the relaying system using a dynamic channel dependent relay gain, the ASERs of all the modulation schemes depend both on the average SNR and on the AT condition of the FSO path. We also find that the fixed-gain relaying strategy achieves twice the diversity order of the channel-dependent relaying strategy albeit at the cost of requiring a high power amplifier (PA) dynamic range at the relay node. Furthermore, by comparing the asymptotic ASERs, we calculate the SNR differences between the different modulation schemes in both the fixed-gain and the channel-dependent relaying system. Finally, simulation results are presented for confirming the accuracy of our expressions and observations.

Symbol Error Analysis of Hybrid Satellite–Terrestrial Cooperative Networks With Cochannel Interference

This letter investigates the effect of cochannel interference (CCI) on a hybrid satellite-terrestrial cooperative relay network (HSTCN), where both the satellite-destination and satellite-relay links undergo the shadowed Rician fading, whereas the relay-destination link follows the Rayleigh fading. By assuming that decode-and-forward (DF) protocol is adopted at the terrestrial relay, and the destination is corrupted by multiple CCI, we first derive the analytical expression for the moment generating function (MGF) of the output signal-to-interference-plus-noise ratio (SINR). Then, based on the Meijer-G functions, we present an approximated yet accurate method to evaluate the average symbol error rate (ASER) of the cooperative network. Moreover, the asymptotic ASER at high signal-to-noise ratio (SNR) with respect to diversity order and array gain are also given to gain further insights. Finally, numerical results are provided to demonstrate the validity of the performance analysis as well as the impact of CCI on the HSTCN.

Joint Relay and Antenna Selection for Dual-Hop Amplify-and-Forward MIMO Relay Networks

Four joint relay and antenna selection strategies for dual-hop amplify-and-forward (AF) multiple-input multiple-output relay networks are studied. Two of them require full channel state information (CSI) whereas the other two require only partial CSI. The relays are either channel-assisted AF or fixed-gain AF type. The first joint selection strategy involves choosing the best relay and the best single transmit antennas at the source and the relay. The second strategy jointly involves choosing the best relay and the best single transmit/receive antenna pairs at the source-to-relay and relay-to-destination channels. Moreover, two partial selection strategies, which can be used when the global CSI is not available, are also proposed and analyzed. In order to quantify the system performance analytically, the exact outage probability of all selection strategies is derived in closed-form. Direct insights into the system-design are obtained by deriving the asymptotic outage probability, asymptotic average symbol error rate, diversity order and array gain.

Performance Analysis of Adaptive Decode-and-Forward Cooperative Single-Carrier Systems

A cyclic prefixed single-carrier (CP-SC) relay network incorporating an adaptive decode-and-forward (ADF) protocol is proposed in this paper. For a two-hop ADF protocol, a general expression for the effective end-to-end signal-to-noise ratio (ESNR) is examined for multiple relays. With the help of a derived probability density function (pdf) for the ESNR, closed-form expressions for the outage probability and an asymptotic average symbol error rate (AASER) are obtained. An asymptotic analysis revealing the diversity gain is also performed. Monte Carlo simulations verify these derived analytical results.