Average Symbol Error Rate Research Articles

Error Rate Analysis of <inline-formula> <tex-math notation="LaTeX">$M$</tex-math></inline-formula>-ary Phase Shift Keying in <inline-formula> <tex-math notation="LaTeX">$\alpha{-}\eta{-} \mu$</tex-math></inline-formula> Fading Channels Subject to Additive Laplacian Noise

This letter considers the average symbol error rate (SER) of $M$ -ary phase shift keying ( $M$ -PSK) over the $\alpha{-}\eta{-} \mu$ fading channels subject to additive Laplacian noise. Specifically, novel unified closed-form expressions for the average SER are derived and evaluated. The derived expressions include other well-known general fading channels such as $\eta{-}\mu, \alpha{-} \mu$ , and their inclusive ones as special cases. Numerical results are presented to study the influence of the fading parameters on the average SER. In addition, simulation results are provided to prove the correctness of the analytical results.

Efficient Full-Duplex Relaying With Joint Antenna-Relay Selection and Self-Interference Suppression

In this paper, we propose a joint relay and transmit/ receive (Tx/Rx) antenna mode selection scheme (RAMS) in the general full-duplex (FD) relay networks consisting of one source, one destination, and N FD amplify-and-forward (AF) relays. Each FD relay is equipped with two antennas, one for receiving and the other for transmitting. In the proposed scheme, each antenna of the FD relay is able to transmit/receive the signal. Each relay adaptively selects its Tx antenna and Rx antenna based on the instantaneous channel conditions, and the optimal single relay with the optimal Tx/Rx antenna configuration is selected to maximize the end-to-end signal to interference and noise ratio (SINR) of the FD relay system. The performance of the proposed scheme is analyzed. The closed-form expressions of the outage probability, average symbol error rate, and the ergodic capacity are derived. The analytical results are verified by the simulations. To reduce the error floor and capacity ceiling caused by the self-loop interference in FD relay, we propose a RAMS scheme with adaptive power allocation (RAMS-PA). We provide an upper bound and a lower bound of the end-to-end SINR for RAMS-PA scheme, and prove that the error floor can be removed in the RAMS-PA scheme. Results show that the proposed scheme achieves an extra spatial diversity in the medium SNR region due to the FD antenna selection at the relay nodes and considerably improve the system performance compared to the conventional FD relay selection scheme with fixed relay Tx and Rx antennas.

Diversity Performance Analysis on Multiple HAP Networks.

One of the main design challenges in wireless sensor networks (WSNs) is achieving a high-data-rate transmission for individual sensor devices. The high altitude platform (HAP) is an important communication relay platform for WSNs and next-generation wireless networks. Multiple-input multiple-output (MIMO) techniques provide the diversity and multiplexing gain, which can improve the network performance effectively. In this paper, a virtual MIMO (V-MIMO) model is proposed by networking multiple HAPs with the concept of multiple assets in view (MAV). In a shadowed Rician fading channel, the diversity performance is investigated. The probability density function (PDF) and cumulative distribution function (CDF) of the received signal-to-noise ratio (SNR) are derived. In addition, the average symbol error rate (ASER) with BPSK and QPSK is given for the V-MIMO model. The system capacity is studied for both perfect channel state information (CSI) and unknown CSI individually. The ergodic capacity with various SNR and Rician factors for different network configurations is also analyzed. The simulation results validate the effectiveness of the performance analysis. It is shown that the performance of the HAPs network in WSNs can be significantly improved by utilizing the MAV to achieve overlapping coverage, with the help of the V-MIMO techniques.

Performance analysis of opportunistic relaying and opportunistic hybrid incremental relaying over fading channels

In this study, the authors develop and present a comprehensive analysis of two opportunistic cooperative relaying schemes for long term evolution (LTE)-advanced networks operating over generalised-K and Nakagami-m fading channels. They present and compare the performance of opportunistic relaying (OR) and opportunistic hybrid automatic repeat request incremental relaying (OHIR). They analyse performance in terms of the average symbol error rate for both conventional OR and OHIR LTE-advanced networks with the radio channel modelled as composite generalised-K fading (encompassing both fading and shadowing) and Nakagami-m fading channels. They also analyse the outage probability for OR operating over these channels. Both the theoretical analysis and simulations confirm that for conventional OR LTE-advanced networks operating over composite generalised-K fading channels, a diversity order of k(N + 1) is achieved when shadowing is more severe than fading, and a diversity order of m(N + 1) is achieved when fading is more severe than shadowing (where k and m represent the generalised-K distribution shape parameters and N represents the number of candidate relays for the OR selection). The simulation results confirm the accuracy of the analytical expressions developed in this study. It is evident from the theoretical analysis and simulations that, for a similar quality of service as that for OR, OHIR not only reduces the amount of required radio resources but also maintains the full diversity order.

Improving the Performance of Wireless Sensor Networks Through Optimized Complex Field Network Coding

Signal transmission and information fusion in wireless sensor networks (WSNs) are conventionally assumed to operate over orthogonal channels, which makes the network bandwidth and throughput inefficient. To remedy this inefficiency and improve the performance of the WSNs, we consider complex field network-coded (CFNC) relay-assisted communications, which operates over nonorthogonal channels and provides both spatial and temporal diversity. We derive the optimal likelihood ratio test-based fusion rule for the considered system. To provide robustness against the multiaccess interference, each sensor in the CFNC-coded system is assigned to a unique predetermined signature. Hence, the signature selection and the relay power allocation become crucial factors affecting the performance of the WSNs. We also develop an analytical method to jointly adjust the sensor signatures and the relay power utilizing the average symbol error rate bound of the network together with some information theoretical results. Finally, we evaluate the detection performance of the proposed scheme and compare it with that of the conventional method. The simulation results suggest that the proposed signature selection and relay power allocation method in the CFNC-coded relay-assisted WSNs considerably improves the network performance.

Performance analysis of semi-blind two-way AF relaying over generalized-k fading channels

In this paper, we present analytical expressions for the outage probability, average symbol error rate (SER), and average sum-rate of two-way dual-hop opportunistic amplify-and-forward (AF) relaying over independent and not necessarily identical generalized-k (KG) fading channels. New closed-form expression for the gain of non-regenerative semi-blind relays is derived. This expression is used to obtain the equivalent signal-to-noise ratio (SNR). Based on the above mentioned formulas, tight bounds of some performance metrics, the outage probability, average SER, and average sum-rate, are derived for the semi-blind and channel state information (CSI) relaying. In order to prove the exactness of the proposed mathematical analysis, a selection of numerical results is provided.

Linear precoding for spatially correlated multiple‐input single‐output wiretap channel

A precoding scheme for physical layer security of multiple-input single-output (MISO) wiretap channel with spatial correlation is designed. Quality-of-service (QoS) of the link is defined in terms of upper bounds on average symbol error rate function at Bob (legitimate user) and Eve (illegitimate user). Specifically, two problems are considered. First, a precoder matrix is designed to minimise the average transmitted power subject to QoS requirements at Bob and Eve. Next, we propose two algorithms to minimize QoS of illegitimate party for a given reliability level, depending on whether main user link has no correlation or is fully correlated. Our result for uncorrelated case demonstrate that by increasing the allocated power, main user can increase secrecy level up to an optimum point above which both legitimate and illegitimate receivers experience adequate QoS in their links. In fully correlated case, the problem is identified as an instance of concave minimisation over a polytope, and optimum power allocation is obtained via the widely known vertex enumeration algorithm. In both cases, our simulations validate the analysis significantly. The results confirm that linear precoding is able to trade average power against minimum achievable Eve performance.

Exact MGF-Based Performance Analysis of Dual-Hop AF-Relayed Optical Wireless Communication Systems

In this paper, we analyze the subcarrier intensity modulation-based-relayed optical wireless communication system in the presence of various channel impairments such as turbulence, path loss and pointing errors. The relay follows an amplify and forward relaying protocol and the optical links are modeled assuming independent but not necessarily identically distributed (i.n.i.d) gamma-gamma fading statistics. We derive the novel analytical expressions for the moment generating function and cumulative distribution function of the equivalent end-to-end signal to noise ratio (SNR) at the destination and utilize these results to obtain the exact analytical expressions for outage probability and average symbol error rate for M-ary phase shift keying and M-ary quadrature amplitude modulation constellations, respectively. The results are obtained in terms of special function such as generalized bivariate Meijer's G-function and to get insight further, we present asymptotic analysis at high SNR values to find the effect of various parameters on the system performance.

Unified analysis of EGC diversity over Weibull fading channels

SummaryIn this paper, the performance analysis based on PDF approach of an L‐branch equal gain combiner (EGC) over independent and not necessarily identical Weibull fading channels is presented. Several closed‐form approximate expressions are derived in terms of only one Fox H‐function as PDF, cumulative distribution function, and moments of the EGC output Signal‐to‐noise ratio (SNR), outage probability, amount of fading, channel capacity, and the average symbol error rate for various digital modulation schemes. All results are illustrated and verified by simulations using computer algebra systems.

Performance analysis of MIMO DF relay network with the Nth-best user selection scheme in the presence of co-channel interference

In this paper, we study the performance of multi-user multiple-input multiple-output (MIMO) relay network in the presence of co-channel interference (CCI) as well as additive white Gaussian noise (AWGN). Specifically, the Nth-best user selection scheme is applied to attain multi-user diversity. Both exact and asymptotic closed-form expressions for the outage probability and average symbol error rate (SER) of the considered system are derived, and corroborated by the Monte Carlo simulations. Based on the asymptotic SER expression, the diversity order and array gain are characterized, and the optimum power allocation between the source and the relay is also designed. The results reveal that the diversity order is NR×min{NS, ND(K−N+1)}, where NS, NR and ND represent the number of antennas at the source, the relay, and each destination, respectively, K is the number of the destinations, and N (1≤N≤K) represents the rank of the user chosen. The findings of this paper show that the CCI deteriorates the system performance by reducing the array gain, and optimal power allocation achieves better performance than that of uniform power allocation by offering extra array gain. These findings provide a valuable insight into the practical system design.

Dual-Hop Amplify-and-Forward Variable Gain Relaying over Mixture Gamma Fading Channels

In this paper, we present the end-to-end performance of a dual-hop amplify-and-forward variablegain relaying system over Mixture Gamma distribution. Novel closed-form expressions for the probability density function and the moment-generation function of the end-to-end Signal-to-noise ratio (SNR) are derived. Moreover, the average symbol error rate, the average SNR and the average capacity are found based on the above new expressions, respectively. These expressions are more simple and accuracy than the previous ones obtained by using generalized-K (KG) distribution. Finally, numerical and simulation results are shown to verify the accuracy of the analytical results.

Performance analysis of cooperative amplify‐and‐forward orthogonal frequency division multiplexing systems with power amplifier non‐linearity

Orthogonal frequency division multiplexing (OFDM) is considered as a key technology for future wireless communication systems. One of the main disadvantages of OFDM systems is the high peak-to-average power ratio (PAPR) of the transmitted signals. When a non-linear power amplifier (PA) is present, the high PAPR may cause the introduction of non-linear distortions. On the other hand, cooperative communications have emerged as a promising technology for wireless networks. A theoretical analysis of an amplify-and-forward OFDM system taking into consideration the non-linear distortions introduced by a PA is done. More specifically, approximate analytical expressions for the outage probability and average symbol error rate (SER) are derived and studied under several special situations. The performance analysis sheds light on the influence of PA non-linearity on the outage probability and the average SER of an OFDM system. Particularly, it is shown that the non-linear PA has a more significant effect over the average SER for medium and high signal-to-noise ratio (SNR) values and for small-order constellations. The analytical results are validated by means of computer simulations for different system configurations and SNR levels.

Impact of MIMO enabled relay on the performance of a hybrid satellite-terrestrial system

In this paper, we investigate a hybrid satellite terrestrial system with multiple input and multiple output enabled fixed relay, which is more reliable than the conventional dual-hop multiple single input and single output relaying network. Providing a small number of antennas on a fixed relay is easier to undertake than setting up on a mobile terminal due to the size limitation. In this study, we consider the impact of cooperating fixed relay with multiple transmitting and receiving antennas on the hybrid satellite-terrestrial system. Amplify-and-forward cooperative protocol is used at the relay node while for signal combining at the relay node, maximum ratio combining and maximum ratio transmission techniques are used. Independent and non-identically distributed fading channels, shadowed Rician, and Nakagami-$$m$$m, are assumed between the source-relay and relay-destination links respectively. An analytical approach is derived to evaluate the performance of the system in terms of outage probability, symbol error rate (SER) and ergodic capacity. The closed form expressions for the probability density function, cumulative distribution function, moment generating function, average SER of the total end-to-end signal-to-noise ratio are derived. We further derive the approximate closed form expression of ergodic capacity. These derived analytical expressions are applied to the general operating conditions together with available satellite channel data of various degrees of shadowing. The analytical results are compared with Monte Carlo simulations. The results show the improvement in the performance of the hybrid satellite-terrestrial system under various antenna arrangements at the relay node.

Asymptotic analysis of digital modulations in κ–μ , η–μ and α–μ fading channels

This study derives several new and simple closed-form approximations for the average symbol error rate (ASER) and outage probability performance metrics of digital communication systems (with/without diversity receivers) impaired by additive white Gaussian noise and fading. These approximations utilise the coefficients of the Poincare series expansion for the probability density function (PDF) of signal-to-noise ratio (SNR) random variable in conjunction with Mellin transform of the conditional error probability and/or its auxiliary functions to generalise some of the known asymptotic ASER/outage probability expressions to a wider range of modulation schemes and different types of propagation environments (including κ–μ, η–μ and α–μ fading channels). A new class of asymptotic approximations for the ASER/outage probability is also derived (based on a normalised asymptotic PDF of SNR) that is considerably better than the conventional high-SNR approximation although both techniques need only the first non-zero term of the Maclaurin (if exists) or the Poincare series expansion of the channel PDF. The authors’ also investigate the utility/efficacy of Welch–Satterthwaite and Moschopoulos approximations for yielding accurate predictions of the ASER in the low-SNR regime for different fading environments. Closed-form approximations for the ergodic (average) channel capacities of different types of fading channels with/without diversity reception are also derived.

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.

Analysis of subcarrier intensity modulation‐based optical wireless DF relaying over turbulence channels with path loss and pointing error impairments

The authors consider a subcarrier intensity-modulated relayed optical wireless communication system under the combined influence of path loss, atmospheric turbulence and pointing error impairments. The turbulence-induced fading is modelled by independent but not necessarily identically distributed (i.n.i.d.) Gamma–Gamma fading statistics where the relaying protocol followed by the system is decode and forward (DF). First, the statistics of instantaneous signal-to-noise ratio at the destination is derived, followed by the novel and exact closed-form expression for outage probability of the system. Then using the moment generating function-based approach, the authors evaluate error performance of the system in terms of average symbol error rate (SER) for M-ary phase shift keying modulation schemes. Further, as a special case for M = 2, that is, binary phase shift keying modulation scheme, the exact closed-form expression of average SER is derived in terms of mathematically tractable Meijer's G-function and extended generalised bivariate Meijer's G-function. Finally, at the end of the paper, various numerical examples are included to demonstrate the effect of different system parameters on the performance of the system and are verified by Monte-Carlo simulations.

Bi-Directional Decode-XOR-Forward Relaying Over <inline-formula> <tex-math notation="TeX">\(\mathcal {M}\) </tex-math></inline-formula>-Distributed Free Space Optical Links

In this letter, we consider the bi-directional cooperative communication where two users communicate to each other with the help of a relay. Considering the generalized M-distribution for the independent free space optical channels, the novel closed form expressions of the outage probability, and average symbol error rate are derived.

Double Differential Transmission for Amplify-and-Forward Two-Way Relay Systems

In this work, we consider an amplify-and-forward two-way relay system with unknown carrier frequency offsets (CFOs) which change randomly. Due to the existence of CFOs, the conventional differential scheme fails. In this case, a double differential transmission scheme is proposed to achieve successful two-way relay transmission over Nakagami-m fading channels. The average symbol error rate (SER) performance of the proposed scheme is analyzed and a closed-form approximation is derived. Simulation results are provided to validate the proposed scheme.

SER and PER Performance of Packet Decode-and-Forward Relaying With Generalized Order Selection Combining

This letter studies the generalized order selection combining (GOSC) scheme in the packet decode-and-forward relay systems, where the i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> , i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> , ⋯, and i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> best relays are selected. The GOSC scheme can be applied to the cases that some best relays are unavailable because of load balancing and rate limitation. The average symbol error rate (SER) and packet error rate (PER) are investigated. The choice probabilities of the possible best relays are discussed as well. Analysis reveals that the SER and PER achieve the same diversity order. We also show that the simulation results coincide with the derived expressions.

Performance Analysis of Composite Fading Channel Based on Point Estimate Method

A simple procedure is outlined to provide a point estimate mixture gamma distribution (PEMG) which closely approximates intractable distribution characterizing composite fading channel. The efficacy of the proposed PEMG to match target channel model in relation to other available approximate distributions is demonstrated using Kullback---Leibler measure of divergence. The simplicity and accuracy of the PEMG facilitates the computation of analytical expressions for some of the widely used performance measures viz., average symbol error rate and channel capacity under different adaptive transmission schemes. Numerical computations in relation to exact results are carried out to validate the accuracy of the derived expressions over the realistic range of parameters for the channel model.