Asymptotic Symbol Error Probability Research Articles

Hybrid selection combining scheme for correlated cooperative communication over [formula omitted]-[formula omitted] fading channels

Due to poor (limited) scattering, a correlation among channels is inevitable, resulting in performance degradation of wireless communication systems. In this paper, we propose a hybrid selection combining (SC), also known as switched scaled – SC for correlated cooperative communication over κ-μ fading channel. By using paired error analysis, we derive the end-to-end symbol error probability of this system over bivariate κ-μ channel fading with M-ary phase shift keying (MPSK) modulation. In addition, we obtain significant parameters of hybrid SS-SC, such as the optimum scaling factor and optimum threshold by using the second derivative test. For every signal to noise ratio (SNR), we obtain different optimum thresholds and scaling factors. Our analytical results were found to overlap significantly with those of the simulation results. They were also compared with the variants of SC and switched diversity techniques. Our study demonstrates that the proposed hybrid technique performs better than the other SC and switched diversity schemes over correlated and uncorrelated fading channels. Furthermore, we derive an asymptotic symbol error probability for the proposed system, and the asymptotic results are in agreement with the analytical results at higher SNRs. Our study also shows that the diversity order of the system depends on the mutually exclusive events of the proposed technique.

Performance Analysis of an IRS-Aided Wireless Communication System With Spatially Correlated Channels

An intelligent reflecting surface (IRS) assisted wireless communication system, with statistically correlated channels between the transmitter and the IRS pair and between the IRS and the receiver pair, is studied in the absence of channel state information (CSI). Assuming the phases added by IRS elements to be deterministic, the closed-form analytical expression for the symbol error probability (SEP) and the upper bound on the channel capacity are derived, with the transmitter employing binary phase-shift keying (BPSK) modulation for data transmission. The asymptotic SEP expression is derived and the achievable diversity order of the system is shown to be independent of the number of IRS elements. A search based algorithm is proposed to obtain the optimal phase at IRS minimizing the average SEP, as a equal phase configuration. The optimal equal phase is also found to maximize the average channel capacity. Numerical results are presented for the case of channels following a practical IRS correlation model.

Full Euclidean Distance Based Selection Combining for SSK DF Cooperative Diversity Systems

Space Shift Keying (SSK) is a multiple-input multiple-output technique that has drawn more attention in recent years because of its low complex transceiver design. In this paper, an investigation on the Symbol Error Probability (SEP) performance of SSK in a Decode-and-Forward (DF) cooperative relaying system is done. The DF cooperative relaying scenario considers an origin node, an intermediate node and an end node with a direct link between origin and end node, and an indirect link between origin to the intermediate node and intermediate to end node. The SSK modulation is considered at the origin and intermediate nodes with Full Euclidean Distance based Selection Combining (FED-SC) employed at the end node for SSK symbol detection. The SEP expression of the SSK FED-SC in the DF cooperative relaying scheme is derived using the Order Statistics Approach (OSA). Further, a closed-form SEP expression is obtained using a Combined Order Statistics Approach (COSA) considering the number of receive antennas at the intermediate node is equal to the number of receive antennas at the end node. In addition, the closed-form asymptotic SEP expression is presented to evaluate the diversity order of the system. The SEP expressions derived through OSA and COSA are verified using the Monte Carlo simulations. The simulation results revealed that the proposed SSK FED-SC outperforms all the existing SSK DF cooperative selection combining schemes.

Energy-Efficient and Low-Latency Massive SIMO Using Noncoherent ML Detection for Industrial IoT Communications

To enable ultrareliable low-latency wireless communications required in the Industrial Internet of Things, in this paper we develop an energy-based modulation [i.e., non-negative pulse amplitude modulation (PAM)] constellation design framework for noncoherent detection in massive single-input multiple-output (SIMO) systems. We consider that one single-antenna transmitter communicates to a receiver with a large number of antennas over a Rayleigh fading channel, and the receiver decodes the transmitted information at the end of every symbol. For such an SIMO system with non-negative PAM modulation, we first propose a fast noncoherent maximum-likelihood decoding algorithm and derive a closed-form expression of its symbol error probability (SEP). We then enhance the system energy efficiency by finding the optimal PAM constellation that minimizes the exact SEP subject to a total signal power constraint for such a system with an arbitrary number of receiver antennas, signal-to-noise ratio (SNR), and constellation size. Furthermore, the closed-form upper and lower bounds on the optimal SEP are derived. Based on these bounds, the exact expression for coding gain of the dominant term of the SEP is presented for such an optimal massive SIMO system. We also present an asymptotic SEP expression at a high SNR regime and the approximate diversity gain of the system. Simulation results for the proposed optimal PAM constellation validate the theoretical analysis, and show that our presented optimal constellation attains significant performance gains over the currently available minimum-distance-based constellation systems.

Performance analysis of wireless communication system over nonidentical cascaded generalised gamma fading channels

SummaryMultiplicative fading statistics usually encountered in different radio propagation environments. In this context, we evaluate and analyse the performance of a wireless communication system over the nonidentical cascaded generalised Gamma Fading Channels, also known as generalised Bessel‐K fading channel. To this end, the closed‐form expressions for the amount of fading (AOF), the outage probability (OP), the average symbol error probability (SEP), and the channel capacity are derived. In addition approximate expressions for the average SEP with maximal ratio combining (MRC) diversity are also provided. The low‐ and high‐power solutions for the channel capacity are also provided. Furthermore, simplified asymptotic average SEP expressions for MRC and selection combining (SC) are presented to gain the system performance with diversity. The proposed methodologies provide more flexibility to accommodate different radio propagation scenarios. To examine the accuracy of the proposed solutions, numerical and simulation results are compared and shown to fit for variety of fading parameters.

Space shift keying for multi-hop multi-branch networks

In this paper, we propose two different multi-hop multiple-input multiple-output (MIMO) space shift keying (SSK) schemes and investigate their error performance. In the first scheme, we consider a multi-hop multi-branch SSK system, in which the source and destination are equipped with multiple transmit and receive antennas, respectively. In this scheme, SSK is applied by using the source transmit antennas. Moreover, in each branch, single-antenna relays are used to amplify the transmitted signal from the source and forward it to the next relay until it reaches to the destination. In the second scheme, we consider a multi-hop MIMO-SSK system with path selection. In this scheme, the best path is selected among multiple branches and a multiple-antenna source communicates with a multiple-antenna destination via the relays of the selected path. Each relay is equipped with multiple transmit and receive antennas. Moreover, the source and all relays employ SSK modulation to transmit information bits and each relay in each path follows the decode-and-forward protocol. Approximate theoretical error probability expressions are derived for both schemes. Furthermore, an asymptotic symbol error probability performance analysis is also performed for the multi-hop MIMO-SSK system with path selection. It is shown that the proposed multi-hop SSK systems outperform conventional multi-hop M-PSK systems in terms of the error performance for especially high data rates and sufficient number of receive antennas at the receiving nodes.

HSSEC strategy for decode‐and‐forward‐relaying systems over Nakagami‐ m fading channels

Distributed switched diversity combining has drawn significant attention in the recent past due to its low-complexity nature in terms of channel state information requirement at the receiving end to achieve full diversity order. In this study, the authors propose a hybrid selection and switch-and-examine combining (HSSEC) scheme, which is a combination of selection combining and SEC schemes, for a multi-relay decode-and-forward system to improve the performance of distributed switched diversity combining schemes proposed in the literature. Furthermore, the performance of HSSEC scheme is investigated over non-identical Nakagami-m fading channels. Average end-to-end symbol error probability (SEP) expression is derived for M-ary phase-shift keying signalling, and in addition asymptotic SEP expression is also derived to analyse diversity order. From the derived asymptotic expression, it is inferred that the HSSEC scheme attains full diversity order over Nakagami-m fading channels, except for the case when threshold signal-to-noise ratio (SNR) is very much lesser than the average SNR. Furthermore, exact outage probability expression is derived for the HSSEC scheme. Finally, in the numerical results, the outage and SEP performances are compared with other schemes proposed in the literature.

Joint Antenna and Relay Selection Strategies for Decode-and-Forward Relay Networks

Cooperative diversity systems with optimal and suboptimal antenna and relay selection have been paid significant attention for more than half a decade. However, optimal antenna and relay selection strategies require global channel state information (CSI), which is a cumbersome process. In this paper, we propose a diversity-optimal and three suboptimal transmit–receive antenna and relay selection strategies, named S1, S2, and S3, for decode-and-forward cooperative relaying systems, equipped with $N_{t}$ and $N_{r}$ antennas at the source (S) and the destination (D), respectively, and considering a multirelay scenario. Furthermore, we study the symbol error probability (SEP) for these strategies, assuming $M$ -ary phase-shift keying signaling over Rayleigh fading channels. In addition, we perform diversity order analysis through closed-form asymptotic SEP expressions. Since the proposed suboptimal strategies, i.e., S2 and S3, involve the so-called switch-and-examine combining scheme, we compare the complexity of S1, S2, and S3 in terms of the average number of CSI required at D to select the best transmit–receive antenna pair and relay. From the derived SEP expressions, it can be concluded that all three suboptimal strategies achieve the same diversity order of $N_{t}N_{r}+N$ , where $N$ is the number of relays, except for the case when the switching threshold signal-to-noise ratio (SNR) is much lower than the average SNR in S2 and S3. Finally, the diversity-optimal strategy achieves full diversity order of $N_{t}N_{r}+N\min(N_{t},N_{r})$ .

Optimal Diagonal Power Loading Minimizing Asymptotic Symbol Error Probability for Distributed MIMO Systems With ZF Receivers

In this paper, we consider a distributed multiple-input–multiple-output (D-MIMO) system, where the channel is flat fading and may be correlated, and experiences both small- and large-scale fading. We assume that full knowledge of channel state information (CSI) is available at the receiver and that only the first-and second-order statistics of the channel are available at the transmitter. For such a system with square quadrature amplitude modulation (QAM), an asymptotic symbol error probability (SEP) is derived for the linear zero-forcing (ZF) receiver. Then, we propose an optimal diagonal power loading (PL) strategy that minimizes the dominant term of the asymptotic SEP subject to either a total transmission power constraint when the total power normalization coefficient can be fed back to the transmitter from the receiver or an individual transmission power constraint. A simple closed-form solution is obtained. Computer simulations show that our presented optimal system attains significant performance gains over the currently available equal PL system.

Performance Comparison of Selection Combining With Full CSI and Switch-and-Examine Combining With and Without Post-Selection

Selection combining (SC) with full channel state information (CSI) achieves full diversity order in a decode-and-forward (DF) relaying system. However, the estimation of CSI of all the links is a cumbersome process. As an alternative, switched-diversity techniques have been proposed in the literature, in which CSI of all the links are not simultaneously required. In this paper, we compare the variants of the switched-diversity and full-CSI SC schemes through a paired error approach for a multi-DF-relaying-based cooperative diversity system. We derive the exact symbol error probability (SEP) expressions for the full-CSI SC, switch-and-examine combining (SEC), and SEC with post-selection (SECps) schemes, considering $M$ -ary phase-shift keying (MPSK) signaling over slow, flat, independent, and nonidentical Nakagami- $m$ fading channels. It is to be noted that the derived SEP expressions are valid for integer values of fading severity parameter $m$ . In addition, we also present the closed-form asymptotic SEP expressions for MPSK signaling to evaluate the diversity order. Concisely, from the numerical results, it is observed that the SECps scheme is able to offer the same performance as that of the full-CSI SC scheme. Furthermore, the SECps scheme outperforms the SEC scheme with more CSI.

Near optimal power allocation in two‐way relay systems with physical layer network coding

In this study, the authors examine the power allocation (PA) in a two-way relay system, where the relay adopts physical layer network coding based on decode-and-forward protocol. In the PA, the optimisation objective is to minimise the end-to-end symbol error probability (SEP) under a total power constraint. Since the optimal power allocation (OPA) scheme requires numerical methods (for exhaustive search) to find the solution, which might be infeasible for practical systems, the authors propose a near optimal power allocation (NOPA) scheme that has a closed-form solution by studying the properties of the OPA scheme. The asymptotic SEP expression of the proposed NOPA scheme is also derived. Simulation results show that the performance of proposed NOPA scheme is quite close to that of the OPA scheme. Furthermore, it is shown that the NOPA scheme can provide asymptotic SNR gains of 1.76 dB and 2.22 dB over two well-known schemes.

Performance analysis of joint relay selection and transmission schemes in multiple-antenna two-way relay systems

In this paper, we consider a two-way relay system with two multi-antenna sources and multiple single-antenna relays and study the performances for various transmission schemes with the assumption that perfect channel state information (CSI) is available at both the sources and the relays. Although a transmission scheme that combines source beamforming and relay selection (BF-RS) is known to improve a system performance, its performance has not been theoretically analyzed yet. In the paper, we focus on the performance analysis in terms of the symbol error probability (SEP) for the BF-RS scheme. The analytical upper and lower bounds of the end-to-end system SEP are derived in the closed form, and the asymptotic SEP expression is given in high SNR regime. By both analytical and simulation results, it is clearly shown that a full transmit and relay selection diversity gain can be achieved without code rate loss. The SEP curves from simulations show that our derived bounds can predict the performance accurately. Based on the derived analytical results, we propose an individual power allocation (IPA) scheme to save the total transmit power. We show that the IPA scheme can result in considerable energy saving with a comparable SEP performance.

Direct Link-Aware Optimal Relay Selection and a Low Feedback Variant for Underlay CR

Cooperative relaying combined with selection has been extensively studied in the literature to improve the performance of interference-constrained secondary users in underlay cognitive radio (CR). We present a novel symbol error probability (SEP)-optimal amplify-and-forward relay selection rule for an average interference-constrained underlay CR system. A fundamental principle, which is unique to average interference-constrained underlay CR, that the proposed rule brings out is that the choice of the optimal relay is affected not just by the source-to-relay, relay-to-destination, and relay-to-primary receiver links, which are local to the relay, but also by the direct source-to-destination (SD) link, even though it is not local to any relay. We also propose a simpler, practically amenable variant of the optimal rule called the 1-bit rule, which requires just one bit of feedback about the SD link gain to the relays, and incurs a marginal performance loss relative to the optimal rule. We analyze its SEP and develop an insightful asymptotic SEP analysis. The proposed rules markedly outperform several ad hoc SD link-unaware rules proposed in the literature. They also generalize the interference-unconstrained and SD link-unaware optimal rules considered in the literature.

Performance analysis of two‐way decode‐and‐forward relaying in the presence of co‐channel interferences

This study investigates the performance of two-way decode-and-forward (DF) relaying networks, considering transmissions over independent but not necessarily identically distributed (i.n.i.d.) Rayleigh fading channels, in the presence of multiple co-channel interferers at both the relay and end-source nodes. Both asymmetrical and symmetrical cases, of whether the channels from source terminals to the relay are identically distributed or not, are considered. Specifically, closed-form expressions for the cumulative distribution function of the equivalent signal-to-interference-plus-noise ratio (SINR) in different cases are derived, based on which the exact symbol error probability (SEP) and the systems’ achievable rate are derived and analysed. Based on the analytic results, the authors study the impacts of system parameters, such as interference power and number of interferers on the performance of the system. Furthermore, the system behavior at high signal-to-noise ratio (SNR) values is studied via deriving the asymptotic SEP. The results of this study are attested through Monte Carlo simulations.

Performances of Transmit Antenna Selection, Receive Antenna Selection, and Maximal-Ratio-Combining-Based Hybrid Techniques in the Presence of Feedback Errors

In this paper, performances of joint transmit and receive antenna selection (JTRAS), transmit antenna selection/maximal ratio combining (TAS/MRC), and transmit antenna selection/receive antenna selection (TAS/RAS) techniques are examined in a unified manner in the (42) presence of feedback errors. Exact and closed-form outage probability, moments, moment-generating function, ergodic capacity, and symbol error probability (SEP) expressions are derived for flat Nakagami-m fading channels. In addition, to obtain diversity order and array gain of the investigated techniques in the presence of feedback errors, asymptotic outage probability and SEP expressions are also derived. Analytical results are validated by Monte Carlo simulations. Results show that the diversity order is significantly reduced in the presence of feedback errors, whereas all the systems provide full diversity order for a perfect feedback channel.

A simple amplify-and-forward opportunistic relaying based on outdated channel state information

Opportunistic relay selection (ORS) is a promising approach for cooperative communications owing to its low complexity by activating only the best relay. However, in mobile scenarios, the channel state information (CSI) estimated in relay selection may be different from the actual CSI employed in data transmission due to relatively fast varying channels, i.e., CSI is outdated, which may lead to incorrect relay selection, and hence system performance deteriorates. To address the problem, this paper designs a relay selection strategy with instaneous and statistical CSIs in amplify-and-forward (AF) cooperative networks whose instantaneous CSIs of two hops employed in relay selection are both outdated. Based on high signal-to-noise ratio (SNR) analysis, we propose a distinctive relay selection strategy which can be described as selecting the relay with the asymptotic optimum average symbol error probability (SEP) and outage probability at high SNR. The corresponding asymptotic outage probability and SEP performance analysis are also provided. Finally, simulation results not only validate our theoretical analysis, but also show that in asymmetrical outdated CSI scenarios, the proposed strategy achieves better performance than existing relay selection strategies at medium and high SNR values.

Noncoherent Reception of Multi-Level ASK in Rayleigh Fading with Receive Diversity

We consider a communication system with receive diversity in flat Rayleigh fading employing multi-level amplitude-shift keying (ASK) and noncoherent reception. Using the statistics of the decision variable of the quadratic receiver, a closed form expression for the symbol error probability (SEP) is derived. A formulation to determine the optimal signal amplitude levels of ASK constellation that minimize the SEP subject to a total signal energy constraint is presented. By approximating the derivative of the objective function, an approximate semi-analytical solution is obtained. We also present an asymptotic SEP expression that shows the variation of the SEP at high signal-to-noise ratio (SNR) and the diversity order of the system. An important result is that the optimum signal amplitude levels at high SNRs follow an approximately geometric progression in contrast to the more typical case of signal amplitude levels in arithmetic progression. Numerical results show the superiority of error performance of ASK with optimal signal amplitude levels as compared to that of ASK with signal amplitude levels in arithmetic progression.

Cooperative mobile-to-mobile communications over double Nakagami- m fading channels

Double Nakagami-m fading model can be used to provide a realistic description of the mobile-to-mobile (M2M) channel. The moment generating function (MGF)-based approach is used to derive the symbol error probability (SEP) expressions for the multiple-mobile-relay-based M2M system. Under the consideration of better performance and lower complexity, both decode-and-forward (DF) and amplify-and-forward (AF) protocols are addressed in this study. For adaptive DF (ADF) relaying, the asymptotic SEP at high signal-to-noise ratio regime in addition to the exact SEP formulations are derived. Furthermore, the impacts of channel estimation error for the insight of non-ideal channel estimation are analysed. For fixed-gain AF (FAF) relaying, the authors present approximate SEP and asymptotic SEP to indicate the cooperative gain. For L mobile relays and under the assumption of independent and identically distributed (i.i.d) source- relay channels and i.i.d relay-destination channels, it is shown in this paper that asymptotic diversity orders of L × min(mRD,1, mRD,2) + min(mSD,1, mSD,2) and L × min(mSR,1, mSR,2, mRD,1, mRD,2) + min(mSD,1, mSD,2) can be achieved for ADF-M2M and FAF-M2M schemes, respectively. Simulations are performed to verify the analytical results.

Keyhole Effect in Dual-Hop MIMO AF Relay Transmission with Space-Time Block Codes

In this paper, the effect of keyhole on the performance of multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay networks with orthogonal space-time block codes (OSTBCs) transmission is investigated. In particular, we analyze the asymptotic symbol error probability (SEP) performance of a downlink communication system where the amplifying processing at the relay can be implemented by either the linear or squaring approach. Our tractable asymptotic SEP expressions enable us to obtain both diversity and array gains. Our finding reveals that with condition nS >; min(nR, nD), the linear approach can provide the full achievable diversity gain of min(nR, nD) when only the second hop suffers from the keyhole effect, i.e., single keyhole effect (SKE), where nS, nR, and nD are the number of antennas at source, relay, and destination, respectively. However, for the case that both the source-relay and relay-destination links experience the keyhole effect, i.e., double keyhole effect (DKE), the achievable diversity order is only one regardless of the number of antennas. In contrast, utilizing the squaring approach, the overall diversity gain can be achieved as min(nR, nD) for both SKE and DKE. An important observation corroborated by our studies is that for satisfying the tradeoff between performance and complexity, we should use the linear approach for SKE and the squaring approach for DKE.

Asymptotic SEP Analysis of Two-Way Relaying Networks With Distributed Alamouti Codes

Asymptotic symbol error probability (SEP) performance with an optimal maximum likelihood (ML) receiver and square quadrature amplitude modulation (QAM) constellations is investigated for two-way amplify-and-forward (AF) half-duplex relaying networks employing distributed Alamouti space-time block codes (DASTCs) recently proposed by Duong By developing a novel strategy to particularly deal with some specific Gaussian integrals, two asymptotic SEP formulas are derived for both fixed- and variable-gain AF protocols. These analytic results reveal that, when the signal-to-noise ratio (SNR) is large, the diversity gain for the variable-gain AF is 2, whereas the diversity gain function for the fixed-gain AF is proportional to SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> ln SNR.