Exact Outage Probability Analysis for Selection Decode-and-Forward Cooperation Systems

In this work, we explore the outage probability (OP) analysis of selective decode and forward (S-DF) cooperation protocol employing multiple-input multiple-output (MIMO) orthogonal space-time block-code (OSTBC) over time varying Rayleigh fading channel conditions with imperfect channel state information (CSI) and mobile nodes. The closed-form expressions of the per-block average OP, probability distribution function (PDF) of sum of independent and identically distributed (i.i.d.) Gamma random variables (RVs), and cumulative distribution function (CDF) are derived and used to investigate the performance of the relaying network. A mathematical framework is developed to derive the optimal source-relay power allocation factors. It is shown that source node mobility affects the per-block average OP performance more significantly than the destination node mobility. Nevertheless, in other node mobility situations, cooperative systems are constrained by an error floor with a higher signal to noise ratio (SNR) regimes. Simulation results show that the equal power allocation is the only possible optimal solution when source to relay link is stronger than the relay to destination link. Also, we allocate almost all the power to the source node when source to relay link is weaker than the relay to destination link. Simulation results also show that OP simulated plots are in close agreement with the OP analytic plots at high SNR regimes.

In this paper, we investigate the outage performance of decode-and-forward (DF) based opportunistic cooperative communications with channel estimation errors at the receivers under Rayleigh fading channels, in which the effect of the direct link has been explicitly evaluated. To be specific, the exact expression of outage probability has been derived for arbitrary values of signal-to-noise ratio (SNR) when pilot power is fixed. Through asymptotic analysis, the closed-form expressions of outage probability in the high SNR region and the diversity order are obtained. The analysis shows that the channel estimation errors due to limited pilot power impose a significant impact on the outage performance, leading to the diversity order be 0 even when the direct link is available. Although deploying more relays can mitigate the estimation errors effectively, the performance limit caused by the estimation errors becomes more obvious as SNR grows. For specific pilot power configuration and relay deployment, the outage probability remains unchanged even if data power approaches to infinity. Furthermore, simulation results are presented to verify our analysis.

In this paper, we apply a reconfigurable intelligent surface (RIS) to a two-way (TW) full-duplex (FD) wireless communication system, where a RIS has N reflecting elements and operates as a relay station forwarding signals between two FD terminals. To demonstrate the advantages of RIS compared with traditional relay, we also present the system and signal models of the TW-FD amplify-and-forward relay (AFR) system. We mathematically analyze the performance of the TW-FD-RIS system by deriving the exact closed-form expressions of the average outage probability (AOP) and the average symbol error rate (ASER) in the case N=1, and approximate expressions of the AOP and the ASER in the case N ≥ 2. Besides, we provide the exact closed-form expression of the AOP and approximate expression of the ASER of the TW-FD-AFR system. Monte-Carlo simulations validate all derived mathematical expressions. Numerical results demonstrate that using the RIS greatly improves the TW-FD communication system's performance compared with using amplify-and-forward (AF) relay. Specifically, even the RIS with one element ( N=1), the AOP and ASER of the TW-FD-RIS system are still lower than those of the TW-FD-AFR system in the low signal-to-noise ratio (SNR) regime. However, in the high SNR regime, the AOP and ASER of the TW-FD-RIS system are higher. In the case N ≥ 2, the AOP and ASER of the TW-FD-RIS system are significantly reduced. On the other hand, the impact of residual self-interference (SI) due to FD transmission mode on the performance of TW-FD-RIS and TW-FD-AFR systems is remarkable, making the AOP and ASER of these two systems reach the error floor in the high SNR regime. Fortunately, the usage of RIS with N ≥ 2 can greatly reduce this impact and avoid the error floor for the TW-FD-RIS system.

This paper investigates the impact of relay selection (RS) on the performance of cooperative non-orthogonal multiple access (NOMA), where relays are capable of working in either full-duplex (FD) or half-duplex (HD) mode. A number of relays (i.e., K relays) are uniformly distributed within the disc. A pair of RS schemes are considered insightfully: 1) single-stage RS (SRS) scheme; and 2) two-stage RS (TRS) scheme. In order to characterize the performance of these two RS schemes, new closed-form expressions for both exact and asymptotic outage probabilities are derived. Based on analytical results, the diversity orders achieved by the pair of RS schemes for FD/HD cooperative NOMA are obtained. Our analytical results reveal that: 1) the FD-based RS schemes obtain a zero diversity order, which is due to the influence of loop interference at the relay; and 2) the HD-based RS schemes are capable of achieving a diversity order of K , which is equal to the number of relays. Finally, simulation results demonstrate that: 1) the FD-based RS schemes have better outage performance than HD-based RS schemes in the low signal-to-noise ratio (SNR) region; 2) as the number of relays increases, the pair of RS schemes considered are capable of achieving the lower outage probability; and 3) the outage behaviors of FD/HD-based NOMA SRS/TRS schemes are superior to that of random RS and orthogonal multiple access based RS schemes.

This paper advocates the performance of wireless multiuser relay networks (MRNs) equipped with a single amplify-and-forward (AaF) relay. For such networks, we focus on opportunistic scheduling, in which the destination with the highest instantaneous end-to-end signal-to-noise ratio (SNR) is scheduled for transmission. The scheduled destination can receive either directly from the source or indirectly through the relay, based on cooperative selection diversity (CSD). Assuming Rayleigh fading channels, we first derive a new expression for the cumulative distribution function (CDF) of the received instantaneous end-to-end SNR. Then, relying on this statistical result, we present new exact expressions for the outage probability and symbol error rate (SER), both of which are obtained in closed-form. Furthermore, we derive simple yet valuable closed-form asymptotic expressions for the outage probability and SER in the high SNR regime. Our results explicitly reveal the impacts of CSD and opportunistic scheduling on the diversity order and array gain. Numerical results are presented to validate the analysis.

We analyze the performance of a dual-hop downlink cellular amplify-and-forward cooperative system in the presence of both channel estimation errors and radio frequency (RF) impairments, where multiple antennas are deployed only at the base station (BS) and single-antenna at relays and mobile stations (MS). Specifically, we derive approximate as well as exact closed-form expressions for the outage probability and expected spectral efficiency. In addition, simple asymptotic expressions at the high signal-to-noise ratio (SNR) regime are obtained, which facilitate the characterization of the achievable diversity order of the system. To validate the derived analytical expressions, we presented simulation results which are sufficiently tight across the entire range of SNRs. Findings of the paper suggest that full diversity order can be achieved only when the RF front-end hardware is assumed to be perfect, while in practice the imperfections in hardware are inevitable and reduce diversity order of the system. Moreover, the influence of key parameters such as the number of antennas, users, and relays on the system performance has been presented with the influence of the level of RF impairments.

In this paper we consider a multi relay Decode and Forward (DF) relay network assisted by Hybrid automatic repeat request (HARQ) in a Rayleigh block fading environment. The system uses an incremental relaying strategy in which the best relay is selected to cooperate with source. A Space-Time Block coding (STB) is used for cooperation between source and selected relay to transmit the data to the destination. Relays and destination use maximum ratio combining (MRC) technique to decode the sent message using previously received versions. We derive a closed-form expression of asymptotic outage probability at high Signal-to-Noise Ratio (SNR) regime. We also derive the average delay and throughput in a delay constrained application. The derivation method is based on the Laplace transform, which proves to be a very effective analytical tool when combined with the properties of the special functions. In addition, we investigate the optimum power allocation strategy to minimize the outage probability and consequently maximize the average throughput perceived by the end user. The simulation results show that the obtained analytical bound for the outage probability is very tight at high SNR regime. In addition the proposed power allocation scheme clearly outperforms the equal power allocation.

Distributed multi-antenna relaying is analyzed in nonregenerative cooperative networks with unbalanced hops and independent but not necessarily identically distributed Rayleigh fading. Exact closed-form expressions are derived for the moment generating function of the end-to-end signal-to-noise ratio (SNR) at the destination. Our analysis applies to arbitrary N number of antennas at the relay and arbitrary average received SNRs. Based on the derived results, we determine the symbol error rate with M-ary phase-shift keying. In addition, we carry out an asymptotic analysis in the high SNR regime. Our results provide fundamental insights into the impact of the number of antennas on the performance of nonregenerative relaying. We explicitly reveal that the diversity order is equal to N + 1. Theoretical analysis is verified by simulation.

In this paper, a comprehensive comparison analysis in terms of outage probability and average symbol error ratio (SER) is presented for cooperative cognitive multiple-input and multiple-output (CC-MIMO) multiuser systems with amplify-and-forward (AF) protocol. Specially, we consider two scenarios where the CC-MIMO multiuser systems have the perfect and imperfect channel state information (CSI). The CC-MIMO multiuser systems consist of one multi-antenna source, one single-antenna relay, and multiple multi-antenna destinations. At the secondary source and destinations, the maximal ratio transmission (MRT) and maximal ratio combining (MRC) are employed, respectively. For such CC-MIMO multiuser systems, we first obtain the exact closed-form expressions of outage probability under the two cases where the CC-MIMO multiuser systems have the perfect and imperfect CSI. Then, to reduce the implementation complexity, the tight lower bounds of outage probability and average SER are derived. Finally, to obtain insight, by using the high signal-to-noise ratio (SNR) approximation, the asymptotic estimations of outage probability are achieved. The numerical results show that the derivations are agreed with the simulations, which validate our derivations. At the same time, the results show that, for the systems without perfect CSI, the achievable diversity order reduces to one, regardless of the number of antennas at the cognitive source and destinations as well as the number of the cognitive destinations. Nevertheless, these key parameters affect the coding gain of the CC-MIMO multiuser systems. When the systems have the perfect CSI (or without feedback delay), the achievable diversity gain is determined by the minimum between the number of source’s antennas and the product of the number of destinations and the number of destination’s antennas. For the effect of PU’s parameters, our results indicate that primary systems only affect the coding gain but not the diversity gain.

In this study, the authors examine the effect of a channel-estimation error on the error and outage probabilities of a multi-relay system with amplify-and-forward relaying over a frequency-flat Rician fading channel. The authors consider orthogonal relaying and study both conventional cooperative systems (i.e. all relays participate in the relaying phase) and opportunistic cooperative systems (i.e. only the best relay participates in the relaying phase). Based on the derivation of an effective signal-to-noise ratio (SNR) at the destination node taking into account channel-estimation error, the authors obtain closed-form expressions for error and outage probabilities in a high SNR regime. Such closed-form solutions are highly desirable because they allow for rapid and efficient evaluation of system performance. Computer simulations are used to validate the authors' analytical results.

The use of aerial platforms has recently attracted significant interest in Internet of Things (IoT)-based heterogeneous communication networks to support flexible and efficient network connection. This work investigates the performance of a ground-aerial autonomous aerial vehicle (AAV)-assisted hybrid power line communication (PLC)/free-space optical (FSO) communication system employing both decode-and-forward (DF) and fixed-gain amplify-and-forward (AF) relaying protocols. It is assumed that the PLC channel gain is Log-normally distributed while the Bernoulli-Gaussian random process models the PLC channel noise. The FSO link established between the FSO transmitter and the AAV considers the combined influence of the generalized Málaga distributed atmospheric turbulence (AT), random fog, nonzero boresight pointing errors, and Angle-of-Arrival (AoA) fluctuations of the AAV. Based on this, we evaluate the cumulative distribution function (CDF) and probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR). Further, capitalizing on the statistical characterization of CDF and PDF, we derive series-based expressions for average symbol error rate (ASER), outage probability (OP), and average channel capacity (ACC) utilizing both heterodyne detection (HD) and direct detection (DD) techniques. Additionally, we conduct an asymptotic analysis of ASER in terms of the coding gain and diversity order in a high SNR regime. Likewise, a detailed analysis is carried out to find the optimal value of the field-of-view (FOV) angle and average SNR to achieve minimum ASER under the combined influence of the aforementioned channel conditions using the DF relaying scheme. Furthermore, the impact of all the considered channel parameters and impairments is demonstrated through the numerical results.

In this study, the authors evaluate the performance of space diversity systems with the N th‐best antenna selection scheme in the presence of interference and outdated channel information (OC1). The N th‐best antenna selection scheme is efficient in situations where the second or even the N th best antenna is mistakenly selected by the destination instead of the first best antenna for data reception. In this study, they first derive the cumulative distribution function (CDF) of the end‐to‐end (e2e) signal‐to‐interference plus noise ratio at the selection scheme combiner output. This CDF is then used to derive exact closed‐form expressions for the e2e outage probability and symbol error probability (SEP) of the system. In the analysis, the channels of the desired user and the interferers are assumed to follow Rayleigh distribution. Furthermore, to obtain more about system insights, the performance is studied at the high signal‐to‐noise ratio (SNR) regime where the diversity order and coding gain are derived. Monte Carlo simulations are provided to validate the derived analytical and asymptotic expressions. Main results illustrate that with an interference power that is not scaling with SNR, the system can still achieve diversity gain when more receive antennas are used. Also, findings show that the diversity order of the system is linearly decreasing with increasing the order of the antenna, and linearly increasing with decreasing it. Furthermore, results illustrate that as the higher the correlation coefficient between the SNRs of antennas at the selection and transmission time instances, the better the achieved performance.

In this paper, we investigate the performance of asymmetric radio frequency (RF) and free space optical (FSO) dual-hop cooperative relay network along with a direct RF link between source and destination. The FSO link experiences double generalized Gamma turbulence in the presence of the generalized non-zero boresight pointing errors, and RF links experience non-identically distributed Nakagami-m fading. Moreover, considering both cognitive radio and non-cognitive scenarios, a partial relay selection (PRS) strategy has been employed. Furthermore, both relay selection and underlay power restriction are governed with the outdated channel state information (CSI). We also assume both heterodyne and intensity modulation/direct detection methods in the FSO receiver. Under the assumption of amplify-and-forward relaying and PRS, we derive closed-form expressions for outage probability (OP) of both scenarios, while bit-error probability and ergodic capacity of the non-cognitive scenario are also obtained. The asymptotic expressions of OP and diversity order of this network are derived for both perfect CSI and outdated CSI cases. It is demonstrated that the diversity order is a function of the fading severity of the RF links, turbulence parameters of the FSO link, and pointing error, regardless of interference channel parameter of the primary user.

In the context of two-wave with diffuse power (TWDP) fading scenarios, this paper analyzes the outage probability and symbol error rate (SER) of single relay cooperative networks using amplify-and-forward (AF) relaying. Each channel in the network is assumed to be independently and non-identically distributed. The statistical result of the upper bound on the received signal-to-noise ratio (SNR) is derived. We derive the closed-form asymptotic expressions to approximate the outage probability and SER in the high SNR regime, respectively. Based on the asymptotic results, the diversity order and coding gain of the cooperative network is analyzed. Simulation results show that these asymptotic results are tight particularly in the high SNR regime for cooperative networks in different fading scenarios.

Multi-hop cooperative MIMO network that consists of multiple nodes each equipped with single antenna is introduced and investigated. Optimal power allocation scheme with selective decode-and-forward (SDF) cooperative strategy is formulated and solved by means of optimization method with the purpose of minimization of system’s symbol error rate (SER), which are derived and analyzed with numerical results presented. Distributed space-time block Code (DSTBC) in multi-hop cooperative MIMO is analyzed and compared with optimal power allocation scheme with SDF strategy. Simulation results reveal that, cooperative diversity could be achieved with optimal power allocation. Optimum power allocation scheme depends on the relay’s position and channel quality between source to relay and relay to destination. Novel performance comparison between optimal power allocation and DSTBC are researched and presented. Simulation results confirm our theoretical analysis, which indicates that multi-node DSTBC outperforms optimal power allocation scheme due to the fact that cooperative diversity gain and coded gain could be obtained simultaneously for DSTBC in multi-hop cooperative MIMO network.