Asymptotic Outage Probability Research Articles

An Opportunistic Source Selection Spectrum Sharing Protocol for Overlay Cognitive Two-Way Relaying System

In this paper, an overlay two-way relaying spectrum sharing protocol is proposed by employing an opportunistic source selection strategy. In this protocol, a secondary user acts as a relay and allocates a fraction of its transmit power to assist two-way communication between two primary users (PUs), thus, gaining spectrum sharing as long as without degrading the primary system performance. Moreover, to exploit the multiuser diversity inherent in the multiuser primary systems, the two PUs transmit their own messages in an opportunistic manner, depending on the instantaneous channel conditions. Specifically, at each transaction, only one of the PUs is selected for transmission such that the instantaneous mutual information on the whole primary network is maximized and as a result, the multiuser diversity gain is achieved by the primary system. Then, we derive the exact closed-form outage probabilities for both the primary and secondary systems. To gain more insights, closed-form asymptotic outage probability expressions are also derived. Based on the approximations, we further obtain analytical results on the diversity order of the primary system and the power-allocation threshold above which the spectrum sharing is allowed for secondary transmission. Numerical results are presented to verify our analysis and highlight the advantages of our proposed scheme compared to another two-phase spectrum sharing protocol based on analog network coding.

Outage performance of fixed-gain and variable-gain AF full-duplex relaying in non-identical Nakagami-m fading channels

We investigate outage performance of fixed-gain and variable-gain amplify-and-forward (AF) full-duplex (FD) relaying systems under residual loop-interference (LI) in non-identical Nakagami-m fading channels. New exact outage probability expressions are derived analytically in a single-integral form by using the cumulative distribution function approach. Moreover, tight lower-bound and asymptotic outage probability expressions are derived in closed-form for the evaluated systems. It is shown that the fixed-gain AF-FD relaying outperforms the variable-gain AF-FD relaying when LI power and/or signal-to-noise ratio increase. The analytical results are verified by Monte-Carlo simulations.

Outage analysis of TAS/MRC in dual hop full-duplex MIMO relay networks with co-channel interferences

In this paper, we investigate the outage performance of transmit antenna selection (TAS) and maximal-ratio combining (MRC) in dual hop full-duplex (FD) amplify-and-forward (AF) relay network over Rayleigh fading channels. In the analysis, Rayleigh faded multiple co-channel interferers (CCIs) are also taken into account at the relay. In the network, source and destination are equipped with multiple antennas, and relay is equipped with one receive and one transmit antennas, respectively and source-destination link is not available. While the TAS is applied at the source without considering residual self-interference (RSI) effect, received signals at the destination are combined based on the MRC technique. For the analysis, we consider three approaches at the relay. In the first, we consider the received signal at the relay is corrupted by faded RSI and noise, in the second one, the RSI is considered as non-fading. In the last one, the noise is neglected. In all cases, the relay suffers from multiple Rayleigh faded CCIs. Outage probability (OP) expression related to all the cases is derived and obtained in single integral forms in case of the faded/non-fading RSI and in closed form in case of the noise neglected approach. Moreover, we also find asymptotic OPs and conduct effective diversity order analysis. The analytical results are verified by the Monte Carlo simulations. Results show that TAS decreases error floor at high signal-to-noise ratio (SNR) region and MRC provides diversity gain at low SNR region. In addition, approaches II and III are good approximations to approach I at low and high SNR regions, respectively.

Dual‐antenna selection with distributed space–time block codes in two‐way relaying networks

Based on the criterion of maximising the end-to-end receiving signal-to-noise power ratio, a dual-antenna selection scheme combining with distributed space–time block code is proposed for two-way relaying networks with amplify-and-forward protocol in Rayleigh fading channels. To facilitate the performance analysis, the authors derive the lower bound and asymptotic expressions for the network outage probability performance. Moreover, a concise solution for optimal power allocation is also determined to minimise the outage probability under a total power constraint. From the asymptotic outage probability analysis, the authors demonstrate that the proposed dual-antenna selection scheme can achieve full outage diversity. Finally, numerical results verify the accuracy of the authors’ analysis. Notably, the proposed scheme achieves competitive performance improvement compared with the beamforming scheme and the existing antenna selection schemes in the state of the arts.

Performance analysis of orthogonal frequency division multiplexing‐based cooperative amplify‐and‐forward networks with non‐linear power amplifier over independently but not necessarily identically distributed Nakagami‐ m fading channels

In this study, performance analysis of variable-gain amplify-and-forward relaying orthogonal frequency division multiplexing-based systems over independently but not necessarily identically distributed Nakagami-m fading channels using non-linear power amplifier (PA) at the relay and maximal ratio combining scheme at destination. Specifically, novel closed-form expressions of outage probability and asymptotic outage probability are investigated for the considered system model. Further, an average symbol error rate (ASER) expression is derived for general-order rectangular quadrature amplitude modulation (RQAM) scheme using cumulative distribution function-based approach, which is also the novel contribution of the work. Since the transfer function of PA used at relay is nonlinear, this introduces non-linear distortion (NLD) in the considered system model. Thus, the impact of NLD and fading parameters on outage probability, diversity gain of the system and ASER performances are analysed. Further, the impact of NLD on constellation order for RQAM scheme is also discussed. The theoretical results are compared with computer simulations to verify the accuracy of the derivations. The derived expressions are generalised over variety of fading environments for integer-valued fading parameter.

Performance analysis of multi-antennas combining and selection schemes for wireless-powered communication

We propose and analyze spatial diversity combining and selection schemes in a wireless-powered communication network with multi-antennas at energy access point (EAP) and data access point (DAP). The EAP adopts either maximal-ratio transmitting or transmit antenna selection to wirelessly transfer power, and the DAP employs either maximal-ratio combining or receive antenna selection to combine the received information. It generates four schemes for the wireless-powered communication network. We derive new closed-form expressions for the statistical characterizations of the received signal to noise ratio (SNR). Based on these expressions, the outage probability and the average throughput are further derived. The diversity order of the proposed schemes is given through the asymptotic outage probability analysis at high SNR regime. Nakagami-m fading with non-identical fading parameters is assumed for both power transfer channel and information transmission channel. Numerical results are given to validate all the analytical results. The impact of EAP transmit power, the number of EAP/DAP antennas, and the energy harvesting time on the performance of the proposed schemes is also investigated.

Outage Analysis of Mixed Underlay Cognitive RF MIMO and FSO Relaying With Interference Reduction

In this paper, we study the outage performance of multiuser mixed underlay radio frequency (RF)/multidestinations free-space optical (FSO) links. For RF links, we consider a secondary network with multiple users that can communicate with multiple destinations through a relaying node. The relay is equipped with an antenna array at the RF side, and it uses the amplify-and-forward (AF) protocol. The primary users (PUs) are equipped with multiple antennas at transmit and receive nodes. The RF link is subjected to the aggregate PUs interference effect on the secondary network. To reduce the effect of PUs interference on secondary network at the relay node, two interference cancellation (IC) schemes are adopted, which vary in terms of complexity and achieved performance. On the other hand, the multidestination FSO links can be exploited to further enhance the quality of the second hop, and their associated channel models account for pointing errors, intensity modulation/direct detection, and heterodyne detection. For the aforementioned system model, we obtain exact and asymptotic closed-form expressions for the end-to-end outage probability. To further enhance system performance, optimal power allocation between the two hops is obtained based on the derived asymptotic outage probability expressions.

Performance of Nth Worst Full-Duplex Relay Selection over Nakagami-M Fading Channels

The performance analysis of Nth worst relay selection for the full-duplex (FD) mode over Nakagami-m fading channels is studied. We assume the relay employs the amplify-and-forward (AF) protocol. The closed-form expres-sions for the outage performance in terms of the received signal-to-noise ratio cumulative distribution function are derived. In the high signal-to-noise ratio regime, asymptotic outage probability is also investigated. Based on these expressions, the effect of several important network parameters, i.e., the number of relays and the order of selected relay, as well as the quality of the relay links, source-relay links, relay-destination links, are analytically characterized. Finally, numerical results are provided to verify and illustrate our mathematical analysis.

Performance Analysis of Secrecy Outage Probability for AF-Based Partial Relay Selection with Outdated Channel Estimates

We study the secrecy outage probability of the amplify-and-forward (AF) relaying protocol, which consists of one source, one destination, multiple relays, and multiple eavesdroppers. In this system, the aim is to transmit the confidential messages from a source to a destination via the selected relay in presence of eavesdroppers. Moreover, partial relay selection scheme is utilized for relay selection based on outdated channel state information where only neighboring channel information (source-relays) is available and passive eavesdroppers are considered where a transmitter does not have any knowledge of eavesdroppers’ channels. Specifically, we offer the exact secrecy outage probability of the proposed system in a one-integral form as well as providing the asymptotic secrecy outage probability in a closed-form. Numerical examples are given to verify our provided analytical results for different system conditions.

Outage Analysis of Partial Relay Selection Schemes with Feedback Delay and Channel Estimation Errors in Nonidentical Rayleigh Fading Channels

This paper investigates the impact of the channel estimation error and outdated channel state information (CSI) on the outage performances of partial relay selection (PRS) and efficient partial relay selection (EPRS). Considering imperfect channel estimation and outdated CSI with decode-and-forward (DF) relaying strategy, closed-form expressions for exact outage probabilities and asymptotic outage probabilities for PRS and EPRS are provided assuming independent and nonidentically distributed Rayleigh fading channels. Numerical investigations verify the analytical expression for outage probability and show how much performance is degraded by the channel estimation errors and the feedback delay that causes the outdated CSI.

Outage Analysis of Multi-Relay Networks With Hardware Impairments Using SECps Scheduling Scheme in Shadowed-Rician Channel

In this paper, we investigate the effect of hardware impairments on the performance of dual-hop amplify-and-forward (AF)/decode-and-forward (DF) multiple relaying networks using switch-and-examine combining with post-selection (SECps) scheduling scheme in shadowed-Rician (SR) channel. Moreover, we consider a more general network, where the hard impairments are both considered at source, relays, and destination. Specifically, to decrease the high-implementation cost, the SECps scheme is adopted to choose an appropriate relay. To evaluate the performance of the considered system, we derive the novel closed-form expression of the outage probability for the AF and DF protocol, respectively. We also derive the asymptotic outage probability results at high SNRs for the DF protocol, which provides a fast way to evaluate the impact of hardware impairments on the dual-hop relay networks in the SR channel. In addition, simulation results are given to validate the correctness of the analytical results.

User-Centric Interference Nulling in Downlink Multi-Antenna Heterogeneous Networks

Heterogeneous networks (HetNets) have strong interference due to spectrum reuse. This affects the signal-to-interference ratio (SIR) of each user, and hence is one of the limiting factors of network performance. However, in previous works, interference management approaches in HetNets are mainly based on interference level, and thus cannot effectively utilize the limited resource to improve network performance. In this paper, we propose a user-centric interference nulling (IN) scheme in downlink two-tier HetNets to improve network performance by improving each user's SIR. This scheme has three design parameters: the maximum degree of freedom for IN (IN DoF), and the IN thresholds for the macro and pico users, respectively. Using tools from stochastic geometry, we first obtain a tractable expression of the coverage (equivalently outage) probability. Then, we characterize the asymptotic behavior of the outage probability in the high reliability regime. The asymptotic results show that the maximum IN DoF can affect the order gain of the asymptotic outage probability, while the IN thresholds only affect the coefficient of the asymptotic outage probability. Moreover, we show that the IN scheme can linearly improve the outage performance, and characterize the optimal maximum IN DoF which minimizes the asymptotic outage probability.

Performance Analysis and Power Allocation for Underlay Cognitive MIMO Relaying Networks with Transmit Antenna Selection Under Antenna Correlation

In this paper, we examine transmit antenna selection with receiver maximal ratio combining (TAS/MRC), and selection combining (TAS/SC) in underlay multiple-input multiple-output cognitive relay networks with decode-and-forward relaying protocol, considering optimal and suboptimal cases. The considered secondary user (SU) network consists of a source, a relay and a destination each equipped with multiple correlated antennas. On the other hand, the primary network is composed of L primary users (PU) destinations, each of which is equipped with multiple correlated antennas. The SU transmission power is limited to the minimum between the maximum allowable power for transmission and the maximum interference power allowed by the PU network. In the analysis, all the channel coefficients between the PU and SU networks and between the SU nodes are assumed to follow independent and identically distributed (i.i.d.) Rayleigh fading distribution. Hence, new exact closed-form expressions are derived to study the outage performance of the considered CRN system. Moreover, for the high SNR values, simple asymptotic expressions for the outage probability are obtained to get more insights on the characterization of the achievable diversity orders and coding gains. The impact of antenna correlation on the system outage probability is investigated for special correlation cases. To enhance SU network performance, a power allocation optimization problem is formulated to minimize the SU asymptotic outage probability by optimally distributing the SU power budget between the SU source and SU relay under the constraints of total allowable SU transmission power and maximum allowable PU interference limit. The derived analytical formulas herein are supported by numerical and simulation results to clarify the main contributions. The results show that although the antenna correlation harms the system coding gain, the considered system can still achieve a full diversity order. Also, The results show that although the outage performance of optimal case outperforms the suboptimal case, the optimal case is more complicated compared to the suboptimal one. Moreover, the optimal power allocation solutions enhance the system outage performance compared to equal distribution model.

Influence of Channel Information Imperfection on Outage Probability of Cooperative Cognitive Networks with Partial Relay Selection

Influence of channel information imperfection on outage probability of cooperative cognitive networks with partial relay selection over independent and non-identical Rayleigh fading channels and under peak transmit power constraint and interference power constraint is thoroughly analyzed in this paper. To eliminate time-consuming simulations, we propose both exact and asymptotic outage probability expressions in closed-form, which facilitate in quickly evaluating this influence in key operation parameters and acquiring useful insights into performance limits. For comparison, we also derive similar expressions for two benchmark communications schemes in cognitive radio networks, namely direct transmission and dual-hop communications with partial relay selection. Various results show considerable system performance deterioration and performance saturation owing to channel information imperfection, and superiority of cooperative communications to direct transmission and dual-hop communications.

Physical layer security of underlay cognitive radio using maximal ratio combining

We investigate the secrecy outage performance of maximal ratio combining (MRC) in cognitive radio networks over Rayleigh fading channels. In a single-input multiple-output wiretap system, we consider a secondary user (SU-TX) that transmits confidential messages to another secondary user (SU-RX) equipped with M (M ≥ 1) antennas where the MRC technique is adopted to improve its received signal-to-noise ratio. Meanwhile, an eavesdropper equipped with N (N ≥ 1) antennas adopts the MRC scheme to overhear the information between SU-TX and SU-RX. SU-TX adopts the underlay strategy to guarantee the service quality of the primary user without spectrum sensing. We derive the closed-form expressions for an exact and asymptotic secrecy outage probability.

Security-Reliability Trade-Off Analysis for Multiuser SIMO Mixed RF/FSO Relay Networks With Opportunistic User Scheduling

In this paper, we study the performance of multiuser single-input multiple-output mixed radio frequency (RF)/free space optical (FSO) relay network with opportunistic user scheduling. The considered system includes multiple users, one amplify-and-forward relay, one destination, and a multiple-antenna eavesdropper. The users are connected with the relay node through RF links and the relay is connected with the destination through an FSO link. Both maximum ratio combining and selection combining schemes are used at the multiple-antenna relay to combine the signal received from the best user on different antennas. The RF/FSO channels models are assumed to follow Nakagami- $m$ /gamma-gamma fading models with pointing errors. Closed-form expressions are derived for the outage probability, average symbol error probability, and ergodic channel capacity. Then, the power of the selected best user is determined to minimize the system asymptotic outage probability under the dominant RF or FSO link. Then, the considered system secrecy performance is investigated, where the closed-form expressions for the intercept probability are derived. Finally, we propose a new cooperative jamming model in which the worst user is selected by the authorized system to jam the existing eavesdropper. Monte-Carlo simulations are provided to validate the achieved exact and asymptotic results.

Performance Analysis of SNR-Based Decode-and-Forward Opportunistic Relaying in the Presence of Cochannel Interference

Opportunistic relaying (OR) for cooperative communications has been proposed as a technique to provide remarkable gains in multiple-relay cooperative networks. In this paper, we study the effect of cochannel interference (CCI) in the decode-and-forward (DF) OR scheme under independent but not necessarily identically distributed (i.n.i.d) Rayleigh fading channels. In particular, we consider the OR scheme with a signal-to-noise ratio (SNR)-based selection criterion and with the destination-performing maximal ratio combining of the signals from the source and the best relay. We derive approximate but tight closed-form expressions for the outage probability (OP) of the SNR-based OR in the presence of CCI. Moreover, we investigate the asymptotic behavior of the OP of the SNR-based OR. The asymptotic OP for OR with a signal-to-interference-plus-noise ratio (SINR)-based selection criterion is also provided. We examine the diversity orders and coding gains of both criteria under CCI. The result shows that the SNR-based OR is more susceptible to interference at the relays than interference at the destination. We further analytically compare the SNR- and the SINR-based OR schemes. Finally, to verify the analytical results, Monte Carlo simulations are performed, in which more benefits can be gained by using the SINR-based OR when more relays are used.

Performance analysis of mixed RF/FSO systems with STBC users

In consideration of either fixed or variable gain relay scheme, end-to-end performance analysis of a dual-hop relay system over the asymmetric links composed of both radio-frequency (RF) and free-space optical (FSO) links with space time block coding (STBC) and two transmit antennas for the RF users is provided. In the analysis the RF links are modeled as the Rayleigh fading channel and the FSO link as the Gamma–Gamma fading channel with pointing errors. Closed-form expressions for the end-to-end outage probability (OP) and average symbol error probability (ASEP) in terms of the Meijer’s G functions are obtained. Based on the asymptotic expansion of the Meijer’s G function at high-SNR region, the asymptotic OP performance of the mixed RF/FSO systems with the fixed gain relay and misalignment FSO channels is discussed. Numerical simulations demonstrate that the system performance deteriorates when channel conditions become severe, and the RF users using STBC can achieve better communication quality than that of the regular RF users. In addition, the system with the fixed gain relay is better than that with the variable gain relay under the same average SNR in both the RF links and the FSO links.

MIMO Cognitive Relay Networks With Correlated Antennas Over Rayleigh Fading Channels

In this paper, we examine orthogonal space–time block coding with receiver maximal ratio combining (OSTBC/MRC) and selection combining (OSTBC/SC) in multiple-input–multiple-output (MIMO) decode-and-forward (DF) relay networks with underlay spectrum sharing, considering optimal and suboptimal cases. The secondary network under consideration is equipped with multiple correlated antennas at the source, the relay, and the destination. On the other hand, the primary network is composed of $L$ primary users (PUs), each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing, the transmit power condition is related by an interference limit on the primary network and the maximum transmission power in the secondary network. In particular, new exact expressions for the outage probability of the adopted system models are obtained. Moreover, simple asymptotic expressions for the outage probability are provided to enable the characterization of the achievable diversity orders and coding gains. To enhance the secondary network performance, optimal power allocation (PA) between the secondary source and the secondary relay is obtained based on the asymptotic outage probability under the constraints of total allowable transmit power at the secondary user (SU) and maximum allowable interference power limit at the PU. The derived analytical formulas herein are supported by numerical results to clarify the main contributions.

Outage Performance of Underlay Multihop Cognitive Relay Networks With Energy Harvesting

This letter studies the outage performance of multihop cognitive relay networks with energy harvesting in underlay paradigms, wherein the secondary users are powered by a dedicated power beacon (PB) and their transmit powers are subject to the harvested energy from PB and the interference constraint from the primary user. We derive the exact outage probability for Rayleigh block fading and prove that the outage probability is monotonically decreasing with respect to the transmit power of PB. Furthermore, we derive the asymptotic outage probability to study the outage saturation phenomenon and propose an iterative algorithm that jointly optimizes the transmit power of PB and the harvest-to-transmit ratio to approximate the minimum outage probability. Simulation results validate the theoretical results.