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Joint Relay and Jammer Selection for Secure Two-Way Relay Networks

Jingchao Chen, Rongqing Zhang, Lingyang Song, Zhu Han, Bingli Jiao

arXiv:1111.7108v1cs.IT

TL;DR

The paper studies physical-layer security in two-way cooperative networks where secrecy constraints and an eavesdropper complicate relay selection. It selects an AF relay and one or two jammers, and introduces switching between jamming and non-jamming modes. Jamming is effective for sparsely distributed nodes over a certain power range, while the hybrid OSW scheme provides the highest secrecy rate across almost the whole transmitted-power regime.

  • Problem

    Physical-layer security in two-way cooperative schemes with secrecy constraints has not yet been well investigated.

  • Method

    The paper selects one conventional AF relay and one or two jamming nodes to assist two-way communication and interfere with the eavesdropper.

  • Results

    The hybrid OSW scheme provides the highest secrecy rate in almost the whole transmitted-power regime, while jamming schemes are effective for sparsely distributed nodes within a certain power range.

  • Takeaways & Limitations

    Non-jamming schemes are preferred when intermediate nodes are confined close together, whereas intelligent switching adapts between the two modes.

Abstract

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In this paper, we investigate joint relay and jammer selection in two-way cooperative networks, consisting of two sources, a number of intermediate nodes, and one eavesdropper, with the constraints of physical layer security. Specifically, the proposed algorithms select two or three intermediate nodes to enhance security against the malicious eavesdropper. The first selected node operates in the conventional relay mode and assists the sources to deliver their data to the corresponding destinations using an amplify-and-forward protocol. The second and third nodes are used in different communication phases as jammers in order to create intentional interference upon the eavesdropper node. Firstly, we find that in a topology where the intermediate nodes are randomly and sparsely distributed, the proposed schemes with cooperative jamming outperform the conventional non-jamming schemes within a certain transmitted power regime. We also find that, in the scenario in which the intermediate nodes gather as a close cluster, the jamming schemes may be less effective than their non-jamming counterparts. Therefore, we introduce a hybrid scheme to switch between jamming and non-jamming modes. Simulation results validate our theoretical analysis and show that the hybrid switching scheme further improves the secrecy rate.

I. INTRODUCTION

The paper addresses physical-layer security in two-way cooperative networks, where secrecy constraints and eavesdroppers complicate relay selection. It proposes joint relay–jammer selection and a hybrid switching scheme, whose effectiveness depends on node topology and transmitted power.

  • Physical-layer security is needed because a stronger source–wiretapper channel can reduce the perfect secrecy rate to zero.
  • Prior work uses cooperative relaying and cooperative jamming to overcome secrecy limitations in wireless networks.Cooperative jamming interferes with the eavesdropper using codewords independent of source messages.
  • Two-way relay channels are attractive for their bandwidth efficiency and potential cellular and peer-to-peer applications.
  • Physical-layer security under secrecy constraints in two-way schemes has not yet been well investigated.
  • The proposed network selects one conventional AF relay and up to two jammers to assist source communication and degrade eavesdropper links.The destinations cannot mitigate the artificial interference, so jamming also degrades desired information channels.
  • The selection algorithms jointly seek assistance for the sources and interference against the eavesdropper under secrecy constraints.
  • Jamming schemes improve secrecy rate substantially only within a certain transmitted-power range and can be less efficient in particular scenarios.
  • The hybrid scheme switches between jamming and non-jamming modes to address scenarios where jamming is less effective.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system is a half-duplex two-way relay network with two sources, intermediate nodes, and an eavesdropper. It models AF relaying, optional cooperative jamming, fading and noise, eavesdropper combining, channel-knowledge assumptions, and ergodic secrecy capacity.

  • A. System Model: The network contains two sources, one eavesdropper, and an intermediate-node set of K nodes.
  • A. System Model: Half-duplex operation divides communication into two phases because intermediate nodes cannot transmit and receive simultaneously.
  • A. System Model: In the broadcasting phase, the sources transmit data to intermediate nodes, while a selected jammer sends intentional interference.The unknown jamming signal also degrades relay-link performance.
  • A. System Model: The eavesdropper can combine signals from both phases using maximal ratio combining to optimize its eavesdropping SINR.
  • A. System Model: The selected relay forwards source messages using amplify-and-forward, and a second intermediate node can serve as another jammer.The destinations cannot mitigate artificial interference.
  • A. System Model: The model assumes slow, flat, block Rayleigh fading with channels static over one coherence interval and independently changing afterward.
  • A. System Model: Channel gains use distance-based path loss, and AWGN has zero mean and unit variance.Source, relay, and jammer powers are represented by PS, PR, and PJ, with PJ = PR/L and L ≫1.
  • A. System Model: The framework considers global instantaneous channel knowledge or average eavesdropper-link knowledge when instantaneous information is unavailable.The resulting overall secrecy performance is measured by ergodic secrecy capacity.

B. Problem Formulation

The paper formulates relay and jammer selection to maximize instantaneous secrecy rates under different channel-feedback conditions, while characterizing overall performance through ergodic secrecy capacity.

  • The instantaneous secrecy rate for source Si is determined for the selected node set Sin, with [x]+ defined as max{0, x}.
  • Overall secrecy performance is measured by ergodic secrecy capacity, defined as the expectation of the two sources’ summed secrecy rates.
  • The selection objective is to choose relay R and jammers J1, J2 to maximize instantaneous secrecy rate under different channel-feedback conditions.
  • The selected jammers J1* and J2* may be the same node across the two communication phases.

C. Selection without Jamming

The conventional selection scheme excludes jamming and selects the relay using source-to-destination link quality, without incorporating eavesdropper channels.

  • In the conventional cooperative network, relay selection proceeds without assistance from jamming nodes.
  • The conventional algorithm selects the relay according to instantaneous SNR on the source-to-destination links only.
  • The conventional SINR formulation describes channels between the sources and does not consider the eavesdropper.
  • Because eavesdropping links are excluded, the CS algorithm may not support secrecy-constrained systems despite being effective without an eavesdropper.

2) Optimal Selection (OS):

The optimal selection approach jointly considers both transmission phases and balances relay assistance against interference at the eavesdropper to maximize overall secrecy performance.

  • 3) Suboptimal Selection (SS):: The suboptimal selection uses knowledge set ψ1, an average estimate of eavesdropper links, avoiding instantaneous channel-feedback requirements.
  • 2) Optimal Selection (OS):: The selection techniques account for both transmission phases when choosing relay and jammers to maximize the overall expectation of secrecy rate.
  • 2) Optimal Selection (OS):: The optimal selection assumes knowledge set ψ0, which provides instantaneous channel knowledge for all links.
  • 2) Optimal Selection (OS):: The OS approach selects relay and jammer sets that promote source assistance while minimizing the eavesdropper’s SINR.
  • 2) Optimal Selection (OS):: Relay and jammer selection involves a trade-off because reducing |hJ1,R| can raise Γi while also increasing ΓEi.

B. Optimal Selection with Max-Min Instantaneous Secrecy Rate (OS-MMISR)

The OS-MMISR scheme maximizes the weaker source’s instantaneous secrecy rate with reduced complexity, while hybrid switching addresses cases where continuous jamming harms legitimate links.

  • B. Optimal Selection with Max-Min Instantaneous Secrecy Rate (OS-MMISR): The reduced-complexity OS-MMISR algorithm selects intermediate nodes that maximize the minimum secrecy rate of the two users for near-optimal performance.
  • B. Optimal Selection with Max-Min Instantaneous Secrecy Rate (OS-MMISR): Individual secrecy rates matter because a low rate for one source can make the whole system secrecy-inefficient.
  • B. Optimal Selection with Max-Min Instantaneous Secrecy Rate (OS-MMISR): OS-MMISR maximizes the worse instantaneous secrecy rate of the two source nodes under knowledge set ψ0.
  • Continuous jamming can interfere directly with destinations and degrade relay-to-destination links, especially when J2 is close to a destination.
  • The hybrid scheme switches between OS-MSISR and OS to reduce jamming’s bottleneck effect.
  • If condition (39) holds, OS-MSISR provides higher instantaneous secrecy rate than OS; otherwise, OS is preferred.
  • Because channel coefficients are uncertain, OSW is expected to outperform either continuous jamming or non-jamming alone.

D. Suboptimal Selection with Maximum Sum Instantaneous Secrecy Rate (SS-MSISR)

SS-MSISR applies maximum-sum secrecy-rate selection using available average eavesdropper-channel knowledge, while suboptimal switching selects between jamming and non-jamming modes. Its design reflects that jamming can impair legitimate relay-destination links and is not always beneficial.

  • SS-MSISR: The practical SS-MSISR implementation uses available channel information ψ1 rather than relying only on instantaneous eavesdropper-link knowledge.The passages state that average knowledge of eavesdropper links is available from long-term supervision, whereas instantaneous quality may require specific protocols.
  • SS-MSISR: SS-MSISR uses the average eavesdropper-link behavior in ψ1 to seek the maximum worse instantaneous secrecy rate.The selection objective is based on the pair {RS1(R, J1, J2), RS2(R, J1, J2)}.
  • Suboptimal switching: Suboptimal switching selects between SS-MSISR and SS modes using a switching criterion based on ψ1.The scheme is introduced because jamming is not always positive for system performance.
  • Jamming assumption: The proposed jamming design assumes the jammers degrade eavesdropper links without adversely affecting legitimate links, but this assumption can fail.In particular scenarios, OSKJ is outperformed by OSW and SSW because jamming changes α and can affect the system’s links.
  • Reference scheme: The control comparison scheme allows destinations to decode the jamming signal while the eavesdropper cannot, and treats OSKJ as a numerical reference.Under this configuration, the source-to-eavesdropper SINR remains ΓEi.

IV. PERFORMANCE ANALYSIS

The performance analysis compares asymptotic secrecy behavior with and without continuous jamming. Non-jamming secrecy rates continue increasing with power, whereas continuous-jamming rates converge, producing a crossover and a power range where jamming is advantageous.

  • Analysis scope: The analysis studies high-power asymptotic performance and qualitative secrecy behavior for the proposed jamming and non-jamming selection schemes.It evaluates typical scenarios under the system model and examines secrecy performance as transmitted power increases.
  • Selections without jamming: 0.3322 is the approximate slope of the non-jamming OS ergodic secrecy-rate curve as transmitted power increases.The analysis describes the OS curve as having a linear increment with transmitted power.
  • Selections with continuous jamming: At high transmitted power, continuous-jamming secrecy rates converge because both legitimate and eavesdropper SINRs become independent of PS.The ergodic secrecy rate therefore stops increasing and approaches a fixed value.
  • Crossover behavior: A crossover point P′ separates a lower-power range where jamming outperforms non-jamming from a higher-power range where it loses that advantage.Continuous-jamming schemes share the same asymptotic behavior, while OSW and SSW are exceptions to the stated limited-range comparison.
  • Crossover behavior: Except for OSW and SSW, the proposed continuous-jamming techniques outperform non-jamming schemes only within a certain transmitted-power range.The analysis notes that practical transmitted power is limited and does not increase infinitely.

C. Secrecy Performance with Sparsely Distributed Intermediate Nodes

Jamming is effective for sparsely distributed intermediate nodes within a crossover-limited power range, but clustering can make interference harmful. Hybrid switching schemes preserve stronger secrecy performance across broader configurations and power ranges.

  • Sparse distribution: When intermediate nodes are randomly and sparsely distributed, continuous-jamming selection can provide higher ergodic secrecy rates than non-jamming below P′.The weak J1-to-R interference link supports the predicted advantage in this power range.
  • Sparse distribution: Above P′, non-jamming secrecy rates continue growing with slope 0.3322, while continuous-jamming rates converge.Thus, the jamming advantage is limited to the lower-power range.
  • Hybrid selection: For secrecy measured by minimum secrecy capacity, OS-MMISR and SS-MMISR optimize overall system secrecy, while OSW and SSW perform better across the full power range.The hybrid schemes overcome the bottleneck caused by negative interference on relay-destination links.
  • Clustered distribution: When intermediate nodes cluster closely, continuous-jamming selection loses efficiency because selected jammers can strongly interfere with the relay or a destination.A strong relay-eavesdropper direct link can also seriously reduce secrecy in the clustered configuration.
  • Hybrid selection: In the clustered configuration, hybrid protocols OSW and SSW remain the most effective schemes when performance is measured by ergodic secrecy rate.The reported results support the practical value of intelligent switching.
  • Eavesdropper near a source: When the eavesdropper is close to a source, jamming is necessary over a broad power range, and hybrid schemes remain the best selection techniques across the whole power scope.The direct source-eavesdropper link is strong in this configuration.

V. NUMERICAL RESULTS

Numerical simulations validate the analysis across sparse and clustered relay topologies. Cooperative jamming helps in selected power regimes, while hybrid switching provides robust secrecy performance across configurations.

  • Sparse-node topology: Average channel knowledge produces nearly the same performance as optimal schemes in the sparse topology, and OS-MSISR is about 0.25 BPCU higher than OS-MMISR.The same relative comparison is observed for the corresponding suboptimal schemes.
  • Sparse-node topology: OSW outperforms the other selection techniques, especially at high power, while SSW achieves nearly the same performance in the sparse topology.At low power, OSW is about 1.2 BPCU higher than OS; at high power, it outperforms both OS-MSISR and OS by a large margin.
  • Secrecy outage probability: For secrecy outage probability at RT = 0.2 BPCU, jamming is better below approximately 20 dB, whereas non-jamming performs better outside that range; OSW outperforms non-switching schemes.The comparison uses transmitted power PS and a target secrecy rate RT of 0.2 BPCU.
  • Clustered-node topologies: When nodes cluster near the eavesdropper, jamming is worse than non-jamming over most power values, but OSW and SSW still provide the highest secrecy rates.The continuous-jamming advantage persists over a slightly larger range because there is no strong R → E link.

VI. CONCLUSIONS

The paper develops joint relay and jammer selection for physically secure two-way cooperative networks, selecting one relay and one or two jammers. Jamming schemes help in sparse topologies over certain power ranges, while intelligent switching provides strong secrecy performance across the transmitted-power regime.

  • Joint relay and jammer selection: The proposed schemes opportunistically select one conventional AF relay and one or two jamming nodes to protect transmission against eavesdroppers.The relay assists communication between the sources, while jammers create intentional interference at the eavesdropper during different transmission phases.
  • Sparse-node scenarios: Jamming schemes are effective within a certain transmitted power range when intermediate nodes are sparsely distributed.The reported schemes include OS-MSISR, OS-MMISR, SS-MSISR, and SS-MMISR.
  • Clustered-node scenarios: Non-jamming schemes are preferred when intermediate nodes are confined close to each other.This reflects a topology-dependent difference between cooperative-jamming and conventional selection strategies.
  • Hybrid switching: The OSW scheme switches between jamming and non-jamming modes and provides the highest secrecy rate across almost the whole transmitted-power regime.Its operation requires instantaneous eavesdropper-channel knowledge.
  • Hybrid switching: The suboptimal SSW scheme uses average eavesdropper-channel knowledge and achieves secrecy performance comparable to OSW.This makes SSW more practical than OSW under the stated channel-knowledge conditions.
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