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Cooperative Jamming for Secure Communications in MIMO Relay Networks

Jing Huang, A. Lee Swindlehurst

arXiv:1107.1544v1cs.IT

TL;DR

Eavesdroppers threaten secure communication in conventional relay networks, especially when they can wiretap both hops. The paper uses inactive relay-network nodes as cooperative jammers and develops linear precoding for single- and multiple-stream DF relaying, including unknown eavesdropper CSI. The proposed schemes produce large secrecy gains, with GSVD-based partial cooperative jamming significantly outperforming GSVD relaying without jamming.

  • Problem

    Secure communication is impeded when an eavesdropper can wiretap both hops of a relay network.

  • Method

    The paper develops cooperative jamming and linear-precoding schemes for single- and multiple-stream DF relaying, including GSVD-based designs and unknown-eavesdropper-CSI operation.

  • Results

    GSVD-based partial cooperative jamming shows significant performance improvement over GSVD relaying without jamming, while cooperative jamming provides large secrecy gains overall.

  • Takeaways & Limitations

    Using inactive nodes for cooperative jamming increases secrecy in two-hop relay networks, including when the eavesdropper’s CSI is unknown.

Abstract

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Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for two-hop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decode-and-forward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closed-form jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)-based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVD-based cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming.

I. INTRODUCTION

The paper addresses physical-layer security in two-hop MIMO relay networks where Eve can wiretap both transmission phases. It develops cooperative jamming and precoding strategies for single- and multiple-stream transmission, including settings with unknown eavesdropper CSI.

  • Motivation and scope: The proposed half-duplex relay system lets Eve wiretap both transmission phases, unlike prior work considering only the relay-to-destination link.The source, relay, and destination rely on themselves for jamming because no outer helpers are available.
  • Cooperative jamming: Normally inactive source and destination nodes transmit jamming signals as temporary helpers during their inactive phases.The paper distinguishes full cooperative jamming, where both helpers transmit simultaneously, from partial cooperative jamming.
  • Single-stream design: For a single-antenna relay and single data stream, the paper jointly designs jamming beamformers and power allocation for secrecy-rate maximization or power minimization at a target secrecy rate.A suboptimal zero-forcing constraint makes jamming and information signals orthogonal at legitimate nodes, enabling closed-form beamformers; geometric programming determines power allocation.
  • Multiple-stream design: For multiple data streams, the paper proposes GSVD-based relaying and cooperative jamming with a corresponding power-allocation strategy.Unlike the single-stream zero-forcing design, GSVD-based jamming is not generally orthogonal to the desired signal.
  • Unknown eavesdropper CSI: When Eve’s CSI is unknown, the transmitter allocates resources to guarantee a fixed target rate and uses the remainder to jam Eve.Known Eve CSI would instead permit beamformer optimization to enhance intended transmission while suppressing leakage.

II. SYSTEM MODEL

The system is a two-phase, half-duplex four-terminal relay network with Alice, Bob, a decode-and-forward relay, and Eve. Alice communicates with Bob through the relay without a direct high-rate link, while inactive nodes may transmit jamming signals.

  • Network components: The four-terminal network consists of Alice, Bob, a decode-and-forward relay, and Eve.The message is transmitted from Alice to Bob through the relay.
  • Transmission protocol: All nodes operate half-duplex in two-hop time-division multiple access: Alice transmits first while the relay listens, then the relay transmits.There is no direct Alice–Bob communication link, except possibly for low-rate control or channel-state information.
  • Operating assumption: Relaying is considered appropriate when direct high-rate communication is too expensive under the available power constraints.Low-rate control information may still be exchanged directly.
  • Jamming and antennas: Alice and Bob can transmit jamming signals during phases when they are otherwise inactive, subject to accounting for Alice’s interference at Bob.All nodes generally have multiple antennas, although the relay is also studied with a single antenna.
  • Signal processing: All nodes, including Eve, use linear precoding and receive beamforming.The antenna counts are denoted N_a, N_b, N_r, and N_e for Alice, Bob, the relay, and Eve.

A. Relay Transmission

During the first hop, Alice sends information to the relay, which forwards it to Bob in the second hop while Eve observes both phases. Linear beamformers and diagonal power loading matrices describe the transmitted signals under per-phase power constraints.

  • First hop: In the first phase, Alice transmits the information signal to the relay, while both the relay and Eve receive it.The relay and Eve experience naturally occurring noise.
  • Beamforming model: Alice and the relay use linear transmit beamformers T_a and T_r, with k denoting the number of transmitted data streams.The model defines m = rank{H_ar}, n = rank{H_rb}, and s = min(m, n).
  • Channel and noise assumptions: Channel matrices H_ij describe links among Alice, Bob, Eve, and the relay, and remain fixed over both hops.Noise vectors at all nodes are assumed Gaussian with covariance σ^2I.
  • Second hop: In the second phase, the relay transmits the information signal toward Bob, while Eve also receives the relay transmission.The relay uses transmit beamformer T_r for its transmitted signal vector.
  • Power loading: The information signals are modeled as scaled versions of a common vector using diagonal power-loading matrices D_a and D_r.The normalization E{zz^H} = I lets D_a and D_r enforce the transmit-power constraints.

B. Cooperative Jamming

The paper models two-phase cooperative jamming in which Alice, Bob, and the relay transmit information and jamming signals under global or individual power constraints. It distinguishes full and partial cooperative jamming and allows jamming to be nulled at legitimate receivers or to leak interference while affecting Eve more strongly.

  • B. Cooperative Jamming: Alice, Bob, and the relay can transmit information and jamming signals across the two phases of the relay protocol.In phase 2, the relay transmits information while the relay and Alice transmit jamming; Bob may also jam simultaneously.
  • B. Cooperative Jamming: Jamming beamformers can project interference into a subspace orthogonal to information signals or permit limited leakage to create more interference at Eve.The latter design is discussed for the GSVD-based transmission strategy.
  • B. Cooperative Jamming: Full cooperative jamming uses nonzero jamming components from both designated sources, whereas partial cooperative jamming sets one component to zero.The paper excludes FCJ when Eve’s CSI is known because splitting Alice’s power between data and jamming is suboptimal, but studies PCJ with Bob jamming.
  • B. Cooperative Jamming: When Eve’s CSI is unavailable, the paper recommends FCJ and discusses this setting separately.The unknown-CSI case changes the choice of cooperative-jamming strategy.
  • B. Cooperative Jamming: The framework considers both global and individual transmit-power constraints for the participating nodes.The global constraint covers aggregate transmit power, while individual constraints are investigated separately.

C. Performance Metric

The paper evaluates relay-network security using a secrecy-rate expression based on the mutual-information difference between the legitimate destination and Eve. When Eve’s CSI is completely unavailable, this expression may not be achievable, so the paper instead uses it to compare physical-layer strategies and adopts a QoS-constrained robust jamming approach.

  • C. Performance Metric: The achievable secrecy-rate metric is the maximum mutual-information difference between the source–destination and source–eavesdropper links over input covariance matrices.The metric assumes Gaussian inputs and is written using I_d and I_e.
  • C. Performance Metric: For half-duplex two-hop relay channels, the same secrecy-rate expression has been used to evaluate amplify-and-forward, decode-and-forward, compress-and-forward, and cooperative-jamming schemes.The cited relay studies apply the metric across multiple relaying modes and cooperative-jamming settings.
  • C. Performance Metric: The analysis focuses on repetition coding at the relay because independent codebooks are expected to yield smaller secrecy rates when encoding schemes and protocols are public.The expression is valid for both independent and repetition codebooks, but the paper restricts attention to repetition coding.
  • C. Performance Metric: When Eve’s CSI is completely unavailable, the secrecy-rate expression may not represent an achievable secrecy rate.An achievable-rate expression for the relay network in this setting remains an open problem.
  • C. Performance Metric: Without Eve’s CSI, transmission parameters cannot optimize the secrecy-rate expression, so the paper targets legitimate-receiver QoS and robustly jams potential eavesdroppers with remaining resources.The mutual-information difference remains a valid relative-security metric for comparing competing approaches.

III. SECURE RELAYING WITH KNOWN ECSI

With Eve’s CSI available to the relay network, the paper first studies a single-antenna DF relay and then extends the analysis to a MIMO relay.

  • III. SECURE RELAYING WITH KNOWN ECSI: The known-ECSI analysis assumes Eve’s CSI is available to the relay network.The section proceeds from a single-antenna relay to a MIMO relay scenario.
  • III. SECURE RELAYING WITH KNOWN ECSI: The section’s progression uses the single-antenna case as the initial setting before investigating MIMO relaying.This establishes the order of the known-ECSI treatment.
  • III. SECURE RELAYING WITH KNOWN ECSI: The relay configurations considered are a single-antenna DF relay followed by a more complicated MIMO-relay scenario.These cases organize the secure-relaying analysis under known ECSI.

A. Single data stream relaying

For a single-antenna DF relay, only one data stream is transmitted, and the paper designs jamming to avoid interference at legitimate reception while reducing Eve’s information.

  • A. Single data stream relaying: A single-antenna DF relay supports only one transmitted data stream.The case assumes N_r = 1.
  • A. Single data stream relaying: Under PCJ, Alice’s jamming can be designed to be completely nulled at the relay.The beamformer is selected so the relay does not receive the jamming component.
  • A. Single data stream relaying: The first-phase beamformer uses the generalized eigenvector associated with the largest generalized eigenvalue.This construction achieves the secrecy capacity for the corresponding single-hop MISO wiretap channel.
  • A. Single data stream relaying: In the second phase, jamming is designed orthogonally to the one-dimensional information-signal subspace so it does not affect Bob’s information reception.This exploits the relay-to-Bob channel geometry.

1) Maximum secrecy rate with power constraints:

The paper formulates secrecy-rate maximization under global and individual power constraints for two-hop DF relaying. It derives beamforming and power-allocation procedures, including generalized-eigenvector jamming designs and GP-based optimization.

  • Problem formulation: The two-hop DF secrecy rate depends on the relay link and Eve’s combined observations across both transmission phases.The relay mutual information is constrained by the inferior phase, while Eve receives data during both phases.
  • Single data stream: For single-stream transmission, Alice’s and the Relay’s powers are adjusted so the two hop SINRs satisfy γar = γrb.This equalization improves power efficiency because the relay rate is limited by the inferior phase.
  • Single data stream: The optimal single-stream jamming covariance is rank one, so one-dimensional jamming is optimal for the corresponding Eve-SINR minimization.The beamformer is obtained from the principal generalized eigenvector of a matrix pencil.
  • Power allocation: The resulting single-stream power-allocation problem can be expressed as a geometric program under global or individual power constraints.The formulation uses posynomial and monomial constraints, enabling efficient global optimization after convex transformation.
  • Implementation: The proposed beamformers require iterative updates because the allocated power is initially unknown, but numerical experiments report few iterations and little added complexity.The algorithm is initialized with pa = P.

B. Multiple data stream relaying

For multiple data streams, the paper develops GSVD-based relaying and a partial cooperative-jamming strategy. GSVD separates the intended and eavesdropper channels into parallel dimensions, while jamming is applied in reverse by normally inactive nodes.

  • GSVD relaying: GSVD decomposes the intended and eavesdropper channels into parallel dimensions for multiple-stream secure relaying.The approach is motivated by GSVD wiretap-channel results that favor dimensions with s1,i ≥ s2,i at high SNR.
  • Simple GSVD-based relaying: The simple GSVD scheme treats each transmission phase as a standard wiretap channel without cooperative jamming.Alice and the Relay use GSVD-based transmit beamformers in the two phases.
  • Power allocation: The GSVD relaying secrecy rate is expressed through parallel-channel powers pa,i and pr,i, then optimized through a generally nonconvex power-allocation problem.Single condensation approximates posynomials by monomials so successive geometric programs can be solved.
  • Power allocation: The successive GP method converges to a point satisfying the original problem’s KKT conditions, from which the global optimum can consequently be obtained.The GP subproblems can be solved with interior-point methods having polynomial-time complexity.
  • Partial cooperative jamming: The partial cooperative-jamming scheme has Bob and Alice transmit jamming signals using GSVD transforms in reverse directions.This contrasts with the simple GSVD relaying scheme and introduces jamming energy into signals received by the Relay and Bob.
  • Cooperative-jamming design: Cooperative jamming uses normally inactive Bob and Alice as temporary helpers, while their jamming power is drawn from the per-hop total power budget.With known ECSI, reverse GSVD beamformers aim to direct jamming toward Eve while avoiding interference at the intended relay receiver.

IV. SECURE RELAYING WITH UNKNOWN ECSI

When Eve’s CSI is unknown, the paper compares partial and full cooperative jamming using information and jamming subspaces. Full cooperative jamming lets transmitters and helpers spread interference across additional dimensions while legitimate receivers reject it.

  • Unknown ECSI: The unknown-ECSI setting prevents Alice and the Relay from using Eve-dependent GSVD beamforming to selectively transmit information and jamming subspaces.The paper therefore considers subspace-based cooperative jamming designs.
  • Subspace design: The proposed strategy divides the signal space into orthogonal information and jamming subspaces, with both partial and full cooperative-jamming variants.The relay and destination use receive beamforming to separate the intended information subspace from interference.
  • PCJ and FCJ: In partial cooperative jamming, only information transmitters allocate jamming power, whereas full cooperative jamming also uses temporary helpers in the jamming subspace.Full cooperative jamming allows legitimate receivers to reject interference from that subspace.
  • Full cooperative jamming: Different transmitter and jammer channels prevent Eve from removing the jamming signal even when she knows the jamming subspace.The receiver broadcasts the subspace in the full-jamming design so interference can be aligned at the desired receiver.
  • Design tradeoffs: The design trades information-subspace dimension against jamming-subspace dimension and power, and assumes the Relay uses the same information dimension as Alice.Using different dimensions with more complicated coding is identified as future work.
  • Full cooperative jamming: Full cooperative jamming provides additional jamming dimensions beyond the preassigned phase-1 subspace because helpers have different channels to Eve.For phase 1, the preassigned jamming subspace has dimension Na−k, while helper channels can enlarge the subspace seen by Eve.
  • Power allocation: The unknown-ECSI algorithm first meets a fixed relay-link target rate, then allocates remaining dimensions and power to jamming, uniformly across available dimensions.Information powers are determined using water filling, while the partial scheme omits helper-supported jamming dimensions.

V. NUMERICAL RESULTS

Numerical results evaluate cooperative jamming under known and unknown eavesdropper CSI across antenna configurations, power constraints, locations, and rate constraints. The proposed schemes generally improve secrecy, with gains depending on power allocation, eavesdropper location, and antenna number.

  • Simulation setup: The simulations compare PCJ, simple GSVD relaying, GSVD-PCJ, FCJ, uniform allocation, and conventional relaying under global or individual power constraints.The study covers single- and multiple-stream relaying with known ECSI, plus unknown-ECSI cases.
  • Known ECSI: PCJ provides significant secrecy-rate improvement over traditional DF relaying in the medium- and high-SNR regime.At low transmit power, conventional relaying can outperform PCJ with individual or uniform allocation because inflexible jamming allocation wastes power that could support data transmission.
  • Known ECSI: Global power allocation improves jamming performance over fixed individual constraints, while geometric-programming allocation outperforms uniform allocation.These comparisons demonstrate that efficient allocation of power between information and jamming signals is important.
  • Eavesdropper location: Secrecy rate is smallest when Eve is at the midpoint and increases as Eve moves away, while the jamming-power fraction decreases.When Eve is closer to Alice or Bob, the other hop can be effectively jammed with minimal power by the nearer transmitter.
  • Multiple data streams: For multiple data streams, global-power GSVD-based cooperative jamming provides considerable secrecy-rate gains, whereas individual constraints reduce the benefit.With higher transmit power, individual-constraint jamming approaches or surpasses optimally allocated GSVD relaying, and optimized allocation outperforms uniform allocation.
  • Unknown ECSI: With unknown ECSI, no-jamming schemes provide little secrecy, FCJ increasingly outperforms PCJ as the target rate or Eve’s antenna number increases, and all methods degrade as Eve gains antennas.FCJ benefits from a higher-dimensional jamming subspace, while PCJ can level off or decline at high relay-rate constraints.

VI. CONCLUSIONS

The paper develops partial and full cooperative jamming strategies for two-hop decode-and-forward relay systems with an eavesdropper monitoring both transmission phases. It derives closed-form single-stream designs, GSVD-based multi-stream schemes, and resource-allocation methods, including settings with unknown eavesdropper CSI.

  • The paper proposes partial and full cooperative jamming strategies for two-hop DF relay systems with an eavesdropper wiretapping both transmission phases.
  • For single-stream relaying, secrecy-rate maximization and transmit-power minimization use zero-forcing jamming, yielding closed-form beamformers and power allocation.
  • For multiple streams, the paper proposes GSVD-based relaying without jamming and a GSVD-based partial cooperative jamming scheme.
  • The GSVD-based partial cooperative jamming scheme shows significant performance improvement despite using potentially suboptimal power allocation.
  • When eavesdropper CSI is unknown, the proposed schemes meet a target relay-network QoS and use remaining resources for jamming; full cooperative jamming is preferred.
  • The optimization formulation uses trace, semidefinite, and linear matrix inequality constraints, enabling efficient semidefinite programming and producing a rank-one jamming covariance.
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