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Optimal Relay Selection for Physical-Layer Security in Cooperative Wireless Networks

Yulong Zou, Xianbin Wang, Weiming Shen

arXiv:1305.0817v1cs.IT

TL;DR

The paper addresses secure relay selection in cooperative wireless networks with multiple relays and an eavesdropper. It proposes AF- and DF-based selection using wiretap information, derives intercept-probability results, and reports better performance than traditional selection and multiple-relay combining.

  • Problem

    The paper asks how optimal relay selection can improve physical-layer security against eavesdropping in cooperative networks with multiple relays.

  • Method

    It proposes P-AFbORS and P-DFbORS, compares them with traditional relay selection and MRC schemes, and derives closed-form intercept probabilities under Rayleigh fading.

  • Results

    The proposed AF and DF optimal relay-selection schemes achieve lower intercept probability than traditional relay selection and multiple relay combining in the reported numerical comparisons.

  • Takeaways & Limitations

    Using wiretap-link CSI in optimal relay selection improves the reported physical-layer security performance for both AF and DF protocols.

Abstract

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In this paper, we explore the physical-layer security in cooperative wireless networks with multiple relays where both amplify-and-forward (AF) and decode-and-forward (DF) protocols are considered. We propose the AF and DF based optimal relay selection (i.e., AFbORS and DFbORS) schemes to improve the wireless security against eavesdropping attack. For the purpose of comparison, we examine the traditional AFbORS and DFbORS schemes, denoted by T-AFbORS and TDFbORS, respectively. We also investigate a so-called multiple relay combining (MRC) framework and present the traditional AF and DF based MRC schemes, called T-AFbMRC and TDFbMRC, where multiple relays participate in forwarding the source signal to destination which then combines its received signals from the multiple relays. We derive closed-form intercept probability expressions of the proposed AFbORS and DFbORS (i.e., P-AFbORS and P-DFbORS) as well as the T-AFbORS, TDFbORS, T-AFbMRC and T-DFbMRC schemes in the presence of eavesdropping attack. We further conduct an asymptotic intercept probability analysis to evaluate the diversity order performance of relay selection schemes and show that no matter which relaying protocol is considered (i.e., AF and DF), the traditional and proposed optimal relay selection approaches both achieve the diversity order M where M represents the number of relays. In addition, numerical results show that for both AF and DF protocols, the intercept probability performance of proposed optimal relay selection is strictly better than that of the traditional relay selection and multiple relay combining methods.

I. INTRODUCTION

The paper studies physical-layer security in cooperative wireless networks with multiple relays and an eavesdropper. It proposes relay-selection schemes that account for wiretap-link information and evaluates intercept probability.

  • Motivation: User cooperation can improve wireless reliability, throughput, and security by exploiting cooperative relays as a virtual antenna array.Physical-layer security uses wireless-channel characteristics rather than secret keys to protect transmissions.
  • Related Work: Existing security research largely focuses on secrecy capacity, including relay-based AF, DF, and CF protocols, cooperative jamming, and MIMO relay networks.These studies examine secrecy-rate or secrecy-capacity improvements under different cooperative architectures.
  • Contributions: The paper proposes AF- and DF-based optimal relay selection schemes, P-AFbORS and P-DFbORS, and derives intercept probability expressions for them and benchmark schemes.The benchmarks include direct transmission, traditional relay selection, and multiple relay combining.
  • System Model: The paper considers a single-source, single-destination network with M single-antenna relays and an eavesdropper over Rayleigh-fading main and wiretap links.Direct links are unavailable in the considered relay-assisted model, and relay notation is R = {R_i | i = 1, 2, ···, M}.
  • System Model: Optimal relay selection uses both main-link and wiretap-link CSI, unlike traditional selection based only on source-relay and relay-destination CSI.The proposed criterion seeks high destination capacity while minimizing eavesdropper capacity.

C. Amplify-and-Forward

The AF protocol forwards a scaled version of the relay’s received signal without decoding. The paper formulates the resulting main-link, wiretap-link, and secrecy capacities before introducing AF relay-selection schemes.

  • AF Relaying: In AF relaying, the source broadcasts to M relays, and the selected relay forwards a scaled version of its received signal without decoding.The source signal is transmitted twice, once by the source and once by the relay, under a fair-comparison power allocation.
  • AF Relaying: The AF relay transmission produces separate capacities from the selected relay to the destination and to the eavesdropper.These capacities are combined to obtain the secrecy capacity for relay R_i.
  • AF Relay Selection: The paper introduces P-AFbORS and presents T-AFbORS and T-AFbMRC as comparison schemes.P-AFbORS selects a relay using the secrecy capacity of AF relaying transmission.

1) P-AFbORS:

P-AFbORS selects the AF relay that maximizes secrecy capacity using main- and wiretap-link CSI. Traditional selection uses only main-link CSI, while MRC forwards through all AF relays.

  • P-AFbORS: P-AFbORS accounts for source-relay, relay-destination, and relay-eavesdropper CSI when selecting the relay.Its criterion therefore incorporates both destination and eavesdropper channel conditions.
  • P-AFbORS: The proposed criterion can support centralized or distributed relay-selection algorithms.A centralized implementation maintains a table of the M relays and their related CSI.
  • T-AFbORS: T-AFbORS selects the relay with the largest AF capacity to the destination and excludes wiretap-link CSI.This is described as the traditional harmonic mean policy.
  • T-AFbMRC: T-AFbMRC uses all AF relays, constrains total source-and-relay transmit power to P, and combines their destination signals.With equal allocation, each source or relay uses power P/(M+1).
  • T-AFbMRC: The T-AFbMRC model derives transmission capacities to the destination and eavesdropper and then forms its secrecy capacity.The eavesdropper-side expression includes H(h_si, h_ie) = |h_si|^2|h_ie|^4 + |h_si|^4|h_ie|^2.

D. Decode-and-Forward

DF relaying decodes and re-encodes the source signal at a selected relay. Its end-to-end capacity is limited by the weaker source-relay or relay-destination hop, and the paper compares proposed and traditional schemes.

  • DF Relaying: In DF relaying, the relay decodes the received source signal and then re-encodes and transmits the decoded outcome.Only the selected relay forwards the re-encoded signal to the destination.
  • DF Relaying: DF transmission uses equal source and relay powers of P/2 for comparison with direct transmission.The total transmit power at the source and relay is limited to P.
  • DF Relaying: The DF capacity through relay R_i is the minimum of the source-relay and relay-destination capacities.Failure of either two-hop link causes failure of the DF transmission.
  • DF Relay Selection: The paper derives DF secrecy capacity using the relay-destination main link and the relay-eavesdropper wiretap link.It then presents P-DFbORS, T-DFbORS, and T-DFbMRC for analysis and comparison.

1) P-DFbORS:

The traditional DF-based relay-selection scheme selects the relay maximizing DF transmission capacity using only main-link CSI, while the multiple-relay combining framework forwards decoded signals from all successful relays and combines them at the destination.

  • T-DFbORS: T-DFbORS selects the relay that maximizes the capacity of DF relaying transmission.
  • T-DFbORS: The traditional DF relay-selection criterion is the conventional max-min rule based only on source-relay and relay-destination channel gains.
  • T-DFbMRC: T-DFbMRC forms a decoding set containing relays that successfully decode the source signal; an empty set causes no relay transmission.
  • T-DFbMRC: When the decoding set is nonempty, all successful relays forward decoded outcomes under a total relay power constraint of P/2.
  • T-DFbMRC: The destination applies maximal ratio combining to received signals from the relays in the decoding set, with corresponding capacities defined for destination and eavesdropper links.

III. INTERCEPT PROBABILITY ANALYSIS OVER RAYLEIGH FADING CHANNELS

The paper derives intercept probabilities for direct transmission and proposed relay-selection schemes over Rayleigh fading, where interception occurs when secrecy capacity is negative. The proposed AF selection has strictly lower intercept probability than proposed DF selection.

  • Closed-form intercept probability expressions are derived for direct transmission, proposed and traditional AF/DF relay selection, and traditional AF/DF multiple-relay combining over Rayleigh fading.
  • An intercept event occurs when secrecy capacity falls below zero, and Rayleigh fading makes the relevant channel gains exponentially distributed.
  • Direct transmission: Direct-transmission intercept probability is independent of transmit power P, so increasing transmit power alone cannot improve wireless security.
  • P-AFbORS: P-AFbORS intercept probability is obtained from the secrecy-capacity criterion using independent exponential distributions for relay-destination and relay-eavesdropper gains.
  • P-DFbORS: P-DFbORS interception is characterized by the event min(|hsi|2, |hid|2) < |hie|2 under exponentially distributed channel gains.
  • Comparison: P-AFbORS has strictly lower intercept probability than P-DFbORS, indicating an AF-security advantage over DF in this analysis.

D. T-AFbORS

The traditional AF relay-selection and multiple-relay combining schemes are analyzed through intercept-probability expressions. Traditional AF relay selection ignores eavesdropper CSI, and its closed-form expression is difficult to obtain.

  • T-AFbORS: T-AFbORS selects a relay without considering the eavesdropper’s channel CSI, making relay selection independent of wiretap-channel information.
  • T-AFbORS: Under identically and independently distributed main-link fading, each relay has selection probability 1/M in the traditional AF analysis.
  • T-AFbORS: A closed-form solution for the T-AFbORS intercept-probability expression is challenging, although numerical results can be obtained through computer simulations.
  • T-DFbORS: T-DFbORS intercept probability is analyzed in Rayleigh fading using the traditional relay-selection rule and the law of total probability.
  • T-AFbMRC: The T-AFbMRC intercept probability is derived from its signal model, with numerical results obtainable through computer simulation.

G. T-DFbMRC

The paper extends diversity-order analysis to intercept probability because the conventional SNR-based definition is inapplicable when intercept probability is SNR-independent. Direct transmission has order one, whereas P-AFbORS achieves order M.

  • The diversity-order analysis covers traditional and proposed AF- and DF-based optimal relay-selection schemes.
  • Because several intercept-probability expressions are independent of SNR, the conventional SNR-asymptotic diversity definition is not applicable.
  • The main-to-eavesdropper ratio (MER) is the ratio of average source-destination channel gain to average source-eavesdropper channel gain.
  • Direct transmission: Direct transmission achieves diversity order one, with intercept probability behaving as 1/λde at high MER.
  • P-AFbORS: P-AFbORS achieves diversity order M, and increasing the number of relays increases its diversity order accordingly.

C. P-DFbORS

The P-DFbORS analysis derives its diversity order from the intercept-probability expression and shows that the scheme achieves diversity order M.

  • C. P-DFbORS: The diversity order of P-DFbORS is obtained from its intercept-probability expression through asymptotic analysis.The section develops the result using conditional probabilities, joint PDFs, bounds, and higher-order-term approximations.
  • C. P-DFbORS: The derivation combines conditional-probability formulations with bounds and asymptotic expansions to obtain the diversity-order result.Intermediate steps include substituting bounds and ignoring higher-order terms.
  • C. P-DFbORS: P-DFbORS achieves diversity order M.Its intercept probability therefore follows an M-dependent high-MER decay behavior.
  • C. P-DFbORS: The analysis models relevant channel quantities as independent exponentially distributed random variables.Their joint probability density function is used in deriving the intercept-probability expression.

E. T-DFbORS

The T-DFbORS section analyzes its asymptotic intercept probability and shows that traditional DF optimal relay selection achieves diversity order M.

  • E. T-DFbORS: The T-DFbORS derivation uses the intercept-probability expression, Taylor expansion, and omission of higher-order terms.These steps produce the asymptotic form used to evaluate diversity order.
  • E. T-DFbORS: T-DFbORS achieves diversity order M.This conclusion follows from substituting the asymptotic expression into the diversity-order formula.
  • E. T-DFbORS: P-AFbORS, P-DFbORS, T-AFbORS, and T-DFbORS all achieve the same diversity order M.In high MER regions, their intercept probabilities behave as (1/λ_de)^M for λ_de →∞.

V. NUMERICAL RESULTS AND DISCUSSIONS

Numerical evaluations show that proposed optimal relay selection reduces intercept probability more effectively than traditional relay selection and multiple relay combining for both AF and DF protocols. Increasing the number of cooperative relays further improves security, while AF-based selection outperforms DF-based selection in the reported comparisons.

  • AF and DF comparisons: The proposed optimal relay selection outperforms traditional relay selection and multiple relay combining in intercept probability for both AF and DF protocols.For DF, P-DFbORS achieves the best performance among the compared schemes; the AF results show the same ordering advantage.
  • Effect of relay count: P-AFbORS and P-DFbORS both achieve lower intercept probabilities as the number of relays increases.The reported evaluations interpret this decrease as improved wireless security from exploiting cooperative relays.
  • AF versus DF: For M = 2, M = 4, and M = 8, P-AFbORS always outperforms P-DFbORS in intercept probability.The advantage of AF over DF becomes more significant as M increases in the relay-count evaluation.
  • Baseline comparison: The direct transmission performs worse than the proposed AF and DF optimal relay-selection schemes in the reported comparisons.This comparison is stated for M = 2, M = 4, and M = 8 in Fig. 4 and for the AF schemes in Fig. 2.
  • Analytical evaluation: The study derives closed-form intercept probability expressions and analyzes diversity order for the traditional and proposed relay-selection schemes.The conclusion states that both approaches achieve diversity order M, where M is the number of cooperative relays.
  • Scope: The study is limited to cooperative relay networks with a single source and a single destination.The paper identifies extension to multiple-source and multiple-destination networks as future work.

APPENDIX A PROOF OF PROPOSITION 1

The appendix analyzes asymptotic moments of intermediate variables as λde tends to infinity. It uses these limits and Taylor expansions to complete the proof of Proposition 1.

  • Asymptotic analysis: As λde → ∞, both the mean and variance of z approach zero, implying z → 0.The appendix obtains the limiting first and second moments and then applies the resulting convergence in the proof.
  • Taylor expansion: The proof substitutes z = (1/(2σ^2_id)) min(x, y) into the relevant expansion and ignores higher-order infinitesimals.This substitution is used to derive the asymptotic expression for the proposition.
  • Asymptotic analysis: The appendix similarly shows that both the mean and variance of t approach zero as λde → ∞.A Taylor series expansion is then used for the limiting analysis of t.
  • Proof completion: The derivation concludes with the proof of Proposition 1.The appendix explicitly states that the preceding calculation completes the proof.
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