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Secrecy Outage and Diversity Analysis of Cognitive Radio Systems

Yulong Zou, Xuelong Li, Ying-Chang Liang

arXiv:1406.5732v1cs.IT

TL;DR

The paper addresses physical-layer security for cognitive transmissions intercepted by independent or collaborating eavesdroppers. It proposes three user-scheduling schemes and derives secrecy-outage and diversity results, finding full secrecy diversity for optimal and suboptimal scheduling while round-robin has diversity order 1.

  • Problem

    Physical-layer security is rarely studied for cognitive radio networks with multiple users and eavesdroppers that may intercept independently or collaborate.

  • Method

    The paper analyzes round-robin, optimal, and suboptimal user scheduling, deriving closed-form secrecy-outage expressions for coordinated and uncoordinated eavesdroppers.

  • Results

    Round-robin achieves secrecy diversity order 1, whereas optimal and suboptimal scheduling achieve diversity order M regardless of eavesdropper collaboration; optimal scheduling has the best secrecy-outage performance.

  • Takeaways & Limitations

    Increasing the number of cognitive users significantly improves secrecy outage for optimal and suboptimal scheduling, but not for round-robin scheduling.

Abstract

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In this paper, we investigate the physical-layer security of a multi-user multi-eavesdropper cognitive radio system, which is composed of multiple cognitive users (CUs) transmitting to a common cognitive base station (CBS), while multiple eavesdroppers may collaborate with each other or perform independently in intercepting the CUs-CBS transmissions, which are called the coordinated and uncoordinated eavesdroppers, respectively. Considering multiple CUs available, we propose the round-robin scheduling as well as the optimal and suboptimal user scheduling schemes for improving the security of CUs-CBS transmissions against eavesdropping attacks. Specifically, the optimal user scheduling is designed by assuming that the channel state information (CSI) of all links from CUs to CBS, to primary user (PU) and to eavesdroppers are available. By contrast, the suboptimal user scheduling only requires the CSI of CUs-CBS links without the PU's and eavesdroppers' CSI. We derive closed-form expressions of the secrecy outage probability of these three scheduling schemes in the presence of the coordinated and uncoordinated eavesdroppers. We also carry out the secrecy diversity analysis and show that the round-robin scheduling achieves the diversity order of only one, whereas the optimal and suboptimal scheduling schemes obtain the full secrecy diversity, no matter whether the eavesdroppers collaborate or not. In addition, numerical secrecy outage results demonstrate that for both the coordinated and uncoordinated eavesdroppers, the optimal user scheduling achieves the best security performance and the round-robin scheduling performs the worst. Finally, upon increasing the number of CUs, the secrecy outage probabilities of the optimal and suboptimal user scheduling schemes both improve significantly.

I. INTRODUCTION

The paper studies physical-layer security in a multi-user, multi-eavesdropper cognitive radio network sharing spectrum with a primary network. It proposes three scheduling schemes and analyzes secrecy outage and diversity under coordinated and uncoordinated eavesdropping.

  • Motivation: Cognitive radio lets unlicensed cognitive users share licensed spectrum with higher-priority primary users, exposing transmissions to malicious attacks.Physical-layer security protects confidentiality by exploiting wireless-channel characteristics when the main channel is better than the wiretap channel.
  • Research focus: The paper examines a multi-user, multi-eavesdropper cognitive radio network where eavesdroppers either intercept independently or collaborate.This extends prior cognitive-radio security work focused on multiple antennas, relays, ergodic secrecy rate, or intercept probability.
  • Contributions: It proposes round-robin, optimal, and suboptimal user scheduling for protecting cognitive transmissions against coordinated and uncoordinated eavesdroppers.Optimal scheduling uses CSI for CU-CBS, CU-PU, and CU-eavesdropper links; suboptimal scheduling uses only CU-CBS CSI.
  • Contributions: The paper characterizes secrecy diversity and shows that round-robin achieves diversity order 1, whereas optimal and suboptimal scheduling achieve diversity order M.Here, M is the number of cognitive users, and the result holds whether eavesdroppers collaborate or not.
  • System model: The system contains M cognitive users transmitting uplink data to a common CBS while sharing spectrum with a primary transmitter-receiver pair and N eavesdroppers.Underlay sharing permits simultaneous transmission when CU interference at the primary receiver remains tolerable and primary QoS is unaffected.

III. MULTI-USER SCHEDULING SCHEMES AND SECRECY OUTAGE ANALYSIS

The paper develops round-robin, optimal, and suboptimal scheduling schemes and derives secrecy-outage expressions for both independent and collaborating eavesdroppers. The optimal scheme selects the CU with highest secrecy capacity, while the suboptimal scheme relies only on CU-CBS CSI.

  • A. Round-Robin Scheduling: Round-robin scheduling lets the M cognitive users take turns transmitting, giving each user an equal chance to access the licensed spectrum.Its secrecy-outage probability is obtained by averaging the individual users’ outage probabilities.
  • Outage analysis: Closed-form secrecy-outage expressions are derived for all three scheduling schemes under both uncoordinated and coordinated eavesdropping.These expressions are used later for numerical evaluation of secrecy-outage performance.
  • B. Optimal User Scheduling: Optimal scheduling selects the CU with the highest secrecy capacity for transmission.The criterion uses CSI from CU-CBS, CU-PR, and CU-eavesdropper links, together with eavesdropper noise and population information.
  • B. Optimal User Scheduling: The optimal scheme’s secrecy-outage analysis is formulated separately for uncoordinated and coordinated eavesdroppers using the corresponding wiretap-channel models.The paper derives outage expressions from the main-channel and wiretap-channel capacities under each eavesdropping scenario.

C. Suboptimal User Scheduling

Suboptimal scheduling selects the CU with the strongest instantaneous CU-CBS fading gain when primary-receiver and eavesdropper CSI is unavailable. Its secrecy-outage expressions are derived for independent and collaborating eavesdroppers.

  • Scheduling rule: Suboptimal scheduling selects the CU with the highest instantaneous fading gain to the CBS using only CU-CBS CSI.This avoids requiring CSI for the primary receiver and eavesdroppers.
  • Scheduling rule: The suboptimal scheme differs from optimal scheduling because it excludes primary-receiver and eavesdropper CSI from user selection.The paper presents this as a practical alternative when those channel measurements are unavailable.
  • Uncoordinated eavesdroppers: The paper derives suboptimal-scheduling secrecy-outage expressions for uncoordinated eavesdroppers using the selected user’s secrecy-capacity relations.The derivation uses the law of total probability and subset-based eavesdropper terms.
  • Coordinated eavesdroppers: For coordinated eavesdroppers, the analysis assumes identically distributed CU-eavesdropper fading and equal eavesdropper noise variances.Under these assumptions, the outage expression is decomposed into Pout,I, Pout,II, and Pout,III terms.
  • Summary: Closed-form secrecy-outage expressions are obtained for round-robin, optimal, and suboptimal scheduling in both eavesdropping scenarios.These expressions support the paper’s subsequent numerical secrecy-outage evaluation.

IV. SECRECY DIVERSITY ANALYSIS

The paper defines secrecy diversity through the asymptotic behavior of the secrecy outage floor and analyzes round-robin scheduling under coordinated and uncoordinated eavesdropping. Round-robin achieves diversity order one in both cases and therefore gains no secrecy-diversity benefit from multiple CUs.

  • Round-robin outage floor: As the interference limit I tends to infinity, round-robin scheduling reaches a non-zero secrecy outage floor as CU transmit power increases.The floor reflects the limiting behavior under unbounded CU transmit power.
  • Diversity definition: The analysis defines secrecy diversity from the asymptotic ratio of the secrecy outage floor to the main-to-eavesdropper ratio as MER increases.In the high-MER region, the outage floor behaves as λ_me^-d_round, so higher diversity order corresponds to faster decrease.
  • Uncoordinated eavesdroppers: Diversity order 1 is achieved by round-robin scheduling with uncoordinated eavesdroppers.The result follows from the asymptotic secrecy-outage analysis for independent interception.
  • Coordinated eavesdroppers: Diversity order 1 also holds for round-robin scheduling with coordinated eavesdroppers.Thus collaboration among eavesdroppers does not change the round-robin diversity order.
  • Overall implication: Round-robin scheduling fails to obtain secrecy-diversity benefits from multiple CUs, regardless of whether eavesdroppers collaborate.This conclusion combines the coordinated and uncoordinated asymptotic results.

B. Optimal User Scheduling

The optimal scheduling analysis derives secrecy outage floors and diversity orders for coordinated and uncoordinated eavesdroppers, while the suboptimal scheme is analyzed using only CU–CBS channel information. Both scheduling schemes achieve diversity order M, but the suboptimal scheme is more practical because it requires less CSI.

  • B. Optimal User Scheduling: The optimal scheduling scheme achieves diversity order M for both uncoordinated and coordinated eavesdroppers.Its secrecy outage floor behaves as (1/λ_me)^M in the high-MER region.
  • B. Optimal User Scheduling: Increasing the number of CUs significantly decreases the optimal scheme’s secrecy outage floor relative to round-robin scheduling.The paper identifies this behavior as an advantage of optimal scheduling.
  • C. Suboptimal User Scheduling: The suboptimal analysis derives secrecy-outage-floor bounds and asymptotic expressions separately for coordinated and uncoordinated eavesdroppers.The derivation uses the limiting interference condition and the defined secrecy-diversity measure.
  • C. Suboptimal User Scheduling: The suboptimal scheduling scheme also achieves diversity order M whether eavesdroppers are coordinated or uncoordinated.This matches the diversity order of the optimal scheduling approach.
  • C. Suboptimal User Scheduling: The suboptimal scheme requires only CU–CBS CSI, whereas the optimal scheme requires CSI for links to the CBS, primary receiver, and eavesdroppers.The reduced CSI requirement makes suboptimal scheduling more attractive for practical cognitive radio systems.

V. NUMERICAL RESULTS AND DISCUSSIONS

The numerical results compare secrecy outage across scheduling schemes, interference limits, secrecy rates, eavesdropper counts, and cognitive-user counts for coordinated and uncoordinated eavesdroppers. Optimal scheduling consistently performs best, while round-robin performs worst and gains no benefit from additional cognitive users.

  • Interference level: As γI increases, the three scheduling schemes approach secrecy outage floors, with optimal and suboptimal scheduling below round-robin.The optimal scheme strictly outperforms the suboptimal scheme in both eavesdropper settings, and coordinated eavesdroppers produce worse secrecy outage performance.
  • Secrecy rate: As Rs increases, secrecy outage probabilities increase for all schemes under coordinated and uncoordinated eavesdroppers.Higher secrecy rates improve throughput performance but make perfect secure transmission less likely.
  • Secrecy rate: Across the whole secrecy-rate region, optimal scheduling achieves the best secrecy outage performance and round-robin scheduling the worst.This ordering holds for both coordinated and uncoordinated eavesdroppers.
  • Number of eavesdroppers: As N increases, secrecy outage probabilities increase for round-robin, suboptimal, and optimal scheduling in both eavesdropper settings.For a fixed number of eavesdroppers, both user-selection schemes outperform round-robin.
  • Number of CUs: As M increases, round-robin secrecy outage remains unchanged, whereas optimal and suboptimal scheduling probabilities significantly decrease.Thus, increasing the number of CUs can improve security with either user-selection scheme even when the eavesdroppers’ average channel gain is two times better than that of legitimate CUs.

VI. CONCLUSION

The paper analyzes secrecy outage and diversity for multi-user cognitive transmissions under coordinated and uncoordinated eavesdropping. Optimal and suboptimal scheduling achieve diversity order M, while round-robin achieves only one; security of primary transmissions and imperfect CSI remain future work.

  • Closed-form secrecy outage expressions are derived for round-robin, optimal, and suboptimal scheduling under coordinated and uncoordinated eavesdroppers.
  • The round-robin scheme achieves secrecy diversity order one, whereas optimal and suboptimal scheduling achieve diversity order M, the number of CUs.
  • The study excludes primary-user security and assumes perfect CSI, leaving joint CU–PU security and CSI-estimation errors for future work.

APPENDIX A PROOF OF (11) AND (12)

Appendix A derives the probability expressions used for the secrecy-outage analysis by characterizing independent fading variables and the aggregate eavesdropper variable. The derivation then combines these distributions and substitutions to obtain the target expressions.

  • The derivation models |h_ib|^2 and |h_ip|^2 as independent exponential variables and obtains the CDF of their associated variable.
  • The resulting CDF is shown to be first-order differentiable, yielding the corresponding PDF.
  • Independent eavesdropper fading variables are used to rewrite the aggregate expression for the eavesdropper-related term.
  • Combining independence, the derived distributions, and substitutions produces the expressions identified as (11) and (12).
  • The aggregate eavesdropper variable is modeled as Gamma distributed with mean Nσ2_ie, where N is the number of eavesdroppers.

APPENDIX B DERIVATION OF (26)

Appendix B derives expression (26) by forming joint distributions for channel variables, exploiting exponential fading and independence, and applying subset expansions before substitution into the outage expression.

  • The derivation begins with the joint distribution of the main-channel and primary-link variables and uses their independence from eavesdropper and competing-user variables.
  • Eavesdropper fading variables are treated as independent exponential random variables, enabling further evaluation of the relevant distribution terms.
  • The intermediate terms are repeatedly substituted and combined to obtain successive expressions for the outage probability.
  • Non-empty subsets of eavesdroppers and competing users are enumerated through set-difference and cardinality notation.
  • The final substitution into the preceding expression yields equation (26).

APPENDIX C DERIVATION OF (28)

Appendix C derives expression (28) by characterizing a Gamma-distributed aggregate variable, forming joint PDFs, partitioning the integration region, and combining the resulting components.

  • The aggregate eavesdropper variable z is Gamma distributed with mean Nσ2_ie.
  • The derivation uses independent channel variables to construct the joint PDF of (X, Y, Z).
  • Independence of exponential fading variables is used to combine the component distributions.
  • The integration region Θ is partitioned into mutually exclusive sets, with Θ1 further divided into Θ11 and Θ12.
  • The resulting outage components Pout,I, Pout,II, and Pout,III are combined through substitutions to derive the target expression.

APPENDIX D PROOF OF (55)

The proof analyzes the asymptotic behavior of z and z2 as λme grows without bound. It shows that z converges to zero with probability 1 and that higher-order infinitesimal terms can be neglected.

  • Moment derivation: The derivation obtains the required means through intermediate computations based on equation (56) and related expressions.
  • Asymptotic behavior: For λme →∞, the mean and variance of z2 are high-order infinitesimals relative to those of z.
  • Proof simplification: Because 0 < θ < 1 and z > 0, z2 exp(−θz) is high-order infinitesimal compared with z as λme →∞.The proof therefore ignores this higher-order term in the subsequent expression.
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