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Security versus Reliability Analysis of Opportunistic Relaying
Yulong Zou, Xianbin Wang, Weiming Shen, Lajos Hanzo
TL;DR
The paper studies how to balance eavesdropper security and destination reliability in wireless communications, where improving one through power or rate changes can worsen the other. It analyzes direct-transmission SRT and proposes opportunistic relay selection, showing that increasing the number of relays improves both security and reliability in the stated asymptotic limits.
Problem
Wireless design faces a security-reliability tradeoff because changes that reduce destination outage can also reduce wiretap outage and increase interception risk.
Method
The paper characterizes direct-transmission SRT and analyzes opportunistic relay selection with decode-and-forward relaying in Rayleigh fading.
Results
As N approaches infinity, outage probability approaches zero for a fixed maximum intercept probability, while intercept probability tends to zero for a fixed maximum outage probability.
Takeaways & Limitations
Opportunistic relay selection improves the security-reliability tradeoff over conventional direct transmission, with benefits increasing as the number of relays grows.
Abstract
from arXiv · showhide
Physical-layer security is emerging as a promising paradigm of securing wireless communications against eavesdropping between legitimate users, when the main link spanning from source to destination has better propagation conditions than the wiretap link from source to eavesdropper. In this paper, we identify and analyze the tradeoffs between the security and reliability of wireless communications in the presence of eavesdropping attacks. Typically, the reliability of the main link can be improved by increasing the source's transmit power (or decreasing its date rate) to reduce the outage probability, which unfortunately increases the risk that an eavesdropper succeeds in intercepting the source message through the wiretap link, since the outage probability of the wiretap link also decreases when a higher transmit power (or lower date rate) is used. We characterize the security-reliability tradeoffs (SRT) of conventional direct transmission from source to destination in the presence of an eavesdropper, where the security and reliability are quantified in terms of the intercept probability by an eavesdropper and the outage probability experienced at the destination, respectively. In order to improve the SRT, we then propose opportunistic relay selection (ORS) and quantify the attainable SRT improvement upon increasing the number of relays. It is shown that given the maximum tolerable intercept probability, the outage probability of our ORS scheme approaches zero for $N \to \infty$, where $N$ is the number of relays. Conversely, given the maximum tolerable outage probability, the intercept probability of our ORS scheme tends to zero for $N \to \infty$.
I. INTRODUCTION
The paper motivates physical-layer security as a lower-overhead approach to eavesdropping protection and frames communication design as a security-reliability tradeoff. It characterizes direct transmission and proposes opportunistic relay selection to improve this tradeoff as the relay population grows.
- Cryptographic protection improves security but increases communication and computational overheads.
- Physical-layer security exploits wireless-channel characteristics to protect communications against eavesdropping attacks.
- Lowering data rate or transmit power can reduce intercept probability but increases main-link outage probability, creating a security-reliability tradeoff.
- The paper characterizes direct-transmission SRT using eavesdropper intercept probability and destination outage probability.
- Opportunistic relay selection is proposed to improve SRT by selecting the best relay and studying the effect of increasing relay count.
A. System Model
The system model considers a source, destination, and eavesdropper communicating over fading wireless links. The source transmits with power P and rate R_d, while the eavesdropper is assumed to know the legitimate-link parameters.
- The direct-transmission model contains one source S, one destination D, and one eavesdropper E.
- The source is characterized by transmit power P and data rate R_d.
- The received signals at D and E are modeled with fading coefficients and zero-mean AWGN of variance N_0.
- The eavesdropper is assumed to know all parameters of the source's legitimate transmission.
- The main and wiretap channels follow Rayleigh fading, so the squared channel magnitudes are exponentially distributed.
B. Security-Reliability Tradeoff Analysis
The analysis defines direct-transmission security and reliability through intercept and outage probabilities under Rayleigh fading. These probabilities are linked by a tradeoff that motivates opportunistic relaying because direct-transmission SRT cannot be improved by adjusting source power or rate.
- An intercept event occurs when the wiretap-channel capacity exceeds the source data rate, defining the direct-transmission intercept probability.
- The direct-transmission outage probability is derived from the capacity of the source-destination channel.
- The cooperative model adds N relay nodes alongside the source, destination, and eavesdropper.
- Increasing intercept probability reduces outage probability, demonstrating the security-reliability tradeoff governed by average channel gains.
- Direct-transmission SRT is independent of transmit power P and data rate R_d, so adjusting them cannot improve the tradeoff.
A. ORS Scheme
The ORS scheme uses decode-and-forward relays and selects the best successfully decoding relay to forward the source signal. This selection targets the strongest relay-to-destination channel while preserving a physical-layer security benefit.
- A. ORS Scheme: ORS uses N decode-and-forward relay nodes to assist transmission when the direct S-D link is unavailable.Relays that successfully decode the source signal form the decoding set D; an empty set leaves all relays silent.
- A. ORS Scheme: The relay-selection process considers only successfully decoding relays and chooses one from the non-empty decoding set for forwarding.If D is empty, no relay forwards; if D is non-empty, one relay forwards its decoded signal.
- A. ORS Scheme: The selected relay is the member of the decoding set with the highest channel capacity to D.This criterion is implemented through centralized CSI-based selection or distributed timers initialized inversely to the relay-to-destination channel strength.
- A. ORS Scheme: Because the wiretap channel is typically independent of the main channel, ORS provides no wiretap-capacity gain from selection while still improving physical-layer security.The relay-selection criterion exploits the main channel rather than the wiretap channel.
B. SRT Analysis
The ORS outage probability is obtained by conditioning on whether the successful decoding set is empty or non-empty. The resulting analysis accounts for both relay decoding failure and forwarding by the selected relay.
- B. SRT Analysis: ORS outage probability is derived using the law of total probability over empty and non-empty successful decoding sets.When the decoding set is empty, no relay forwards; otherwise, a relay selected by the ORS criterion forwards the source signal.
P ORS
The paper derives outage and intercept probabilities for ORS under Rayleigh fading and analyzes their asymptotic security-reliability tradeoff as the relay count grows. With a fixed constraint on either metric, the other tends to zero as N approaches infinity.
- P ORS: ORS outage and intercept probabilities are derived by combining relay decoding events with the selected relay’s main and wiretap channel capacities.The eavesdropper may combine copies received from the source and selected relay, whereas D relies on the relay when the direct link is unavailable.
- P ORS: As N →∞, the probability of an empty successful decoding set tends to zero.This result is substituted into the asymptotic ORS expressions for the outage and intercept probabilities.
- P ORS: Given a fixed outage constraint 0 < P_out^ORS < 1, the ORS intercept probability asymptotically tends to zero for N →∞.Thus, increasing the number of relays can drive the intercept probability down while maintaining the prescribed outage constraint.
- P ORS: Given a fixed intercept constraint 0 < P_int^ORS < 1, the ORS outage probability also tends to zero for N →∞.The paper states that ORS minimizes the outage probability asymptotically under the maximum tolerable intercept probability.
- P ORS: The required number of relay nodes depends on the tolerable SRT constraints and the average channel gains of the main links and wiretap channels.These gains can be estimated from fading averages, path-loss conditions, and transmission distances.
IV. NUMERICAL RESULTS AND DISCUSSIONS
The numerical results show that ORS improves the security–reliability tradeoff over direct transmission, with stronger benefits as the relay population increases. Under fixed intercept- or outage-probability constraints, the corresponding outage or intercept probability decreases toward zero as N grows.
- SRT comparisons: For a specific outage probability, ORS with N = 2, N = 4, and N = 6 has lower intercept probability than traditional direct transmission.This confirms that ORS outperforms direct transmission in SRT at λme = 10dB.
- SRT comparisons: As the allowed outage probability increases from 10^-3 to 10^-1, the intercept probability improves for both direct transmission and ORS.The numerical comparison is presented for λme = 10dB.
- Fixed-security constraints: As the intercept-probability constraint increases from 10^-3 to 10^-1, the ORS outage probability is significantly reduced.The result is shown for MER λme = 5dB.
- Fixed-security constraints: For Pint = 10^-1, Pint = 10^-2, and Pint = 10^-3, ORS outage probability tends to zero as N increases from 1 to 10^3.This demonstrates reliability improvement with more relays under each stated intercept-probability constraint.
- Fixed-reliability constraints: For Pout = 10^-1, Pout = 10^-2, and Pout = 10^-3, ORS intercept probability decreases as N increases from 1 to 10^4.The figure uses MER λme = 5dB and different outage constraints.
- Fixed-reliability constraints: Given a maximal tolerable outage probability, ORS intercept probability tends to zero as N approaches infinity.This is the asymptotic security result supported by the numerical discussion.
V. CONCLUSIONS
The paper analyzes security–reliability tradeoffs under eavesdropping and evaluates decode-and-forward opportunistic relay selection in Rayleigh fading. ORS strictly outperforms conventional direct transmission, with security and reliability benefits increasing as the number of relays grows, while the study remains limited to one source, destination, and eavesdropper.
- Contributions: The paper derives the security–reliability tradeoff for conventional direct transmission and quantifies decode-and-forward ORS in Rayleigh fading.The tradeoff is expressed through intercept and outage probabilities.
- Main findings: ORS strictly outperforms conventional direct transmission in terms of security–reliability tradeoff.This conclusion is based on the paper’s numerical results.
- Main findings: As the number of relays increases, ORS security–reliability performance significantly improves.The conclusion attributes the improvement to the security and reliability benefits of multiple relays.
- Scope and limitation: The study considers a single-source, single-destination, and single-eavesdropper network assisted by multiple relays.More general multi-source, multi-destination, and multi-eavesdropper scenarios are identified as future work.
APPENDIX A DERIVATION OF (29)
Appendix A derives the closed-form intercept-probability expression for the ORS scheme by decomposing relay-selection events and applying exponential fading distributions. The derivation uses the best-relay condition and channel-statistics assumptions to obtain equation (29).
- Fading statistics: The appendix applies exponential fading statistics to the eavesdropper-channel coefficients when evaluating the intercept probability.The relevant fading coefficients include those of the source–eavesdropper and best-relay–eavesdropper links.
- Relay-selection decomposition: The best relay is selected from the decoding set according to the relay-selection condition comparing destination-channel gains.The derivation applies the law of total probability over possible best-relay events.
- Relay-selection decomposition: The calculation partitions the other decoding relays into non-empty subsets and uses their cardinalities in the probability expression.These subsets are denoted Ak, with |Ak| giving each subset’s cardinality.
- Derivation of (29): The appendix derives the ORS intercept-probability expression by substituting intermediate probability terms into equation (A.2).The resulting expression is equation (29).