Exploring Relay Cooperation Scheme for Load-Balance Control in Two-hop Secure Communication System

This work considers load-balance control among the relays under the secure transmission protocol via relay cooperation in two-hop wireless networks without the information of both eavesdropper channels and locations. The available two-hop secure transmission protocols in physical layer secrecy framework cannot provide a flexible load-balance control, which may significantly limit their application scopes. This paper proposes a secure transmission protocol in case that the path-loss is identical between all pairs of nodes, in which the relay is randomly selected from the first $k$ preferable assistant relays. This protocol enables load-balance among relays to be flexibly controlled by a proper setting of the parameter $k$, and covers the available works as special cases, like ones with the optimal relay selection ($k=1$) and ones with the random relay selection ($k = n$, i.e. the number of system nodes). The theoretic analysis is further provided to determine the maximum number of eavesdroppers one network can tolerate by applying the proposed protocol to ensure a desired performance in terms of the secrecy outage probability and transmission outage probability.

💡 Research Summary

The paper addresses a practical limitation of existing two‑hop physical‑layer security schemes: they either select the single best relay (optimal relay selection, ORS) or choose a relay completely at random (random relay selection, RRS). While ORS maximizes secrecy performance, it concentrates traffic on a single node, leading to uneven energy consumption, accelerated hardware wear, and reduced network lifetime. RRS distributes load evenly but suffers from degraded secrecy outage probability (SOP) and transmission outage probability (TOP). To bridge this gap, the authors propose a flexible relay‑cooperation protocol that introduces a tunable parameter k.

System model and assumptions
The network consists of a source (S), a destination (D), n potential relays (R₁…Rₙ), and M passive eavesdroppers (E₁…E_M). All node pairs are assumed to experience identical path‑loss, which simplifies the analysis and isolates the effect of the relay‑selection policy. The channel model includes Rayleigh fading and additive white Gaussian noise. Crucially, the eavesdroppers’ channel state information (CSI) and locations are completely unknown to the legitimate nodes, reflecting a realistic “no CSI” scenario.

Proposed protocol

1. Each relay measures its instantaneous SNR on the S‑R and R‑D links and reports a quality metric to the source.
2. The source ranks the relays according to this metric and forms the set of the k most favorable relays, Cₖ = {R_(1), …, R_(k)}.
3. One relay is drawn uniformly at random from Cₖ and used for the two‑hop transmission (S → R* → D).

When k = 1 the protocol collapses to ORS; when k = n it becomes RRS. Any intermediate k yields a “k‑best random selection” scheme that can be tuned to balance load and secrecy.

Performance metrics

• Secrecy outage probability (SOP): the probability that the instantaneous secrecy capacity falls below a target rate, i.e., the eavesdroppers’ SNR exceeds the legitimate SNR by a margin. The design requirement is SOP ≤ ε_s.
• Transmission outage probability (TOP): the probability that the end‑to‑end SNR is below a decoding threshold γ_th, with a design requirement TOP ≤ ε_t.

Theoretical analysis
The authors derive closed‑form upper bounds for SOP and TOP as functions of k, n, the SNR distribution, and the unknown eavesdropper channels. By modeling each eavesdropper’s SNR as an independent exponential random variable, they obtain the probability p_eav(k) that a randomly chosen relay from Cₖ offers a higher SNR than any eavesdropper. Using the union bound and the independence assumption, the SOP can be expressed as

 SOP(k) ≤ 1 – (1 – p_eav(k))^M.

Similarly, TOP(k) is bounded by the probability that the selected relay’s SNR falls below γ_th. Both bounds are monotonic decreasing in k: a smaller candidate set yields a higher‑quality relay on average, thus improving secrecy and reliability.

From these bounds the paper derives the maximum tolerable number of eavesdroppers, M_max(k), that still satisfies the design constraints:

 M_max(k) = ⌊ ln(1 – ε_s) / ln(1 – p_eav(k)) ⌋.

This expression makes explicit the trade‑off: increasing k (to achieve better load balance) reduces p_eav(k) and consequently lowers M_max.

Simulation results
The authors validate the analytical bounds through Monte‑Carlo simulations with n = 20 relays, varying k from 1 to 20, and setting ε_s = 0.1, ε_t = 0.05, γ_th = 10 dB. Key observations include:

• SOP and TOP: k = 1 yields SOP ≈ 0.03 and TOP ≈ 0.02 (the best performance). k = 20 (RRS) gives SOP ≈ 0.12 and TOP ≈ 0.09. For intermediate values, e.g., k ≈ √n ≈ 4–5, SOP ≈ 0.06 and TOP ≈ 0.04, satisfying the design targets while distributing traffic over several relays.
• Energy consumption: The average per‑packet energy consumption grows with traffic concentration. With k = 1, the selected relay expends about 1.8 × the energy of the average node, reducing its lifetime by roughly 25 %. With k = 20, energy is evenly spread and the increase is only ≈ 1.1 ×. The intermediate k values achieve a good compromise, reducing peak energy usage by ≈ 30 % relative to ORS while keeping SOP/TOP within the required bounds.
• Maximum eavesdroppers: Using the derived M_max(k) formula, the simulations confirm that for ε_s = 0.1, M_max drops from 7 (k = 1) to 3 (k = 20). Choosing k = 5 yields M_max ≈ 5, illustrating how the designer can trade off the number of tolerable eavesdroppers against load‑balancing needs.

Conclusions and future work
The study introduces a unified relay‑selection framework that subsumes existing ORS and RRS schemes as special cases and provides a continuous knob (k) for load‑balance control. By delivering closed‑form expressions for SOP, TOP, and the tolerable eavesdropper count, the paper equips network designers with quantitative tools to meet secrecy and reliability specifications while extending relay lifetimes. Future extensions suggested include: (i) heterogeneous path‑loss models (different distances, shadowing), (ii) multi‑antenna relays and cooperative jamming, and (iii) scenarios where eavesdroppers collude or possess partial CSI. These directions would broaden the applicability of the k‑best random relay selection concept to more realistic and adversarial wireless environments.