Full-Duplex vs. Half-Duplex Secret-Key Generation

Full-duplex (FD) communication is regarded as a key technology in future 5G and Internet of Things (IoT) systems. In addition to high data rate constraints, the success of these systems depends on the ability to allow for confidentiality and security. Secret-key agreement from reciprocal wireless channels can be regarded as a valuable supplement for security at the physical layer. In this work, we study the role of FD communication in conjunction with secret-key agreement. We first introduce two complementary key generation models for FD and half-duplex (HD) settings and compare the performance by introducing the key-reconciliation function. Furthermore, we study the impact of the so called probing-reconciliation trade-off, the role of a strong eavesdropper and analyze the system in the high SNR regime. We show that under certain conditions, the FD mode enforces a deteriorating impact on the capabilities of the eavesdropper and offers several advantages in terms of secret-key rate over the conventional HD setups. Our analysis reveals as an interesting insight that perfect self-interference cancellation is not necessary in order to obtain performance gains over the HD mode.

💡 Research Summary

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The paper investigates secret‑key generation (SKG) over reciprocal wireless channels when the legitimate terminals operate either in half‑duplex (HD) or full‑duplex (FD) mode. The authors consider a three‑node system (Alice, Bob, and a passive eavesdropper Eve) each equipped with a single antenna. The wireless links are modeled as real‑valued flat‑fading channels that stay constant over a coherence block and change independently from block to block. The key‑agreement protocol spans n such blocks and consists of two phases: (i) a probing phase, during which Alice and Bob exchange pilot symbols to obtain noisy observations of the reciprocal channel, and (ii) a public‑reconciliation phase, during which Alice sends a quantized description of her observations to Bob over a rate‑limited public channel.

System models.
In the HD case each block yields one scalar observation at Alice (x), one at Bob (y) and two observations at Eve (z₁, z₂). The observations are linear functions of the underlying channel coefficients plus independent unit‑variance Gaussian noise, scaled by the signal‑to‑noise ratios (SNR, SNRₐₑ, SNR_bₑ). Correlations among the channel coefficients are captured by parameters ρₐₑ, ρ_bₑ, ρ_bₐ, and δ (the latter models a possible delay between the two reciprocal measurements).

In the FD case Alice and Bob transmit and receive simultaneously. Consequently, each observation contains a residual self‑interference (SI) term modeled as α·√SNR·n_I, where α>0 quantifies the SI power relative to the desired signal. The SI is assumed to be independent Gaussian noise after cancellation; α=1 corresponds to SI as strong as the desired signal, while α→0 corresponds to perfect cancellation. The eavesdropper now receives a single observation that is the sum of the two legitimate links plus noise.

Key‑reconciliation function.
The authors introduce a “key‑reconciliation function” that maps the fraction β of blocks allocated to probing and the public‑reconciliation rate R_r to an achievable secret‑key rate R_s. The function explicitly shows a trade‑off: allocating more blocks to probing improves the quality of the correlated observations (reducing the conditional entropy H(X|Y)), but leaves fewer blocks for public communication, which limits the amount of side‑information that can be exchanged.

Strong eavesdropper analysis.
A “strong Eve” is modeled by allowing higher correlation ρ_e between Eve’s observations and the legitimate channels, and by letting Eve’s noise variance be arbitrarily small. Under this model the authors derive conditions on β, α, and the SNRs under which FD still outperforms HD. The key insight is that the simultaneous transmission in FD provides an extra degree of freedom: while Alice is sending her reconciliation message, Bob can still receive the pilot from Alice, thereby effectively doubling the amount of useful information exchanged per block compared with HD, where time‑sharing is required.

High‑SNR asymptotics.
In the high‑SNR regime the secret‑key rates grow as (1/2)·log₂(SNR) for both modes, but the FD rate contains an additional constant term that depends on α. Specifically, the FD secret‑key rate ≈ (1/2)·log₂(SNR) – log₂(1+α²) while the HD rate ≈ (1/2)·log₂(SNR) – log₂(2). Hence, as long as α² < 1 (i.e., SI is attenuated by more than 3 dB), FD yields a higher constant offset, confirming that perfect SI cancellation is not required for FD to be beneficial.

Multi‑user extension.
The paper also sketches a three‑user key‑agreement scenario (Alice‑Bob‑Charlie) where Bob simultaneously receives Alice’s reconciliation message and transmits his own to Charlie. This illustrates how FD can be exploited in larger networks to achieve two‑way public reconciliation without additional time slots, further amplifying the advantage over HD.

Conclusions.
The study provides a rigorous information‑theoretic framework for comparing HD and FD secret‑key generation. By defining the key‑reconciliation function, it quantifies the probing‑reconciliation trade‑off, shows that FD can outperform HD even with realistic residual SI, and identifies the parameter regimes (β, α, SNR) where the gain is guaranteed. These results suggest that future 5G/IoT systems can incorporate FD transceivers for physical‑layer security without demanding impractically high SI‑cancellation performance.