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IEEE Wireless Communications Letters

Optimal Pilot Length for Key Generation in Correlated Wireless Channels

Danqi Li, Shihao Yan, Jia Zhang, Jiande Sun, Feng Shu

Published Aug 16, 2024• 0 citations
Publisher

Abstract

This letter examines the optimal pilot length for key generation in correlated wireless channels. We first deduce the secret key capacity as a function of the pilot length N and other system parameters. Then, derive two fixed-point equations to identify the optimal N with and without an eavesdropper. Our analysis and numerical results confirm the existence of the optimal N that maximizes the secret key capacity, and both results for optimal N are consistent. Furthermore, the optimal N generally decreases with average signal-to-noise ratio and maximum Doppler shift. Our examination can provide useful guidelines in designing practical key generation systems.

DOI
10.1109/lwc.2024.3444821

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This letter examines the optimal pilot length for key generation in correlated wireless channels. We first deduce the secret key capacity as a function of the pilot length N and other system parameters. Then, derive two fixed-point equations to identify the optimal N with and without an eavesdropper. Our analysis and numerical results confirm the existence of the optimal N that maximizes the secret key capacity, and both results for optimal N are consistent. Furthermore, the optimal N generally decreases with average signal-to-noise ratio and maximum Doppler shift. Our examination can provide useful guidelines in designing practical key generation systems.
This letter investigates the secret key capacity of key generation from correlated wireless channels in a source model. We systematically study a practical scenario by taking into account all relevant parameters including sampling delay, eavesdroppers' location, qualities of legitimate and eavesdropping channels, Doppler spread, and pilot length. Our findings indicate that secret key capacity is determined by the cross correlation of the channel measurements, and a better legitimate channel is not necessary when the correlation between legitimate channels is higher than correlation between legitimate and eavesdropping channels. We also find that it is possible to tune the secret key capacity by carefully designing the sampling delay, pilot length, and channel qualities. This letter offers practical design guidelines on secure key generation systems.
This paper investigates the secret key capacity of key generation in the slow-fading wireless channel by considering the temporal correlation between channel measurements in the previous and current frame. We derive the analytical expression of secret key capacity in the slow-fading channel, and propose the design guideline for practical key generation schemes in slow fading channel environments. We systematically analyze the impact of all corresponding parameters on secret key capacity, including sampling period, sampling delay, eavesdroppers' location, signal-to-noise ratio, Doppler spread, and pilot length. Theoretical and simulation results indicate that secret key capacity in the slow fading channel is affected by frame-to-frame correlation and increasing transmission power or sampling period can suppress this effect.
Through a wireless channel, two users can transmit pilot signals to each other, and then utilize the received signals to agree upon a secret key through communications in a public channel without leaking any secret about this key to anyone else. This paper addresses the optimization of the two pilots to maximize the capacity of secret key generation for a MIMO channel with any given receive and transmit correlation matrices. This study shows how the globally optimal pilots can be obtained if the transmission power is either low or high. For an arbitrary transmission power, the algorithm developed is at least locally optimal. Comparison to pilots based on minimum channel estimation errors and uniform power distribution is also presented. It is also shown that the designed pilots meet the requirement for anti- eavesdropping channel estimation.
In this paper, we propose a novel physical-layer secret key generation (SKG) scheme, which is based on reduced random pilot selection at a legitimate transmitter and channel interpolation at a legitimate receiver. As a result, the proposed scheme is capable of reducing pilot overhead and increasing secret key capacity (SKC) while suppressing information leakage to an eavesdropper in a correlated eavesdropping channel. More specifically, a subset of full pilot sequence is activated based on the legitimate channels at the legitimate transmitter, and the full channel coefficients are estimated from the received pilot symbol subset at the legitimate receiver with the aid of our channel interpolation. Additionally, despite the non-reciprocal channel due to the presence of a Doppler shift and an additive noise, our scheme achieves high SKG reliability in comparison to that without our reduced pilot selection or channel interpolation. We also derive the theoretical SKC for the proposed scheme. Our simulation results demonstrate that the proposed SKG scheme exhibits a higher performance in terms of both the SKC and key disagreement ratio.
We study secret key generation from reciprocal multipath wireless channels modeled as multiple parallel fading channels. We consider two channel characteristics that heavily impact secret key capacity: channel sparsity and correlation between main and eavesdropper's channels. We propose a joint model to capture the channel sparsity and correlated eavesdropping. For the case without eavesdroppers, we show that at each transmitter SNR γ there is an optimal sparsity 0 ≤ ρopt≤ 1, which specifies the fraction of non-zero channel coefficients, that yields the maximum secret key capacity. The reduction in secret key capacity due to eavesdropping is due to two sources. First is the overlap between the main and eavesdropper channels, i.e., the pattern of non-zero subchannels common to both. The second is the correlation between the channel coefficients of the overlapping channels. We show that when the power of the training signal is uniformly distributed over the non-zero channels, there is a cutoff SNR γcbelow which the secret key rate is zero, but non-zero (and increasing in γ) when γ > γc. We also show that in the low SNR regime, the optimal input signal is peaky (a non-uniform training signal) by which the secret key capacity is non-zero at all γ > 0.
Fundamental limits of secret-key agreement over reciprocal wireless channels are investigated. We consider a two-way block-fading channel where the channel gains in the forward and reverse links between the legitimate terminals are correlated. The channel gains between the legitimate terminals are not revealed to any terminal, whereas the channel gains of the eavesdropper are revealed to the eavesdropper. We propose a two-phase transmission scheme, that reserves a certain portion of each coherence block for channel estimation, and the remainder of the coherence block for correlated source generation. The resulting secret-key involves contributions of both channel sequences and source sequences, with the contribution of the latter becoming dominant as the coherence period increases. We also establish an upper bound on the secret-key capacity, which has a form structurally similar to the lower bound. Our upper and lower bounds coincide in the limit of high signal-to-noise-ratio (SNR) and large coherence period, thus establishing the secret-key agreement capacity in this asymptotic regime. Numerical results indicate that the proposed scheme achieves significant gains over training-only schemes, even for moderate SNR and small coherence periods, thus implying the necessity of randomness-sharing in practical secret-key generation systems.