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Entropy

Analysis of the Mutual Information of Channel Phase Observations in Line-of-Sight Scenarios

Maximilian Matthé, Arsenia Chorti

Published Jul 10, 2023• 2 citations
Publisher

Abstract

The mutual information of the observed channel phase between devices can serve as an entropy source for secret key generation in line-of-sight scenarios. However, so far only simulated and numeric results were available. This paper derives the probability distribution of the channel phase and corresponding expressions for the mutual information. Moreover, the orientation distribution is optimized in order to maximize the mutual information. All presented results are validated numerically. These outcomes serve as a basis for further analytic investigations on the secret key generation rate and subsequent physical layer security performance analysis in line-of-sight scenarios, such as those encountered in drone-aided communications.

DOI
10.3390/e25071038

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•Jul 1, 2011•5 citations
The mutual information of the observed channel phase between devices can serve as an entropy source for secret key generation in line-of-sight scenarios. However, so far only simulated and numeric results were available. This paper derives the probability distribution of the channel phase and corresponding expressions for the mutual information. Moreover, the orientation distribution is optimized in order to maximize the mutual information. All presented results are validated numerically. These outcomes serve as a basis for further analytic investigations on the secret key generation rate and subsequent physical layer security performance analysis in line-of-sight scenarios, such as those encountered in drone-aided communications.
In this paper, we evaluate the achievable rates of the physical layer security (PLS)-based secret key generation (SKG) in a line-of-sight (LoS) channel, which occurs with a high probability in unmanned aerial vehicle (UAV) communications. SKG is a promising technique for lightweight scalable key distribution, and, despite the mature theory of PLS, this technique remains to be seen in practical applications. Thus, modelling realistic scenarios is of particular interest. One of the reasons why SKG has not been used in practice is due to the deterministic properties of LoS channels. To overcome this problem, in this paper we propose the rotation of the device antennas as an entropy source, reflected by the channel phases, from which the keys are derived. Simulation results show that by utilizing rotation in LoS scenarios, a number of secret bits can be generated, also given the presence of an eavesdropper. It is also shown that by controlling the transmit power we can maximize the conditional mutual information.
By exploiting multipath fading channels as a source of common randomness, physical layer (PHY) based key generation protocols allow two terminals with correlated observations to generate secret keys with information-theoretical security. The state of the art, however, still suffers from major limitations,e.g., low key generation rate, lower entropy of key bits and a high reliance on node mobility. In this paper, a novel cooperative key generation protocol is developed to facilitate high-rate key generation in narrowband fading channels, where two keying nodes extract the phase randomness of the fading channel with the aid of relay node(s). For the first time, we explicitly consider the effect of estimation methods on the extraction of secret key bits from the underlying fading channels and focus on a popular statistical method - maximum likelihood estimation (MLE). The performance of the cooperative key generation scheme is extensively evaluated theoretically. We successfully establish both a theoretical upper bound on the maximum secret key rate from mutual information of correlated random sources and a more practical upper bound from Cramer-Rao bound (CRB) in estimation theory. Numerical examples and simulation studies are also presented to demonstrate the performance of the cooperative key generation system. The results show that the key rate can be improved by a couple of orders of magnitude compared to the existing approaches.
In this paper, the feasibility of implementing a lightweight key distribution scheme using physical layer security for secret key generation (SKG) is explored. Specifically, we focus on examining SKG with the received signal strength (RSS) serving as the primary source of shared randomness. Our investigation centers on a frequency-selective line-of-sight (LoS) multipath channel, with a particular emphasis on assessing SKG rates derived from the distributions of RSS. We derive the received signal distributions based on how the multipath components resolve at the receiver. The mutual information (MI) is evaluated based on LoS 3GPP channel models using a numerical estimator. We study how the bandwidth, delay spread, and Rician K-factor impact the estimated MI. This MI then serves as a benchmark setting bounds for the SKG rates in our exploration.
The emergence of Internet of things (IoT) applications brings the challenge of finding lightweight schemes for secret key distribution. A promising solution coming from the physical layer is the so called secret key generation (SKG) from shared randomness. SKG allows two communicating parties to extract the shared randomness already present in wireless channels. This work investigates the achievable SKG rates using received signal strength (RSS) as a key generation parameter. A multi-path scenario is considered and the probability density function of the RSS in different channel conditions is evaluated. Next, through a numerical evaluation, the SKG rates are derived in the form of mutual information (MI) estimates, using a 3GPP standard channel model. The simulations are performed for different values of bandwidth and delay spread. We demonstrate that while both parameters have similar impact on how multi-path components are resolved, their effect on the MI is opposite.
This letter considers a data-driven approach to a secret key rate analysis of physical layer secret key generation based on mutual information neural estimator (MINE), which achieves the state-of-the-art estimation accuracy. Since MINE does not require any statistical knowledge of randomness sources, the proposed approach is applicable to any source model and even real data which cannot be fully expressed by a simple model. We first demonstrate by simulations that the proposed estimation provides good approximations to the theoretical secret key rate for a simple model, and then show that the achievable secret key rate highly depends on sources of randomness and employed channel estimation schemes for a realistic wireless channel model. As an application of our analysis, we present a method to train quantization through backpropagation that maximizes the estimated secret key rate.
Two methods are developed that can be applied to generate secret keys automatically from fading propagation channels that are reciprocal but have arbitrary (i.e. non Gaussian) statistics. Such methods may be necessary for physical-layer key generation in cases where the line-of-sight (LOS) component produces Rician channel statistics, not only because channel quantization based on Gaussian statistics will not provide equally probable symbols, but also because the symbol error rate (SER) and efficiency analysis based on Gaussian channels does not reflect true performance. An improved channel quantization method compared to [1], [2] is developed, where the empirical cumulative distribution function (cdf) of the channel is used directly to ensure equal probability of the key symbols. The results show that LOS channels can have slightly better SER performance than strictly Gaussian channels, especially at low SNR. Second, the idea of positional coding is developed, where a secret key can be transmitted by dividing empirical channel observations into multiple codewords and conveying a secret message from Alice to Bob in the sequence of channels fed forward from Alice to Bob. Analysis of the method illustrates that key mismatch rate can be made arbitrarily low by properly selecting the codeword length.