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Radio circuitry calibration for reciprocal channel-based secret key establishment

Attiya Mahmood, Michael A. Jensen

Published Jun 1, 2016• 1 citation
Publisher

Abstract

Successful establishment of secret encryption keys based on bidirectional estimates of the multipath propagation channel depends critically on the reciprocity of the observed channel coefficients. Since typical radio circuitry is not reciprocal, calibration is required to remove the impact of non-reciprocal channel contributions. This paper reports on the impact of circuit non-reciprocity on key establishment performance and demonstrates calibration to recover the lost performance.

DOI
10.1109/aps.2016.7695873

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Successful establishment of secret encryption keys based on bidirectional estimates of the multipath propagation channel depends critically on the reciprocity of the observed channel coefficients. Since typical radio circuitry is not reciprocal, calibration is required to remove the impact of non-reciprocal channel contributions. This paper reports on the impact of circuit non-reciprocity on key establishment performance and demonstrates calibration to recover the lost performance.
This work integrates electromagnetic analysis with circuit theory to explore the impact of antenna mutual coupling and radio frequency circuit design on the achievable performance of methods that establish secret encryption keys using reciprocal propagation channels. The analysis includes the impact of the impedance match between the coupled antennas and the transmit sources or receiver loads, demonstrating that an optimally-designed matching network can significantly improve the achieved performance. The model is then used to account for the fact that transceiver circuit paths differ during transmission and reception, therefore destroying the channel reciprocity required for key establishment. A total least squares method for removing the impact of the non-reciprocal contributions to the channel is then applied, with the results showing that the algorithm is able to achieve key rates similar to those obtained when the non-reciprocal contributors are known perfectly.
Propagation-based secret key generation (SKG) is a physical layer method for establishing encryption keys based on two radios observing a reciprocal propagation channel. However, nonreciprocal contributions to the channel introduced by the radio circuitry significantly degrade the ability to reliably generate keys using such methods, necessitating the development of calibration methods for removing the impact of channel nonreciprocity. This paper uses a total least squares (TLS) algorithm coupled with a detailed model of the multiple-input multiple-output radio frequency circuitry and propagation for the radio system to achieve such a calibration. Simulations show that the method is highly effective in removing the impact of nonreciprocal circuit contributions over a range of operational parameters.
Propagation-based key establishment is a physical layer method for generating encryption keys based on two radios observing a reciprocal propagation channel. This work explores the impact of mutual coupling when communicating nodes are equipped with multiple antennas, multipath richness in the propagation environment, and practical limitations caused by the nonreciprocal nature of RF circuits on key establishment. First, network theory is used to formulate a model of a realistic communication system which incorporates transmit sources and receive loads, impedance matching networks, low-noise amplifiers (LNAs), mutually coupled antenna arrays, and a passive eavesdropper. Afterwards, a detailed analysis is performed to quantify the impact of coupling, type of impedance matching network, and proximity of a multi-antenna eavesdropper on key rate metrics. Next, the degradation on key establishment caused by the radiocircuitry non-reciprocal contributions to the propagation channel is analyzed. A calibration technique based on total least square algorithm is used to overcome the non-reciprocity. Results demonstrate that the method is highly effective in removing the impact of non-reciprocal circuit contributions over a range of operational parameters. Lastly, for key establishment, the propagation conditions can cause the available key rate to be significantly different from the secure key rate which takes into account the presence of a passive eavesdropper. To study this in detail, a realistic multiple-input multiple-output (MIMO) propagation environment is modeled for two communicating radios and an eavesdropper. Afterwards different propagation conditions are assumed and results demonstrate that secure key rate converges to available key rate when K-factor is small and the eavesdropper is not located very close (< 2.5 wavelength) to one of the nodes.
The performance of techniques for establishing secret encryption keys from the reciprocal electromagnetic propagation between two wireless radios is generally measured by comparing the number of key bits generated to the key rate, or the information theoretic bound on the number of key bits that can be determined for a single independent channel estimate. While typically this bound is computed by assuming that the radios have no information regarding the channel, recent work has demonstrated an approach for computing this bound for nodes using beamformed antenna arrays that know the spatial covariance of a wide-sense stationary channel. Since this bound does not directly indicate how to perform practical channel estimation to obtain estimates that can achieve the bound, the prior work demonstrates an approximation that indicates a practical channel estimation procedure while yielding a mutual information near that of the key rate in rich multipath fading environments. This paper demonstrates appreciable degradation in the mutual information achieved using this approximation when the channel includes a line-of-sight component and proposes a modified approximation technique that performs well over a broad range of propagation conditions.
While secret encryption keys are commonly-used for securing wireless transmissions, establishment of such keys has traditionally been accomplished using computational techniques at the higher layers of the wireless communication protocol stack. However, the multipath electromagnetic propagation typical of many environments can also be an excellent source of random variables useful for encryption key generation. Furthermore, antennas play an important role in how the transmitter and receiver excite or sense the channel and therefore become a critical component in the performance of techniques that exploit the multipath channel for key establishment. This paper focuses on how using multiple antennas can dramatically improve the performance of such key establishment methods.