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Digest - IEEE Antennas and Propagation Society. International Symposium

Channel estimation for secret key establishment in MIMO systems

Britton T. Quist, Michael A. Jensen

Published Jul 1, 2013• 1 citation
Publisher

Abstract

This paper proposes a technique for channel estimation that approximately optimizes the number of secret encryption key bits that can be generated from estimation of the reciprocal electromagnetic propagation in a multipath environment for systems with multiple antennas. Numerical studies demonstrate that the method dramatically improves performance for low signal-to-noise ratio or large antenna arrays.

DOI
10.1109/aps.2013.6710939

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Digest - IEEE Antennas and Propagation Society. International Symposium•Jul 1, 2014•3 citations
This paper proposes a technique for channel estimation that approximately optimizes the number of secret encryption key bits that can be generated from estimation of the reciprocal electromagnetic propagation in a multipath environment for systems with multiple antennas. Numerical studies demonstrate that the method dramatically improves performance for low signal-to-noise ratio or large antenna arrays.
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.
Establishing secret keys from the commonly-observed randomness of reciprocal wireless propagation channels has recently received considerable attention. In this work we propose improved strategies for channel estimation between MIMO or beamforming systems for secret key generation. The amount of mutual information that can be extracted from the channel matrix estimates is determined by the quality of channel matrix estimates. By allocating increased energy to channel estimation for higher gain beamforming combinations at the expense of low-gain combinations, key establishment performance can be increased. Formalizing the notion of preferential energy allocation to the most efficient excitations is the central theme of this dissertation. For probing with beamforming systems, we formulate a theoretically optimal probing strategy that upper bounds the number of key bits that can be generated from reciprocal channel observations. Specifically, we demonstrate that the eigenvectors of the channel spatial covariance matrix should be used as beamformer weights during channel estimation and we optimize the energy allocated to channel estimation for each beamformer weight under a total energy constraint. The optimal probing strategy is not directly implementable in practice, and therefore we propose two different modifications to the optimal algorithm based on a Kronecker approximation to the spatial covariance matrix. Though these approximations are suboptimal, they each perform well relative to the upper bound. To explore how effective an array is at extracting all of the information available in the propagation environment connecting two nodes, we apply the optimal beamformer probing strategy to a vector current basis function expansion on the array volume. We prove that the resulting key rate is a key rate spatial bound that upper bounds the key rate achievable by any set of antenna arrays probing the channel with the same total energy constraint. For MIMO systems we assume the channel is separable with a Kronecker model, and then for that model we propose an improved probing strategy that iteratively optimizes the energy allocation for each node using concave maximization. The performance of this iterative approach is better than that achieved using the traditional probing strategy in many realistic probing scenarios.
While conventional antenna array synthesis determines the beamforming weights that create a specified antenna radiation pattern, secure array synthesis formulates the beamforming weights that enhance security for wireless transmission of sensitive data. This paper focuses on creating beamformers that improve the generation of secret encryption keys based on bidirectional estimation of the reciprocal electromagnetic propagation channel between two radios. The technique uses semidefinite programming to determine the array weights that maximize the average secure key rate under a constraint on the total transmit power. The numerical implementation of the technique incorporates array mutual coupling, and the results demonstrate that the technique outperforms a conventional beamforming solution, with the improvement becoming significant for certain channel correlation conditions.