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arXiv:2309.12502 · IEEE Transactions on Signal Processing

Secure Degree of Freedom of Wireless Networks Using Collaborative Pilots

Yingbo Hua, Qingpeng Liang, Md Saydur Rahman

Published Jan 1, 2023• 5 citations
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Abstract

A wireless network of full-duplex nodes/users, using anti-eavesdropping channel estimation (ANECE) based on collaborative pilots, can yield a positive secure degree-of-freedom (SDoF) regardless of the number of antennas an eavesdropper may have. This paper presents novel results on SDoF of ANECE by analyzing secret-key capacity (SKC) of each pair of nodes in a network of multiple collaborative nodes per channel coherence period. Each transmission session of ANECE has two phases: phase 1 is used for pilots, and phase 2 is used for random symbols. This results in two parts of SDoF of ANECE. Both lower and upper bounds on the SDoF of ANECE for any number of users are shown, and the conditions for the two bounds to meet are given. This leads to important discoveries, including: a) The phase-1 SDoF is the same for both multi-user ANECE and pair-wise ANECE while the former may require only a fraction of the number of time slots needed by the latter; b) For a three-user network, the phase-2 SDoF of all-user ANECE is generally larger than that of pair-wise ANECE; c) For a two-user network, a modified ANECE deploying square-shaped nonsingular pilot matrices yields a higher total SDoF than the original ANECE. The multi-user ANECE and the modified two-user ANECE shown in this paper appear to be the best full-duplex schemes known today in terms of SDoF subject to each node using a given number of antennas for both transmitting and receiving.

DOI
10.1109/tsp.2023.3310252

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A wireless network of full-duplex nodes/users, using anti-eavesdropping channel estimation (ANECE) based on collaborative pilots, can yield a positive secure degree-of-freedom (SDoF) regardless of the number of antennas an eavesdropper may have. This paper presents novel results on SDoF of ANECE by analyzing secret-key capacity (SKC) of each pair of nodes in a network of multiple collaborative nodes per channel coherence period. Each transmission session of ANECE has two phases: phase 1 is used for pilots, and phase 2 is used for random symbols. This results in two parts of SDoF of ANECE. Both lower and upper bounds on the SDoF of ANECE for any number of users are shown, and the conditions for the two bounds to meet are given. This leads to important discoveries, including: a) The phase-1 SDoF is the same for both multi-user ANECE and pair-wise ANECE while the former may require only a fraction of the number of time slots needed by the latter; b) For a three-user network, the phase-2 SDoF of all-user ANECE is generally larger than that of pair-wise ANECE; c) For a two-user network, a modified ANECE deploying square-shaped nonsingular pilot matrices yields a higher total SDoF than the original ANECE. The multi-user ANECE and the modified two-user ANECE shown in this paper appear to be the best full-duplex schemes known today in terms of SDoF subject to each node using a given number of antennas for both transmitting and receiving.
Anti-eavesdropping channel estimation (ANECE) is useful for a network of cooperative full-duplex radio devices/users. Using ANECE, a secret key can be generated by each pair of users, and additional secret information can be transmitted between a pair of users. This paper analyzes the capacity of the secret key based on ANECE, and compares it with the conventional method for channel training. The paper also analyzes the secrecy capacity of information transmission using an one-way scheme, and compares it with a two-way scheme. It is shown that the total amount of secrecy generated from ANECE can be substantially larger than that based on the conventional method especially when an eavesdropper may have an unlimited number of antennas. The paper also formulates a total secure degree of freedom (TSDoF) of the ANECE based scheme, and compares it with a prior scheme of secret information transmission from a multi-antenna node to another against a multi-antenna eavesdropper where channel state information is unknown everywhere initially. The comparison shows that there is a substantial gain of TSDoF by exploiting full-duplex radios and reciprocal channels via ANECE. Most of the key insights are highlighted in twelve proven properties.
This paper explores the pair-wise secure degree of freedom (SDoF) of a network with multiple full-duplex multiple-input multiple-output nodes, where the nodes communicate with each other while being wiretapped by a multi-antenna eavesdropper. This paper aims to fill the gap in the theoretical analysis of the optimal pair-wise SDoF of multiple full-duplex node systems from an information theory perspective when the channel state information remains unknown to each node at the beginning of the coherence interval. To this end, we first derive an upper bound of the achievable SDoF of the system using the optimal signal structure of the pair-wise secrecy rate. Then, by demonstrating that the upper bound is achievable using Gaussian signals, the optimal SDoF of the system is derived. The numerical results verify that the obtained optimal pair-wise SDoF extends the existing research with two legitimate nodes and increases the optimal SDoF by adjusting the number of out-of-pair transmit antennas appropriately.
This paper examines the role of full-duplex radio for securing wireless network from a new perspective. It first studies the secrecy capacity of two single-antenna full-duplex users against a multi-antenna eavesdropper (Eve) who has the perfect knowledge of the channel state information (CSI) from users to Eve. It is shown that if Eve uses a basic matched-filtering, the probability of zero secrecy (or outage) can be made small by a large jamming power from both users and a small gain of residual self-interference (RSI) power. But if Eve uses the optimal matched-filtering, the probability of outage grows rapidly as either the jamming power from the users increases or the number of antennas on Eve increases, regardless of the RSI gain. To prevent any Eve from obtaining its CSI, this paper then proposes a novel anti-eavesdropping channel estimation (ANECE) method, which allows users to obtain their own CSI while keeping all Eves in handicap. This method also prevents Eves from colluding with each other at any layer. The design of ideal pilots for ANECE for multiple multi-antenna users and multiple broadband multi-antenna users is discussed. It is also shown that the capacity of Eve with any number of antennas but without its CSI can be virtually eliminated over a time window corresponding to the number of antennas at the transmitter for each realization of the CSI.
This paper reviews the basic principles of prior methods for the purpose of wireless anti-eavesdropping channel estimation (ANECE), and highlights their major shortcomings and limitations such as failure for carrier synchronization without a pilot and limited transmission range of a full-duplex radio. This paper also proposes and analyses a new scheme of ANECE using multi-antenna half-duplex radios. This new scheme consists of three phases of transmissions between two radio nodes (Alice and Bob). In phase 1, Bob sends out a pilot via one of his antennas so that Alice can carry out carrier synchronization and channel estimation. In phase 2, Alice sends out a pilot via one of her antennas so that Bob can carry out carrier synchronization and channel estimation. In phase 3, perfectly synchronized with phase 2, Alice applies transmit beamforming and sends out a stream of information via all her other antennas. This new scheme of ANECE for multi-antenna half-duplex radios is derived from an ANECE design for antenna-isolation based full-duplex radios.
This letter focuses on the optimal sum secure degree of freedom (SDoF) in a two-way wiretap channel (TW-WC), wherein two legitimate full-duplex multiple-antenna nodes cooperate with each other and are wiretapped by a multiple antenna eavesdropper simultaneously. It aims to find the optimal sum SDoF pertaining to secret-key capacity for the TW-WC. First, we analyze the upper bound and lower bounds of the optimal sum SDoF by establishing their equivalence to the expression of the optimal SDoF corresponding to the secrecy rate for the TW-WC. Subsequently, in scenarios where the legitimate nodes are configured with an equal number of transmit and receive antennas, it is elucidated that the upper and lower bounds of the optimal SDoF converge. Furthermore, the findings suggest that a higher SDoF can be achieved than the existing works, thereby heralding an enhancement in secure spectral efficiency.
Anti-eavesdropping channel estimation (ANECE) is a method that uses specially designed pilot signals to allow two or more full-duplex radio devices each with one or more antennas to estimate their channel state information (CSI) consistently and at the same time prevent eavesdropper (Eve) with any number of antennas from obtaining its CSI consistently. This paper presents optimal designs of the pilots for ANECE based on two criteria. The first is the mean squared error (MSE) of channel estimation for the users, and the second is the mutual information (MI) between the pilot-driven signals observed by the users. Closed-form optimal pilots are shown under the sum-MSE and sum-MI criteria subject to a symmetric and isotropic condition. Algorithms for computing the optimal pilots are shown for general cases. Fairness issues for three or more users are discussed. The performances of different designs are compared.