Secrecy Rate of Cooperative MIMO in the Presence of a Location Constrained Eavesdropper

Abstract

We propose and study the cooperative MIMO architecture to enable and to improve the secrecy transmissions between clusters of mobile devices in the presence of an eavesdropper with certain location constraint. The cooperative MIMO system in this paper (referred to as Reconfigurable Distributed MIMO) is formed by temporarily activating clusters of nearby trusted mobile devices, with each cluster being centrally coordinated by its corresponding cluster head. We assume that the transmitters apply a practical eigen-direction precoding scheme to transmit the confidential signal and artificial noise, while the eavesdropper can be located in multiple possible locations in the proximity. We first obtain the expression of the secrecy rate, where the required average mutual information between the transmitters and the eavesdropper is characterized by closedform approximations. The proposed approximations are especially useful in the secrecy rate maximization, where the original non-convex problem can be solved by the successive convex approximations. Numerical results show that the secrecy rate can be significantly improved by leveraging the location constraint of the eavesdropper, compared to the existing result. We also demonstrate that the secrecy rate can be further improved by increasing the cluster size.Index Terms-Physical-layer security, cooperative MIMO, reconfigurable distributed MIMO, mobile networks, artificial noise injection, random matrix theory.legitimate transceivers and circumvents the challenges in the conventional key-based encryption, such as key distribution and management, which are especially critical in wireless communication due to its broadcasting nature.Throughout this paper, we refer to the legitimate transmitter(s) and the legitimate receiver(s) as Alice and Bob, respectively, and refer to the eavesdropper as Eve. Under the secrecy constraint, the maximum information rate between Alice and Bob is characterized by the "secrecy capacity." As shown in [2] and [3], the secrecy capacity is the difference between the Shannon rates of two channels, the legitimate channel between Alice and Bob and the eavesdropping channel between Alice and Eve, under the condition that the mutual information between Alice and Eve is zero.Multi-antenna transceivers increase the spatial degrees of freedom of the communication, which can be leveraged to improve the secrecy rate [4]. When Alice has a single antenna and Bob has multiple antennas, a.k.a. the Single-Input Multi-Output (SIMO) system, the secrecy capacity and the outage secrecy capacity were investigated in [5] and [6], while the corresponding MISO case was studied in [7] and [8]. The secrecy capacity of a special case of the MIMO wiretap channel was considered in [9], where Alice and Bob are equipped with dual antennas, and Eve is equipped with a single antenna. Recently, the physical-layer security has also been considered for the Distributed-MIMO (D-MIMO) systems in [10]-[14], where Alice has a distributed antenna array composed of remote fixed antenna por...

Secure UAV-to-Ground MIMO Communications: Joint Transceiver and Location Optimization

“…2) In the secrecy rate construction, the Shannon rate of the legitimate channel is lower-bounded by Minkowski's inequality of the information rate of an equivalent lower dimensional MIMO channel, which avoids the cumbersome zonal polynomials. On the other hand, the Shannon rate of the eavesdropping channel is obtained by exploiting the random position of the eigenspaces of the legitimate and eavesdropping channel matrices, where the Haar matrix insertion technique of [39] is applied. 3) In the secrecy rate optimization, an alternating optimization framework is proposed for designing the transmit signals and the deployment of the UAV for circumventing the non-convexity of the objective function.…”

“…To avoid the aforementioned issues, we observe that the precoder is aligned with the eigenspace of the legitimate channel, while it is randomly projected into the eigenspace of the eavesdropping channels. Therefore, we follow the HMI technique proposed in [39], which approximates the information rate (19) by replacing the fixed unitary matrix V by the randomly distributed unitary Haar matrix. The approximations are rendered accurate by beneficially exploiting the random relative positions between the eigenspaces of the legitimate and the eavesdropping channels.…”

“…On the other hand, the precoder W is misaligned with the eavesdropping channels hence the corresponding eigenchannels cannot be reduced. To address this issue, we apply the Haar matrix insertion (HMI) technique to approximate the information rate R τ (ψ, p u ), which was previously proposed in [39] and yields reasonably accurate agreement with the exact ergodic rate for a wide range 1 If artificial noise injection is applied at the transmitter, the transmit signal x can be reformulated as x = Vdiag(ψ…”

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