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IEEE Vehicular Technology Conference

Joint SVD-GSVD Precoding Technique and Secrecy Capacity Lower Bound for the MIMO Relay Wire-Tap Channel

Marouen Jilani, Tomoaki Otsuki Ohtsuki

Published May 1, 2012• 8 citations
Publisher

Abstract

We consider a problem of secure communications for the communication system consisting of multiple outputs for a source and a relay and multiple inputs for the relay, a destination and an eavesdropper. For the above-mentioned communication system, we establish a lower bound on the secrecy capacity at which secure communications between the source and the destination are attainable. We make use of the singular value decomposition (SVD) and its generalization to decompose the whole system into parallel independent channels. At the source, the generalized singular value decomposition (GSVD) is performed to simultaneously diagonalize the channel matrices of the relay and the destination and independently code across the resulting parallel channels. At the relay, the SVD is performed to beamform the signal towards the destination. The scalar case of what we are considering in this paper has been investigated in previous literature, to prove that the introduction of a fourth party, the relay, in the wire-tap channel facilitates secure wireless communications. Our simulation results are in line with the scalar case's and prove to be successful in achieving secrecy capacity where the conventional model failed, i.e. when no relay is introduced and the eavesdropper's channel incurs as little noise as the legitimate receiver.

DOI
10.1109/vetecs.2012.6240145

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We consider a problem of secure communications for the communication system consisting of multiple outputs for a source and a relay and multiple inputs for the relay, a destination and an eavesdropper. For the above-mentioned communication system, we establish a lower bound on the secrecy capacity at which secure communications between the source and the destination are attainable. We make use of the singular value decomposition (SVD) and its generalization to decompose the whole system into parallel independent channels. At the source, the generalized singular value decomposition (GSVD) is performed to simultaneously diagonalize the channel matrices of the relay and the destination and independently code across the resulting parallel channels. At the relay, the SVD is performed to beamform the signal towards the destination. The scalar case of what we are considering in this paper has been investigated in previous literature, to prove that the introduction of a fourth party, the relay, in the wire-tap channel facilitates secure wireless communications. Our simulation results are in line with the scalar case's and prove to be successful in achieving secrecy capacity where the conventional model failed, i.e. when no relay is introduced and the eavesdropper's channel incurs as little noise as the legitimate receiver.
We consider a problem of secure communications for the communication system consisting of multiple inputs for a source and a relay and multiple outputs for the relay, a destination and an eavesdropper. For the above-mentioned communication system, we establish a lower bound on the secrecy capacity at which secure communications between the source and the destination are attainable. We make use of the singular value decomposition (SVD) and its generalization to decompose the whole system into parallel independent channels. At the source, the generalized singular value decomposition (GSVD) is performed to simultaneously diagonalize the channel matrices of the relay and the destination and independently code across the resulting parallel channels. At the relay, the SVD is performed to beamform the signal towards the destination. The scalar case of what we are considering in this article has been investigated in previous literature, to prove that the introduction of a fourth party, the relay, in the wire-tap channel facilitates secure wireless communications. Our simulation results are in line with the scalar case’s and prove to be successful in achieving secrecy capacity where the conventional model failed, i.e., when no relay is introduced and the eavesdropper’s channel incurs as little noise as the legitimate receiver.
In this paper, we investigate the security issue of a two-hop amplify-and-forward MIMO wireless relay networks in the existence of a multi-antenna eavesdropper. The optimal scheme to achieve the secrecy capacity involves a non-convex optimization and is still an open problem. Aiming to find an efficient way to enhance the secrecy rate, we propose a suboptimal joint source and relay linear precoding scheme. In the scheme, the source node adopt a generalized singular value decomposition (GSVD) based precoding to transmit the signal in the first phase, and the relay node forwards the received signal based on SVD in the null-space of the wiretap channel in the second phase. Power allocations in both phases are optimized to maximize the secrecy rate. An alternating iterative optimization algorithm is proposed to solve the problem. The algorithm is computationally efficient and guarantees to converge to a local optimum. Numerical evaluation results are provided to show the effectiveness of the iterative algorithm and the proposed secrecy scheme.
Secure communications can be impeded by eavesdroppers in conventional relay systems. This paper proposes cooperative jamming strategies for two-hop relay networks where the eavesdropper can wiretap the relay channels in both hops. In these approaches, the normally inactive nodes in the relay network can be used as cooperative jamming sources to confuse the eavesdropper. Linear precoding schemes are investigated for two scenarios where single or multiple data streams are transmitted via a decode-and-forward (DF) relay, under the assumption that global channel state information (CSI) is available. For the case of single data stream transmission, we derive closed-form jamming beamformers and the corresponding optimal power allocation. Generalized singular value decomposition (GSVD)-based secure relaying schemes are proposed for the transmission of multiple data streams. The optimal power allocation is found for the GSVD relaying scheme via geometric programming. Based on this result, a GSVD-based cooperative jamming scheme is proposed that shows significant improvement in terms of secrecy rate compared to the approach without jamming. Furthermore, the case involving an eavesdropper with unknown CSI is also investigated in this paper. Simulation results show that the secrecy rate is dramatically increased when inactive nodes in the relay network participate in cooperative jamming.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy capacity of the multiple antenna MIMO wiretap channel is found for aribtrary numbers of antennas under the assumption that the transmitter performs beamforming based on the generalized singular value decomposition (GSVD). More precisely, the optimal allocation of power for the GSVD-based precoder that achieves the secrecy capacity is derived. This solution is shown to have several advantages over prior work that considered secrecy capacity for the general MIMO Gaussian wiretap channel under a high SNR assumption. Numerical results are presented to illustrate the proposed theoretical findings.
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes achieving the secrecy capacity are developed subsequently, and the secrecy capacity is compared with the generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed precoding for this problem. Numerical results show that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. The input covariance matrix that achieves the secrecy capacity is determined. In particular, it is shown that the secrecy capacity of this channel can be achieved by linear precoding. Precoding and power allocation schemes that maximize the achievable secrecy rate, and thus achieve the secrecy capacity, are developed. The secrecy capacity is then compared with the achievable secrecy rate of generalized singular value decomposition (GSVD)-based precoding, which is the best previously proposed technique for this problem. Numerical results demonstrate that substantial gain can be obtained in secrecy rate between the proposed and GSVD-based precodings.