Abstract
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.
Highlights
Wireless communications are prone to eavesdropping by nature: it is inevitable for electromagnetic waves propagated over the public medium to be subject to wire-tapping from an unwanted party, which makes the security one of the biggest challenges for the wireless community to ever encounter
In [10] it has been proved that the singular value decomposition (SVD)-based precoding technique achieves capacity, proving the same for the generalized singular value decomposition (GSVD) in our model is beyond the scope of this article
A lower bound on the secrecy capacity for the Gaussian relay wire-tap channel is expressed as [9]
Summary
Wireless communications are prone to eavesdropping by nature: it is inevitable for electromagnetic waves propagated over the public medium to be subject to wire-tapping from an unwanted party, which makes the security one of the biggest challenges for the wireless community to ever encounter. In [8,9], the limits to the Gaussian wire-tap model in ensuring secure communications were pushed further by the introduction of a relay in the communication system. The behavior of the above defined model following the introduction of a multi-antenna relay is to be analyzed in this article. The generalized singular value decomposition (GSVD) will serve as a precoding technique in the model under investigation as did the singular value decomposition (SVD) for the Gaussian MIMO channel in [10]. In [10] it has been proved that the SVD-based precoding technique achieves capacity, proving the same for the GSVD in our model is beyond the scope of this article.
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