Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel

By Ashish J. Khisti, Gregory W. Wornell. arXiv.org, 2010

461 citations recorded by the source corpus.

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7a121a2d25bb41b75a97f7168a013c20c36cf6f0

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Citations in the corpus

Optimal Cooperative Jamming to Enhance Physical Layer Security Using Relays (2011, methodology): “To improve the secrecy rate under unfavorable conditions, a possible approach is to use multiple-input multiple-output (MIMO) systems where multiple antennas at the transmitter and receiver allow the use of beamforming to steer a null to the eavesdropper [ 3 ], or the generation of artificial noise ”
Cooperation With an Untrusted Relay: A Secrecy Perspective (2009, background): “ducing correlation between the output seen by the second eavesdropper and other outputs of the channel, which tightens the upper bound as in other Sato-type bounds; see [5] for example.”
Secure Wireless Communication via Intelligent Reflecting Surface (2019, background): “tion from an AP to a user in the presence of an eavesdropper. secrecy communication rate, various techniques such as jamming with artiﬁcial noise (AN) and multi-antenna beamforming have been proposed [9]–[11]. However, in scenarios where the channel of the legitimate communication link and that of t”
The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming (2007, methodology): “Multiple-input–multiple-output (MIMO) channels were considered in [ 36 ] and [37].”
Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel (2007, methodology): “Furthermore, in the companion paper [15], we treat the multi-input, multi-output, multi-eavesdropper (MIMOME) case.”
Spatially Selective Artificial-Noise Aided Transmit Optimization for MISO Multi-Eves Secrecy Rate Maximization (2013, methodology): “ no-AN SRM designs are exactly the same. This means that ANmay be not necessary for the one Eve case. In fact, it is known that the no-AN SRM design achieves the secrecy capacity for the one Eve case [4], and the simulation result here has further conﬁ rmed that. However, the picture becomes drastic”
Secrecy Rate Maximization for Intelligent Reflecting Surface Assisted Multi-Antenna Communications (2019, methodology): “ Θ By ﬁxing Θ, the optimization with respect to W becomes: maximize W0 hH BWhB +σ 2 n,B hH E WhE +σ2 n,E subject to tr(W)≤ P, (3) where hB =HH AIΘ Hh IB +hAB and hE =HH AIΘ Hh IE + hAE. According to [15], [16], the optimal solution to W is W⋆ =Pw˜w˜H, (4) where w˜ is the normalized dominant generali”
Secure Transmission With Multiple Antennas—Part II: The MIMOME Wiretap Channel (2010, methodology): “For the MISOME channel, such an approach is near optimal, as shown in [4].”