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IEEE Transactions on Wireless Communications

Diversity-Multiplexing Tradeoff for the Multiple-Antenna Wire-tap Channel

Melda Yüksel, Elza Erkip

Published Jan 21, 2011• 55 citations
Publisher

Abstract

In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversity-multiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the transmitter (CSIT), the eavesdropper steals only transmitter antennas. This dependence on the availability of CSI is unlike the DMT results without secrecy constraints, where the DMT remains the same for no CSI and full CSI at the transmitter under short term power constraints. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.

DOI
10.1109/twc.2011.010411.090943

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In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversity-multiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the transmitter (CSIT), the eavesdropper steals only transmitter antennas. This dependence on the availability of CSI is unlike the DMT results without secrecy constraints, where the DMT remains the same for no CSI and full CSI at the transmitter under short term power constraints. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.
In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity gain and the secret multiplexing gain are defined. Using these definitions, the secret diversitymultiplexing tradeoff (DMT) is calculated analytically for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, under the assumption of Gaussian codebooks, it is shown that the eavesdropper steals both transmitter and receiver antennas, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the transmitter (CSIT), the eavesdropper steals only transmitter antennas. This dependence on the availability of CSI is unlike the DMT results without secrecy constraints, where the DMT remains the same for no CSI and full CSI at the transmitter under short term power constraints. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.
In this paper fading multiple-antenna (MIMO) wiretap channels are investigated under short term power constraints. The secret diversity-multiplexing tradeoff (DMT) is calculated analytically, when the destination and the eavesdropper have receiver side channel state information (CSI) and the source has transmitter side CSI (CSIT). It is shown that the eavesdropper steals transmitter antennas and the secret DMT depends on the effective number of antennas left. This is in contrast to the no CSIT case, where the eavesdropper effectively steals both transmit and receive antennas. A zero-forcing type scheme is shown to achieve the secret DMT when CSIT is available.
In this paper the fading multiple antenna (MIMO) wire-tap channel is investigated. Thesecretdiversity gain and thesecretmultiplexing gain are defined. Using these definitions, the secret diversity-multiplexing tradeoff (DMT) is calculated analytically when the source node does not have transmitter side channel state information (CSI). It is shown that the wire-tapperstealsdegrees of freedom from the source-destination channel, and the secret DMT depends on the remaining degrees of freedom. When CSI is available at the source, unlike the case when there are no security constraints, transmitter CSI changes the secret DMT significantly.
In this paper we study about the secure communication among wireless shared medium using secrecy performance of a codebook based transmission beamforming with limited feedback. And avoid attacker from stealing the confidential data. In the feedback method transmitter is using a predefined codebook known to transmitter and receiver knows it after producing index value as feedback during beamforming. The secrecy outage probability is analyzed to find whether it is stealed. The bound values are provided on the secrecy outage probability. The fading in multiple antenna (MIMO) wire-tap channel is investigated under short term power constraints. The secret diversity multiplexing tradeoff (DMT) is found for no transmitter side channel state information (CSI) and for full CSI. When there is no CSI at the transmitter, while using Gaussian codebooks, it seems that both transmitter and receiver antennas are stealed, and the secret DMT depends on the other degrees of freedom. When CSI is available at the transmitter (CSIT), then transmitter antenna is only stealed.
We consider secret-key agreement with public discussion over Rayleigh fading quasi-static channels. First, the secret-key diversity gain and the secret-key multiplexing gain are defined. Then, the secret-key diversity multiplexing tradeoff (DMT) is established. The eavesdropper is shown to “steal” only transmit antennas. We show that likewise the DMT without secrecy constraint, the secret-key DMT is the same either with or without full channel state information (CSI) at the transmitter (CSI-T). This insensitivity of secret-key DMT toward CSI-T highlights a fundamental difference between secret-key agreement and the wiretap channel whose secret DMT depends crucially on CSI-T. Several secret-key DMT-achieving schemes are presented in case of full CSI-T.
We study the problem of secret-key agreement between two legitimate parties, Alice and Bob, in the presence of an eavesdropper Eve. There is a public channel with unlimited capacity that is available to the legitimate parties and is also observed by Eve. Our focus is on Rayleigh fading quasistatic channels. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge of their channels. We study the system in the high-power regime. First, we define the secret-key diversity gain and the secret-key multiplexing gain. Second, we establish the secret-key diversity multiplexing tradeoff (DMT) under no channel state information (CSI) at the transmitter (CSI-T). The eavesdropper is shown to “steal” only transmit antennas. We show that, like the DMT without secrecy constraint, the secret-key DMT is the same either with or without full channel state information at the transmitter. This insensitivity of secret-key DMT toward CSI-T features a fundamental difference between secret-key agreement and the wiretap channel, in which secret DMT depends heavily on CSI-T. Finally, we present several secret-key DMT-achieving schemes in case of full CSI-T. We argue that secret DMT-achieving schemes are also key DMT-achieving. Moreover, we show formally that artificial noise (AN), likewise zero-forcing (ZF), is DMT-achieving. We also show that the public feedback channel improves the outage performance without having any effect on the DMT.