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On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels

On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels,10.1109/TWC.2011.011811.100356,IEEE Transactions on Wireless Communications,Jiangyuan Li,At

On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels   (Citations: 3)
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A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a trans- mitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper chan- nel is available at the transmitter. This is a non-convex optimiza- tion problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.
Journal: IEEE Transactions on Wireless Communications - TWC , vol. 10, no. 4, pp. 1176-1187, 2011
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    • ...h�� ∈���� (0, I). For Gaussian input, the optimal covariance matrix to maximize the achievable ergodic secrecy rate is shown to be a rank one matrix [7], i.e., a beamforming vector, and the achievable ergodic secrecy rate can be found by solving the following optimization problem...

    Shafi Basharet al. On the Secrecy Rate of Multi-Antenna Wiretap Channel under Finite-Alph...

    • ...the case where only statistical channel knowledge is available and ergodic secrecy rate is studied [8], [29])...

    Jing Huanget al. Cooperative Jamming for Secure Communications in MIMO Relay Networks

    • ...In [11], a Gaussian multiple-input single-output (MISO) wiretap channel was studied assumingthatonlystatisticalinformationabouttheeavesdropperchannel isavailableatthetransmitter,whileforthelegitimatechanneltwocases were considered, namely, full CSI, or statistical information only...
    • ...For the above scenario, we find the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint .As imilar scenario was used in [11] and [13] for the MISO eavesdropper channel...
    • ...The fact that the eavesdropper employs multiple antennas makes the proof of optimality of beamforming more difficult than that of [11] and [13]...
    • ...Unlike [11] and [13], we use the framework of Fritz John conditions [28, p. 164], [29, Ch. 4] (without any regularity conditions) to show that the solution satisfies the Karush–Kuhn–Tucker (KKT) conditions (note that KKT require regularity conditions)...
    • ...Another significant difference with [11] and [13] is that in this work we show that Piyavskii’s algorithm can be used to obtain the global optimizer of the resulting univariate problem...
    • ...Certainly, these results can be used in the problems of [11] and [13]...
    • ...Unlike [11] and [13], we use the framework of Fritz John conditions (without any regularity conditions) to show that the solution satisfies the KKT conditions (note that KKT conditions require regularity conditions)...
    • ...This method of reduction is also used in [11] and [13]...
    • ...The same lemma was also used in [11] and [13]...

    Jiangyuan Liet al. Ergodic Secrecy Rate for Multiple-Antenna Wiretap Channels With Rician...

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