Abstract-This paper studies a multi-antenna wiretap channel with a passive eavesdropper and an external helper, where only quantized channel information regarding the legitimate receiver is available at the transmitter and helper due to finite-rate feedback. Given a fixed total bandwidth for the two feedback channels, the receiver must determine how to allocate its feedback bits to the transmitter and helper. Assuming zero-forcing transmission at the helper and random vector quantization of the channels, an analytic expression for the achievable ergodic secrecy rate due to the resulting quantization errors is derived. While direct optimization of the secrecy rate is difficult, an approximate upper bound for the mean loss in secrecy rate is derived and a feedback bit allocation method that minimizes the average upper bound on the secrecy rate loss is studied. A closed-form solution is shown to be possible if the integer constraint on the bit allocation is relaxed. Numerical simulations indicate the significant advantage that can be achieved by adaptively allocating the available feedback bits.Index Terms-Cooperative jamming, feedback bits allocation, limited feedback, MISO wiretap channel.

This paper considers a multiple-input multipleoutput (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 rate of the multiple antenna MIMO wiretap channel is maximized for arbitrary 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 maximizes the achievable secrecy rate is derived. Numerical results are presented to illustrate that the achievable secrecy rate of the GSVD-based precoding approach is nearly identical to that of the optimal scheme.

We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees no decrease in the secrecy capacity of the wiretap channel. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no non-trivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios. Index TermsPhysical-layer security, interference channel, MIMO wiretap channel, cooperative jamming.

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This paper considers a multiple-input multipleoutput (MIMO) Gaussian wiretap channel with a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. We first study the rank of the optimal input covariance matrix that achieves the secrecy capacity of the MIMO Gaussian wiretap channel under an average power constraint. The rank and other properties of the optimal solution are derived based on certain relationships between the channel matrices for the legitimate receiver and eavesdropper. Next, by obtaining necessary and sufficient conditions on the MIMO wiretap channel parameters, we determine the conditions under which the optimal input covariance matrix is full-rank or rank-deficient. For the case that the optimal input covariance is full-rank, we fully characterize the solution. When the optimal input covariance is rank-deficient, we show that the given MIMO wiretap channel can be modeled by an equivalent wiretap channel whose optimal input covariance is full rank and achieves the same secrecy capacity as the original system. Numerical results are presented to illustrate the proposed theoretical findings.Index Terms-MIMO Wiretap Channel, physical layer security, secrecy capacity.

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