Optimal power allocation for GSVD-based beamforming in the MIMO Gaussian wiretap channel

Abstract

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.

Solutions for the MIMO Gaussian Wiretap Channel With a Cooperative Jammer

“…(29)- (30), we still have a design parameter, N, that should be chosen in its acceptable range Λ 22 N Λ 2 such that the power constraint Tr(K w ) = P h is satisfied. Finding the optimal N that minimizes I(X 1 ; Y 2 ) when K x and K w are given by (13) and (30), respectively, is as intractable as the general optimization problem in (5). Instead, we simply restrict the N we consider to those that can be linearly parameterized within the acceptable range, as follows:…”

“…The secrecy capacity of a Gaussian wiretap channel, which is in general a difficult non-convex optimization problem, has been addressed and solved for in [3]- [7]. The secrecy capacity under an average power constraint is treated in [4] and [5], where in [4] a beamforming approach, based on the generalized singular value decomposition (GSVD), is proposed that achieves the secrecy capacity in the high SNR regime. In [5], we propose an optimal power allocation that achieves the secrecy capacity of the GSVD-based multiple-input, multipleoutput (MIMO) Gaussian wiretap channel for any SNR.…”

“…The secrecy capacity under an average power constraint is treated in [4] and [5], where in [4] a beamforming approach, based on the generalized singular value decomposition (GSVD), is proposed that achieves the secrecy capacity in the high SNR regime. In [5], we propose an optimal power allocation that achieves the secrecy capacity of the GSVD-based multiple-input, multipleoutput (MIMO) Gaussian wiretap channel for any SNR. In [7], a closed-form expression for the secrecy capacity is derived under a certain power-covariance constraint.…”

Robust transmit design for secure AF relay networks with imperfect CSI

“…One way to achieve non-zero secrecy rate in this case is to introduce multi-antenna nodes [3][4][5][6][7][8][9][10][11], wherein multiantenna techniques can enable directional transmission, thus allowing secret communication even when the eavesdropper's channel has a much better quality. However, due to the cost or size limitations, multi-antenna nodes may not be available in some practical applications.…”

Linear MMSE transceiver optimization for general MIMO wiretap channels with QoS constraints

“…Recently a significant research effort has been invested for the computation of the secrecy capacity of a range of communication channels [1]- [4]. It was shown in [3] that generalized singular value decomposition (GSVD) scheme is a secrecy capacity-approaching scheme for the multi-input, multi-output, multi-eavesdropper (MIMOME) channel in the high signal-to-noise ratio (SNR) regime, and the optimal power allocation that achieves the secrecy capacity for the GSVD scheme was derived in [5]. In [6], a closed-form transmit beamforming scheme based on maximizing signal-to-leakage-plus-noise ratio (SLNR) was proposed for the MIMOME channels, and it was shown that the SLNR-based scheme outperforms GSVD-based scheme.…”