This paper presents a two-phase process consisting of advantage distillation (AD) and information reconciliation for achieving secret sharing over a wiretap channel. By using the feedback bits from the legitimate receiver to transmitter, we propose a novel AD scheme for multiple-input multiple-output (MIMO) wiretap (MIMO-WT) channels. We first generalize the extended orthogonal space-time block codes (EO-STBCs). Then, based on the generalized EO-STBCs (GEO-STBCs) and channel state information (CSI), the feedback bits transmitted from the legitimate receiver to the transmitter are generated to increase the signal-to-noise ratio (SNR) gap between the legitimate receiver and the eavesdropper. Simulation results show that the feedback performance gain of the proposed AD scheme increases rapidly with the number of transmit antennas and the value of SNR. A bit error rate (BER) performance gain up to 5.5 dB is obtained by the legitimate receiver over the eavesdropper at the BER of 10-5. Moreover, it is also shown that the secrecy capacity of two-way MIMO-WT channels with feedback grows rapidly in low SNR regime and grows slowly in high SNR regime.
This paper presents a two-phase process consisting of advantage distillation (AD) and information reconciliation for achieving secret sharing over a wiretap channel. By using the feedback bits from the legitimate receiver to transmitter, we propose a novel AD scheme for multiple-input multiple-output (MIMO) wiretap (MIMO-WT) channels. We first generalize the extended orthogonal space-time block codes (EO-STBCs). Then, based on the generalized EO-STBCs (GEO-STBCs) and channel state information (CSI), the feedback bits transmitted from the legitimate receiver to the transmitter are generated to increase the signal-to-noise ratio (SNR) gap between the legitimate receiver and the eavesdropper. Simulation results show that the feedback performance gain of the proposed AD scheme increases rapidly with the number of transmit antennas and the value of SNR. A bit error rate (BER) performance gain up to 5.5 dB is obtained by the legitimate receiver over the eavesdropper at the BER of 10-5. Moreover, it is also shown that the secrecy capacity of two-way MIMO-WT channels with feedback grows rapidly in low SNR regime and grows slowly in high SNR regime.
The three-phase process of achieving secret sharing over a wiretap channel are, respectively, advantage distillation, information reconciliation, and privacy amplification. In this paper, we first generalize the extended orthogonal space time block codes (EO-STBCs). Then, based on the generalized EO-STBCs (GEO-STBCs) and the feedback bits from the legitimate receiver, we propose a new advantage distillation scheme for multiple-input multiple-output (MIMO) wiretap channels. Simulation results show that the bit error rate (BER) performance gain up to 4.2 dB is obtained by the legitimate receiver over the eavesdropper at the BER of 10−5. Moreover, it is shown that the feedback performance gain of the proposed advantage distillation scheme grows exponentially with signal-to-noise ratio (SNR).
Wyner's wiretap channel is generalized to the case when the sender, the receiver and the eavesdropper have multiple antennas. We consider two cases: the deterministic case and the fading case. In the deterministic case, the channel matrices of the intended receiver and the eavesdropper are fixed and known to all the nodes. In the fading case, the channel matrices experience block fading and the sender has only the intended receiver's channel state information (CSI) and statistical knowledge of the eavesdropper's channel. For the deterministic case, a scheme based on the generalized-singular-value-decomposition (GSVD) of the channel matrices is proposed and shown to achieve the secrecy capacity in the high signal-to-noise-ratio (SNR) limit. When the intended receiver has only one antenna (MISO case) the secrecy-capacity is characterized for any SNR. Next, a suboptimal "artificial noise" based scheme is considered. Its performance is characterized and observed to be nearly optimal in the high SNR regime for the MISO case. This scheme extends naturally to the fading case and results are reported for the MISO case. For the independent Rayleigh fading distribution as we simultaneously increase the number of antennas at the sender and the eavesdropper, the secrecy capacity approaches zero if and only if the ratio of the number of eavesdropper antennas to transmitter antennas is at least two.
We study strategies for enhanced secrecy using cooperative jamming in secure communication systems with limited rate feedback. A Gaussian multiple-input multiple-output (MIMO) wiretap channel with a jamming helper is considered. The transmitter and helper both require channel state information (CSI), which is quantized at the receiver and fed back through two sum-rate-limited feedback channels. The quantization errors result in reduced beamforming gain from the transmitter, as well as interference leakage from the helper. First, under the assumption that the eavesdropper's CSI is completely unknown, we derive a lower bound on the average main channel rate and find the feedback bit allocation that maximizes the jamming power under a constraint on the bound. For the case where statistical CSI for the eavesdropper's channel is available, we derive a lower bound on the average secrecy rate, and we optimize the bound to find a suitable bit allocation and the transmit powers allocated to the transmitter and helper. For the case where the transmitter and helper have the same number of antennas, we obtain a closed-form solution for the optimal bit allocation. Simulations verify the theoretical analysis and demonstrate the significant performance gain that results with intelligent feedback bit allocation and power control.
In this paper, a novel transmit antenna selection scheme for multiple input multiple output (MIMO) wiretap channels is proposed. This new scheme achieves higher secrecy performance by exploiting eavesdropper's channel state information. The key idea behind our proposal is to perform the antenna selection aiming to maximize the overall secrecy rate instead of maximizing the instantaneous signal-to-noise ratio of the main channel. In our analysis, we assume that the legitimate receiver and the eavesdropper employ a maximal-ratio combining technique to combine the received signals from the transmitter. Considering Nakagami-m fading channels, a closed-form expression for the secrecy outage probability is derived, which can be used as a quality of service metric. Further, an asymptotic analysis is carried out and the diversity/array gains are obtained. The ergodic secrecy rate is also investigated for the case of multiple input single output wiretap channels. Representative numerical examples are plotted and validated through Monte Carlo simulations. Insightful discussions are drawn from the proposed analysis.
While the impact of finite-rate feedback on the capacity of fading channels has been extensively studied in the literature, not much attention has been paid to this problem under secrecy constraint. In this work, we study the ergodic secret capacity of a multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channel with quantized channel state information (CSI) at the transmitter and perfect CSI at the legitimate receiver, under the assumption that only the statistics of eavesdropper CSI is known at the transmitter. We refine the analysis of Lin et al.'s random vector quantization (RVQ) based artificial noise (AN) scheme, where a heuristic upper bound on the secrecy rate loss (compared to the perfect CSI case) was given. We propose a lower bound on the ergodic secrecy capacity. We show that the lower bound and the secrecy capacity with perfect CSI coincide asymptotically as the number of feedback bits and the AN power go to infinity. For practical applications, we propose a very efficient quantization codebook construction method for the two transmit antennas case.
In this paper, we investigate the ergodic secrecy capacity of a block-fading wiretap channel with limited channel knowledge at the transmitter. We consider that the legitimate receiver, the eavesdropper, and the transmitter are equipped with multiple antennas and that the receiving nodes are aware of their respective channel matrices. On the other hand, the transmitter is only provided by a B-bit feedback of the main channel state information. The feedback bits are sent by the legitimate receiver, at the beginning of each fading block, over an error-free public link with limited capacity. The statistics of the main and the eavesdropper channel state information are known at all nodes. Assuming an average transmit power constraint, we establish upper and lower bounds on the ergodic secrecy capacity. Then, we present a framework to design the optimal codebooks for feedback and transmission. In addition, we show that the proposed lower and upper bounds coincide asymptotically, as the capacity of the feedback link becomes large, i.e., B→∞, hence fully characterizing the ergodic secrecy capacity in this case. Besides, we analyze the asymptotic behavior of the presented secrecy rates, at high signal-to-noise ratio, and evaluate the gap between the bounds.