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IEEE Transactions on Wireless Communications

Secure Multiple-Antenna Block-Fading Wiretap Channels With Limited CSI Feedback

Amal Hyadi, Zouheir Rezki, Mohamed‐Slim Alouini

Published Jul 18, 2017• 16 citations
Publisher

Abstract

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.

DOI
10.1109/twc.2017.2727043

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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.
We study the ergodic secrecy capacity of a block- fading wiretap channel when there are multiple antennas at the transmitter, the legitimate receiver and the eavesdropper. We consider that the receivers are aware of their respective channel matrices while the transmitter is only provided by a B-bits 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. Assuming an average transmit power constraint, we provide an upper and a 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; hence, fully characterizing the secrecy capacity in this case.
We study the ergodic secrecy capacity of a block- fading wiretap channel when there are multiple antennas at the transmitter, the legitimate receiver and the eavesdropper. We consider that the receivers are aware of their respective channel matrices while the transmitter is only provided by a B-bits 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. Assuming an average transmit power constraint, we provide an upper and a 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; hence, fully characterizing the secrecy capacity in this case.
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers, under both a short term power constraint (STPC) and a long term power constraint (LTPC). We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free public channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that the lower and the upper bounds coincide asymptotically as q → ∞. When applied to Rayleigh fading channels, we show that, a 4-bit feedback achieves about 90% of the secrecy capacity when perfect main CSI is available at the transmitter. Finally, asymptotic analysis at high and low Signal-to-Noise Ratio (SNR) is presented. It is found that the capacity is bounded at high-SNR, whereas at asymptotically low-SNR, the lower bounds and the upper bound scale linearly with SNR under STPC. Furthermore, subject to LTPC, the capacity at low-SNR is equal to the capacity of the main channel without secrecy constraint and with perfect CSI at both the transmitter and the receiver, under a mild condition on the fading statistics. We also show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q=1.
In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a b -bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.
In this paper, we investigate the problem of secure broadcasting over block-fading channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having imperfect channel state information (CSI) via a finite rate feedback on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. First, we partially characterize the ergodic secrecy capacity of the system when the source broadcasts the same information to all the receivers, i.e., common message transmission. Then, we look at the independent messages case, where the transmitter broadcasts multiple independent messages to the legitimate receivers. For this case, we present lower and upper bounds on the ergodic secrecy sum-capacity. In both scenarios, we show that the proposed lower and upper bounds coincide asymptotically as the capacity of the feedback links becomes large, hence, fully characterizing the secrecy capacity in this case.
We study the secret message capacity of an ergodic block fading wiretap channel with partial channel state information at the transmitter and perfect channel state information at the receivers. We consider that in addition to the statistics of the main and the eavesdropper channel state information (CSI), the sender is provided by the legitimate receiver with a q-bit feedback, at the beginning of each coherence block, through an error-free feedback channel, with capacity q bits. We establish upper and lower bounds on the secrecy capacity. We show that a positive secrecy rate is achievable even when the feedback is at the end of each coherence block and q = 1. We also show that the lower and the upper bounds coincide asymptotically as q → ∞. Finally, asymptotic analysis at high Signal-to-Noise Ratio (SNR) are presented where it is found that the capacity is bounded at high-SNR and present a simple suboptimal scalar quantizer that is capacity achieving, without the need of any numerical optimization, as q → ∞. When applied to Rayleigh fading channels, we show that, at high-SNR, a 4-bit feedback achieves 90% of the secrecy capacity when perfect main CSI is available at the transmitter.