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 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.
In this work, we examine the secrecy capacity region of the block-fading broadcast channel with confidential messages (BCC) when the transmitter has limited knowledge of the channel. In particular, we consider a two-user communication system where the transmitter has one common message to be transmitted to both users and one confidential message intended to only one of them. The confidential message has to be kept secret from the other user to whom the information is not intended. The transmitter is not aware of the channel state information (CSI) of neither channel and is only provided by limited CSI feedback sent at the beginning of each fading block. Assuming an error-free feedback link, we characterize the secrecy capacity region of this channel and show that even with a 1-bit CSI feedback, a positive secrecy rate can still be achieved. Then, we look at the case where the feedback link is not error- free and is rather a binary erasure channel (BEC). In the latter case, we provide an achievable secrecy rate region and show that as long as the erasure event is not a probability 1 event, the transmitter can still transmit the confidential information with a positive secrecy rate.
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 investigate the problem of secure broadcasting over fast fading channels with imperfect main channel state information (CSI) at the transmitter. In particular, we analyze the effect of the noisy estimation of the main CSI on the throughput of a broadcast channel where the transmission is intended for multiple legitimate receivers in the presence of an eavesdropper. Besides, we consider the realistic case where the transmitter is only aware of the statistics of the eavesdropper's CSI and not of its channel's realizations. First, we discuss the common message transmission case where the source broadcasts the same information to all the receivers, and we provide an upper and a lower bounds on the ergodic secrecy capacity. For this case, we show that the secrecy rate is limited by the legitimate receiver having, on average, the worst main channel link and we prove that a non-zero secrecy rate can still be achieved even when the CSI at the transmitter is noisy. Then, we look at the independent messages case where the transmitter broadcasts multiple messages to the receivers, and each intended user is interested in an independent message. For this case, we present an expression for the achievable secrecy sum-rate and an upper bound on the secrecy sum-capacity and we show that, in the limit of large number of legitimate receivers K, our achievable secrecy sum-rate follows the scaling law log((1-a ) log(K)), where is the estimation error variance of the main CSI. The special cases of high SNR, perfect and no-main CSI are also analyzed. Analytical derivations and numerical results are presented to illustrate the obtained expressions for the case of independent and identically distributed Rayleigh fading channels.