In this paper, we investigate the effect of partial channel state information on the achievable secure communication rates and secret-key generation rates over ergodic fading channels. In particular, we establish the strong secret-key capacity as well as lower bounds for the strong secrecy capacity of ergodic and block-ergodic fading channels with partial Channel State Information at the Transmitter(CSIT). Our analysis sheds light on the usefulness of CSIT to harness the benefits of fading for secrecy and allows us to quantify the penalty incurred by the lack of full CSIT. In particular, we numerically illustrate situations in which little CSIT is required to recover most of the benefits of fading and in which the legitimate terminals have an incentive to precisely characterize their channel.
In this paper, we investigate the effect of partial channel state information on the achievable secure communication rates and secret-key generation rates over ergodic fading channels. In particular, we establish the strong secret-key capacity as well as lower bounds for the strong secrecy capacity of ergodic and block-ergodic fading channels with partial Channel State Information at the Transmitter(CSIT). Our analysis sheds light on the usefulness of CSIT to harness the benefits of fading for secrecy and allows us to quantify the penalty incurred by the lack of full CSIT. In particular, we numerically illustrate situations in which little CSIT is required to recover most of the benefits of fading and in which the legitimate terminals have an incentive to precisely characterize their channel.
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.
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.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels.
We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average signal-to-noise ratio (SNR) goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Overall, channel fading has a positive impact on the secrecy capacity and rate adaptation, based on the main channel CSI, is critical in facilitating secure communications over slow fading channels.
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.
This work examines the advantages of having only channel state information at the transmitter (CSIT), and not at the receiver and the eavesdropper, when achieving secrecy in fading wiretap channels. The key idea is that, with only CSIT, the transmitter can pre-compensate for the amplitude and phase distortions on the main channel. This allows the receiver to decode coherently even without knowledge of the CSI, while leaving the eavesdropper confused by the unknown variations of its own channel. When the channel is reciprocal, this CSI assumption can be achieved in practice through reverse training, i.e., by having the receiver emit the training signal so that the transmitter can estimate the channel by itself. Two secrecy-enhancing transmission schemes are proposed to exploit the CSIT. The truncated channel inversion scheme is used when the receiver and the eavesdropper have no CSI available, and the truncated phase compensation scheme is adopted when they can practically measure the SNR. The achievable secrecy rates of these schemes are derived for both single-antenna and multi-antenna wireless fading scenarios. Numerical results show significant improvements in secrecy rate compared to the case with full CSI at all terminals.