Wireless security has become an important issue for modern wireless networks. Due to the broadcast nature of wireless channels possibility of eavesdropping the transmission is provided for non-legitimate receivers. In the present paper, we consider a multi-antenna wiretap channel in a fast-fading environment with only statistical channel state information available at the receiver. The overall performance of such channel is characterized by the ergodic secrecy capacity, which, in general, cannot be characterized explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation for the achievable ergodic secrecy rate under arbitrary channel inputs. The obtained large-system approximation matches well with the actual simulated secrecy rates, revealing some interesting behavior of the secrecy rates in the given scenario.
Wireless security has become an important issue for modern wireless networks. Due to the broadcast nature of wireless channels possibility of eavesdropping the transmission is provided for non-legitimate receivers. In the present paper, we consider a multi-antenna wiretap channel in a fast-fading environment with only statistical channel state information available at the receiver. The overall performance of such channel is characterized by the ergodic secrecy capacity, which, in general, cannot be characterized explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation for the achievable ergodic secrecy rate under arbitrary channel inputs. The obtained large-system approximation matches well with the actual simulated secrecy rates, revealing some interesting behavior of the secrecy rates in the given scenario.
Security issues in wireless networks have become a subject of growing interest in recent years due to the broadcast nature of wireless channels. In this paper, we investigate secure communication over a multi-antenna wiretap channel in the presence of randomly distributed eavesdroppers. In the fast fading environment, the overall performance of this channel is traditionally characterized by the ergodic secrecy capacity, which, in general, cannot be derived explicitly. Nevertheless, based on the assumption that the numbers of antennas at legitimate terminals and the number of eavesdroppers grow large without bound, we derive a deterministic approximation of an achievable ergodic secrecy rate for arbitrary inputs. In addition, we characterize the secrecy rates for practically relevant separate-decoding scheme at the receiver. We validate the proposed large-system approximation through numerical simulations and observe a good match with the actual secrecy rates. Finally, we also analyze some interesting behavior of the secrecy rates in the given scenario depending on the geometry of the nodes.
In this paper, we consider the secure transmission in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity result with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is forming an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of which the same as the eavesdropper's channel matrix. Next, subject to the total power constraint overall transmit antennas, we solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, with aids of the proposed degraded channel, we show that the stochastic MIMOME optimization problem can be transformed to be a Schur-concave problem to find its optimal solution. Finally, we find that the MIMOME secrecy capacities scale with the signal-to-noise ratios with large enough numbers of antennas at legitimate receiver. However, as shown in previous works, such a scaling does not exist for wiretap channels with single antenna at legitimate receiver and eavesdropper each.
With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual information. Leveraging results from random matrix theory, we are able to characterize the achievable ergodic secrecy rates. Based on this characterization, we address the problem of covariance optimization at the transmitter. Our numerical results demonstrate a good match between the large-system approximation and the actual simulated secrecy rates, as well as some interesting features of the precoder optimization.
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 consider the secure transmission in ergodic fast Rayleigh fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels. We assume that the statistics of both the legitimate and eavesdropper channels are the only available channel state information at the transmitter (CSIT). By introducing a new secrecy capacity upper bound, we prove that the secrecy capacity is achieved by the Gaussian input without prefixing. To attain this result, we form another MISOSE channel for upper-bounding by relaxing the equivocation constraint, and tighten the bound by carefully selecting correlations between the legitimate and eavesdropper channel gains. The resulting upper bound is tighter than the others in the literature which are based on modifying the correlation between the noises at the legitimate receiver and eavesdropper. Next, we fully characterize the secrecy capacity by showing that the optimal channel input covariance matrix is a scaled identity matrix. The key to solve such a stochastic optimization problem is by exploiting the completely monotone property of the secrecy capacity. Finally, we prove that with only statistical CSIT of both channels, the capacity will neither scale with signal-to-noise ratio (SNR) nor the number of antenna. Our numerical results also match these observations and further confirm that having the legitimate CSIT (realizations) is very beneficial to increase the secrecy capacity.
This chapter considers securing wireless communications at the physical layer using multiple antennas. In particular, the multiple antenna (MIMO) wiretap channel is presented and its secrecy capacity is provided. Further investigation of the high-SNR characterization of the secrecy capacity, i.e., secure degrees of freedom, reveals that the secrecy capacity of the MIMO wiretap channel does not scale with the transmit power when the eavesdropper has an advantage over the legitimate transmitter in the number of antennas. An external multi-antenna cooperative jammer terminal is introduced to the channel model in order to improve its secrecy capacity scaling with power. The secure degrees of freedom for this new multi-terminal multi-antenna channel is characterized. While for these models the eavesdropper channel state information is known at the legitimate terminals, the chapter next removes this assumption and presents results that utilize multiple antennas in order to provide secure communications irrespective of the eavesdropper channel state. An achievable strong secrecy rate and the secure degrees of freedom characterization for the MIMO wiretap channel when the eavesdropper channel is arbitrary, varying, and unknown at the legitimate terminals are presented. Finally, the extension of this model to the two-user multiple access MIMO wiretap channel is considered and its secure degrees of freedom region is characterized. Introduction The wiretap channel and the notion of secrecy capacity, introduced in [1] and generalized by [2], have provided the framework for physical layer design for wireless channels with information theoretic guarantees against eavesdropping. A natural model in wireless communications is one which utilizes multiple antennas for transmission and reception at each node. The improvement in secrecy rate that can be obtained using multiple antennas in a point-to-point channel with an eavesdropper has been studied extensively in several references, including [3, 4]. Specifically, the secrecy capacity of the Gaussian model consisting of a multiple antenna legitimate transmitter, a multiple antenna legitimate receiver, and a multiple antenna eavesdropper, termed the multiple-input multiple-output (MIMO) wiretap channel, has been identified in full generality in [5, 6].