A Gaussian multiple-input single-output (MISO) fading channel is considered. We assume that the transmitter, in addition to the statistics of all channel gains, is aware instantaneously of a noisy version of the channel to the legitimate receiver. On the other hand, the legitimate receiver is aware instantaneously of its channel to the transmitter, whereas the eavesdropper instantaneously knows all channel gains. We evaluate an achievable rate using a Gaussian input without indexing an auxiliary random variable. A sufficient condition for beamforming to be optimal is provided. When the number of transmit antennas is large, beamforming also turns out to be optimal. In this case, the maximum achievable rate can be expressed in a simple closed form and scales with the logarithm of the number of transmit antennas. Furthermore, in the case when a noisy estimate of the eavesdropper's channel is also available at the transmitter, we introduce the SNR difference and the SNR ratio criterions and derive the related optimal transmission strategies and the corresponding achievable rates.
A Gaussian multiple-input single-output (MISO) fading channel is considered. We assume that the transmitter, in addition to the statistics of all channel gains, is aware instantaneously of a noisy version of the channel to the legitimate receiver. On the other hand, the legitimate receiver is aware instantaneously of its channel to the transmitter, whereas the eavesdropper instantaneously knows all channel gains. We evaluate an achievable rate using a Gaussian input without indexing an auxiliary random variable. A sufficient condition for beamforming to be optimal is provided. When the number of transmit antennas is large, beamforming also turns out to be optimal. In this case, the maximum achievable rate can be expressed in a simple closed form and scales with the logarithm of the number of transmit antennas. Furthermore, in the case when a noisy estimate of the eavesdropper's channel is also available at the transmitter, we introduce the SNR difference and the SNR ratio criterions and derive the related optimal transmission strategies and the corresponding achievable rates.
A Gaussian multiple-input single-output (MISO) fading channel is considered. We assume that the transmitter, in addition to the statistics of all channel gains, is aware instantaneously of a noisy version of the channel to the legitimate receiver. On the other hand, the legitimate receiver is aware instantaneously of its channel to the transmitter, whereas the eavesdropper instantaneously knows all channel gains. We evaluate an achievable rate using a Gaussian input without indexing an auxiliary random variable. A sufficient condition for beamforming to be optimal is provided. When the number of transmit antennas is large, beamforming also turns out to be optimal. In this case, the maximum achievable rate can be expressed in a simple closed form and scales with the logarithm of the number of transmit antennas. Furthermore, in the case when a noisy estimate of the eavesdropper's channel is also available at the transmitter, we introduce the SNR difference and the SNR ratio criterions and derive the related optimal transmission strategies and the corresponding achievable rates.
We consider a wiretap channel consisting of a source with multiple antennas, a legitimate receiver and an eavesdropper with a single antenna each. The channels between the source and the receivers undergo fast fading. We assume that the transmitter, in addition to the statistics of both channels, is only aware of a noisy version of the CSI to the legitimate receiver referred to as main channel. The legitimate receiver is aware of both its instantaneous channel gain and the transmitter's estimate of the main channel. On the other hand, the eavesdropper's receiver, in addition to its instantaneous channel realization, is aware of the actual main CSI and the transmitter's estimate as well. While the capacity of this channel is still open even with perfect CSI at the transmitter, we provide in this paper upper and lower bounds on the secrecy capacity. The upper bound is tighter than the one corresponding to perfect main CSI and the gap between the two upper bounds is characterized in function of the channel estimation error variance, at high-SNR. Furthermore, we show that our upper and lower bounds coincide in the case of no main CSI providing a trivial secrecy capacity.
A Gaussian MISO (multiple input single output) channel is considered where a transmitter is communicating to a receiver in the presence of an eavesdropper. The transmitter is equipped with multiple antennas, while the receiver and the eavesdropper each have a single antenna. The transmitter maximizes the communication rate, while concealing the message from the eavesdropper. The channel input is restricted to Gaussian signalling, with no preprocessing of information. For these channel inputs, and under different channel fading assumptions, optimal transmission strategies are found, in terms of the input covariance matrices. It is shown that, the optimal communication strategy in all cases, is beamforming.
This paper studies the design of artificial-noise-aided (AN-aided) secure transmission in slow-fading multiple-input–single-output (MISO) channels. We consider the scenario where a multiantenna transmitter sends messages to a single-antenna legitimate receiver in the presence of multiple noncolluding single-antenna eavesdroppers. It is assumed that the transmitter possesses instantaneous channel state information (CSI) of the legitimate channel but only the statistics of the eavesdropper's channels. Instead of adopting the well-known adaptive and nonadaptive transmission schemes, we consider the newly proposed semiadaptive scheme, in which the communication rate is fixed, and the secrecy rate is adaptively adjusted according to the legitimate channel's CSI. Compared with the adaptive scheme, a major advantage of fixing the communication rate is that the codebook can be fixed, and thus, the encoder and decoder designs are both simplified. We consider a generalized AN-aided beamforming structure, which allows arbitrary beamforming direction. Specifically, we focus on the problem of maximizing the secrecy throughput on the premise of reliable and secure transmission. By solving this problem, the optimal beamforming direction, power-allocation parameters, and secrecy rate are derived in closed form, and the optimal communication rate is obtained numerically. Finally, simulation results are presented to show the performance of the semiadaptive scheme.
We consider transmission of confidential data over multiple-input single-output multiple-eavesdropper (MISOME) Rayleigh-fading wiretap channels. The transmitter has access to full channel state information (CSI) of a legitimate link but only partial CSI of an eavesdropper link in forms of the average received signal-to-noise power ratio (SNR). In this location-aware scenario, we develop the optimal power allocation strategy that maximizes the secrecy rate achievable by beamforming. The optimal power control is regulated in an on-off fashion with the threshold depending only on the numbers of antennas and the average SNRs. By rescuing the vanishing high-SNR degree of freedom for secure communication from this optimal on-off beamforming with the artificial noise scheme, we further derive the achievable ergodic secrecy rate of MISOME wiretap channels in closed form.
Gaussian wireless channels are studied under two forms of security attacks: (i) the jamming attack, where the adversary is active and transmits corruptive signal, but is not interested in the content of the communication, (ii) the eavesdropping attack, where the adversary is passive and overhears the communication and tries to obtain the message that has been transmitted. The active attack is studied in a multi-user setting. The behavior of two users and one jammer in an additive white Gaussian channel (AWGN) with and without fading is investigated, when they participate in a non-cooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop the channel and can use the information obtained to perform correlated jamming. We also differentiate between the availability of perfect and noisy information about the user signals at the jammer. Under various assumptions on the channel characteristics, and the extent of channel state information available at the users and the jammer, we show the existence, or otherwise non-existence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist. For the passive eavesdropping attack, we study multiple-input multiple-output (MIMO) AWGN channels. We first consider a multiple-input single-output (MISO) channel, where the transmitter has multiple antennas, while the receiver and the eavesdropper have single antennas each. We find achievable rates for this channel. With the channel input restricted to Gaussian signalling with no pre-processing of information, optimal transmission strategies that maximize the achievable secrecy rates are found, in terms of the input covariance matrices. It is shown that, under the optimal communication strategy, the system reduces to a single-input single-output (SISO) channel. We then extend the achievability results to fading Gaussian MISO channels. Finally, as a step toward generalizing the problem to one with multiple antennas at the receiver, we discuss the Gaussian 2-2-1 channel with a transmitter and a receiver with two antennas each, and a single antenna eavesdropper. We develop an achievability scheme similar to those of the SISO and MISO channels, and further show that in fact, it achieves the secrecy capacity of this 2-2-1 channel.