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Signalling and Resource Allocation for Secure Communication in Gaussian Wireless Channels

Shabnam Shafiee

Published Mar 7, 2008• 1 citation
OpenAlex

Abstract

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.

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Achievable Rates in Gaussian MISO Channels with Secrecy Constraints

Shabnam Shafiee, Şennur Ulukuş

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.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2007•313 citations

Mutual Information Games in Multiuser Channels With Correlated Jamming

Shabnam Shafiee, Şennur Ulukuş

We investigate the behavior of two users and one jammer in an additive white Gaussian noise (AWGN) channel with and without fading when they participate in a noncooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop on 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 information available at the users and the jammer, we show the existence, or otherwise nonexistence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist.

arXiv:cs/0601110•IEEE Transactions on Information Theory•Sep 16, 2009•84 citations

Information-theoretic Secrecy in Multi-user Channels

Ersen Ekrem

Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective. First, we study the Gaussian multiple-input multiple-output (MIMO) wiretap channel. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner. Next, we study the secure broadcasting problem, where a transmitter wants to have secure communication with multiple legitimate users in the presence of an external eavesdropper. We study several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region. Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message. Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region. Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel. Next, we focus on the multiple access wiretap (MAC-WT) channel whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where each user's link to the legitimate receiver is stronger than its link to the eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable region in an n-letter form. We evaluate a looser version of our outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT. Then, we investigate the effects of user cooperation on the secrecy of broadcast channels by considering the cooperative relay broadcast channel (CRBC). We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation. We further investigate the effects of user cooperation on secrecy by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC. We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF. Next, we study the two-user one-eavesdropper discrete memoryless compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel, and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users. Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and the transmitter sends a confidential message to each group of legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group. Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading, both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain. Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation. Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.

•Jan 1, 2012•0 citations

Going beyond Secrecy Rate via Information Jamming

Haiyang Zhang, Lingjie Duan

Cooperative jamming approach has been commonly used in the field of physical layer security to achieve a good secrecy rate of wireless networks. In this approach, the Gaussian noise signal sent by a friendly jammer can disrupt the reception of the eavesdropper, however, it may also interfere with the legitimate receiver. In this paper, we propose a novel approach, namely, information jamming, to go beyond the secrecy rate achieved by the traditional cooperative jamming approach in a multiple-input single-output (MISO) wiretap channel. We propose that a multi-antenna friendly jammer transmits the source message rather than Gaussian noise signal for simultaneously enhancing the signal strength at the legitimate receiver and canceling the received signal at the eavesdropper. In particular, we aim to maximize the achievable secrecy rate by optimizing the information jammer's beamforming vector. Though the optimization problem is non-convex, we successfully solve it optimally via a two-stage based numerical approach. To gain more useful analytical results, we also propose two suboptimal jamming schemes with low computation, by targeting at improving the legitimate reception and avoiding the eavesdropping, respectively. Finally, numerical results show that the proposed information jamming approach significantly helps go beyond the secrecy rate of the existing cooperative jamming approach, especially when the transmit power of the jammer is large enough.

Globecom•Dec 1, 2018•7 citations

Solutions for the MIMO Gaussian Wiretap Channel With a Cooperative Jammer

S. Ali. A. Fakoorian, Arnold Lee Swindlehurst

We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.

arXiv:1101.4435•IEEE Transactions on Signal Processing•Jul 7, 2011•131 citations

The Secrecy Capacity Region of the Gaussian MIMO Multi-Receiver Wiretap Channel

Ersen Ekrem, Şennur Ulukuş

In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas; however, there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.

arXiv:0903.3096•IEEE Transactions on Information Theory•Mar 15, 2011•243 citations
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.
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.
We investigate the behavior of two users and one jammer in an additive white Gaussian noise (AWGN) channel with and without fading when they participate in a noncooperative zero-sum game, with the channel's input/output mutual information as the objective function. We assume that the jammer can eavesdrop on 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 information available at the users and the jammer, we show the existence, or otherwise nonexistence of a simultaneously optimal set of strategies for the users and the jammer, and characterize those strategies whenever they exist.
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective. First, we study the Gaussian multiple-input multiple-output (MIMO) wiretap channel. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner. Next, we study the secure broadcasting problem, where a transmitter wants to have secure communication with multiple legitimate users in the presence of an external eavesdropper. We study several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region. Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message. Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region. Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel. Next, we focus on the multiple access wiretap (MAC-WT) channel whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where each user's link to the legitimate receiver is stronger than its link to the eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable region in an n-letter form. We evaluate a looser version of our outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT. Then, we investigate the effects of user cooperation on the secrecy of broadcast channels by considering the cooperative relay broadcast channel (CRBC). We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation. We further investigate the effects of user cooperation on secrecy by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC. We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF. Next, we study the two-user one-eavesdropper discrete memoryless compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel, and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users. Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and the transmitter sends a confidential message to each group of legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group. Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading, both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain. Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation. Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.
Cooperative jamming approach has been commonly used in the field of physical layer security to achieve a good secrecy rate of wireless networks. In this approach, the Gaussian noise signal sent by a friendly jammer can disrupt the reception of the eavesdropper, however, it may also interfere with the legitimate receiver. In this paper, we propose a novel approach, namely, information jamming, to go beyond the secrecy rate achieved by the traditional cooperative jamming approach in a multiple-input single-output (MISO) wiretap channel. We propose that a multi-antenna friendly jammer transmits the source message rather than Gaussian noise signal for simultaneously enhancing the signal strength at the legitimate receiver and canceling the received signal at the eavesdropper. In particular, we aim to maximize the achievable secrecy rate by optimizing the information jammer's beamforming vector. Though the optimization problem is non-convex, we successfully solve it optimally via a two-stage based numerical approach. To gain more useful analytical results, we also propose two suboptimal jamming schemes with low computation, by targeting at improving the legitimate reception and avoiding the eavesdropping, respectively. Finally, numerical results show that the proposed information jamming approach significantly helps go beyond the secrecy rate of the existing cooperative jamming approach, especially when the transmit power of the jammer is large enough.
We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.
In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimum-mean-square-error and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semi-definite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas; however, there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirty-paper coding with Gaussian signals.