Wireless Physical Layer Security with Imperfect Channel State Information: A Survey
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paper_title: The wire-tap channel

paper_content:

We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (dmc) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second dmc). Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire-tapper. The designer attempts to build the encoder-decoder in such a way as to maximize the transmission rate R, and the equivocation d of the data as seen by the wire-tapper. In this paper, we find the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission. In particular, if d is equal to Hs, the entropy of the data source, then we consider that the transmission is accomplished in perfect secrecy. Our results imply that there exists a C s > 0, such that reliable transmission at rates up to C s is possible in approximately perfect secrecy.
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paper_title: Secret-key agreement over unauthenticated public channels-Part II: the simulatability condition

paper_content:

For pt.I see ibid., vol.49, no.4, p.822-31(2003). In the first part, we showed that when two parties, willing to generate a secret key, but connected only by a completely insecure communication channel, have access to independent repetitions of some random experiment, then the possibility of secret-key agreement depends on a certain property, called simulatability, of the probability distribution modeling the parties' initial knowledge. More generally, the simulatability condition is important in the context of identification and authentication among parties sharing some correlated but not necessarily identical partially secret keys. Unfortunately, this condition is a priori not very useful since it is not clear how to decide efficiently whether it is satisfied or not for a given distribution P/sub XYZ/. We introduce a new formalism, based on a mechanical model for representing the involved quantities, that allows for dealing with discrete joint distributions of random variables and their manipulations by noisy channels. We show that this representation leads to a simple and efficient characterization of the possibility of secret-key agreement secure against active adversaries.
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paper_title: Wireless Information-Theoretic Security

paper_content:

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.
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paper_title: Minimum energy per bit for secret key acquisition over multipath wireless channels

paper_content:

We study fundamental limits on the generation of secret keys based on the randomness inherent to reciprocal wireless multipath channels. Estimates of the common channel at the two ends of a link are jointly Gaussian sources from which secret keys can be generated. The key generation problem is cast as an equivalent communication problem to characterize the secret key capacity. We analyze the low-SNR regime to quantify the minimum energy per secret key bit required for reliable key acquisition. Our results show that, in contrast to the low SNR behavior of conventional channel capacity, there is a non-zero SNR γ* that achieves the minimum energy per key bit. A time-sharing scheme is proposed to achieve the minimum energy per key bit at any SNR below γ*. We also investigate the reliability of secret key generation via error exponent analysis. In particular, our results yield a tight upper bound on the minimum energy required to generate a finite-length key with a specified probability of error in key acquisition.
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paper_title: Simultaneously generating multiple keys and multi-commodity flow in networks

paper_content:

The problem of simultaneously generating multiple independent keys for multiple pairs of users is considered. This problem is motivated by the fact that typically in wireless networks, multiple pairs of users need to establish secret keys for secure communications between these pairs. We propose a secure routing based key distribution approach to establish keys for the terminals. This approach connects the problem at the hand to that of multi-commodity flow problem studied in graph theory. Using the Max Bi-Flow Min Cut Theorem in the graph theory and developing a matching outer-bound, we show that the proposed approach achieves the key capacity region for the case of establishing two keys. For the general case of establishing more than two keys, an upper bound on the achievable sum rate is derived based on the concept of multicut and our proposed approach can achieve a sum rate equals to the upper bound divided by a constant factor.
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paper_title: Secret-key agreement over unauthenticated public channels I: Definitions and a completeness result

paper_content:

This is the first part of a three-part paper on secret-key agreement secure against active adversaries. In all three parts, we address the question whether two parties, knowing some correlated pieces of information X and Y, respectively, can generate a string S about which an adversary, knowing some information Z and having read and write access to the communication channel used by the legitimate partners, is almost completely ignorant. Whether such key agreement is possible, and if yes at which rate, is an inherent property of the joint probability distribution P/sub XYZ/. In this part, we first prove a number of general impossibility results. We then consider the important special case where the legitimate partners as well as the adversary have access to the outcomes of many independent repetitions of a fixed tripartite random experiment. In this case, the result characterizing the possibility of secret-key agreement secure against active adversaries is of all-or-nothing nature: either a secret key can be generated at the same rate as in the (well-studied) passive-adversary case, or such secret-key agreement is completely impossible. The exact condition characterizing the two cases is presented.
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paper_title: Broadcast channels with confidential messages

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Given two discrete memoryless channels (DMC's) with a common input, it is desired to transmit private messages to receiver 1 rate R_{1} and common messages to both receivers at rate R_{o} , while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R_{1},R_{e},R_{o}) where R_{e} is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Korner-Marton on the broadcast Channel.
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paper_title: The Gaussian wire-tap channel

paper_content:

Wyner's results for discrete memoryless wire-tap channels are extended to the Gaussian wire-tap channel. It is shown that the secrecy capacity Cs is the difference between the capacities of the main and wire.tap channels. It is further shown that Rd= Cs is the upper boundary of the achievable rate-equivocation region.
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paper_title: On the Secrecy Capacity of Fading Channels

paper_content:

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 analyze the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and eavesdropper, and the main channel CSI scenario, where only the legitimate receiver channel gain is known at the transmitter. In each scenario, the 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.
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paper_title: The wire-tap channel

paper_content:

We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (dmc) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second dmc). Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire-tapper. The designer attempts to build the encoder-decoder in such a way as to maximize the transmission rate R, and the equivocation d of the data as seen by the wire-tapper. In this paper, we find the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission. In particular, if d is equal to Hs, the entropy of the data source, then we consider that the transmission is accomplished in perfect secrecy. Our results imply that there exists a C s > 0, such that reliable transmission at rates up to C s is possible in approximately perfect secrecy.
---
paper_title: Secret-key agreement over unauthenticated public channels I: Definitions and a completeness result

paper_content:

This is the first part of a three-part paper on secret-key agreement secure against active adversaries. In all three parts, we address the question whether two parties, knowing some correlated pieces of information X and Y, respectively, can generate a string S about which an adversary, knowing some information Z and having read and write access to the communication channel used by the legitimate partners, is almost completely ignorant. Whether such key agreement is possible, and if yes at which rate, is an inherent property of the joint probability distribution P/sub XYZ/. In this part, we first prove a number of general impossibility results. We then consider the important special case where the legitimate partners as well as the adversary have access to the outcomes of many independent repetitions of a fixed tripartite random experiment. In this case, the result characterizing the possibility of secret-key agreement secure against active adversaries is of all-or-nothing nature: either a secret key can be generated at the same rate as in the (well-studied) passive-adversary case, or such secret-key agreement is completely impossible. The exact condition characterizing the two cases is presented.
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paper_title: On the ergodic secrecy capacity of the wiretap channel under imperfect main channel estimation

paper_content:

The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.
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paper_title: Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel

paper_content:

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.
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paper_title: Rethinking the Secrecy Outage Formulation: A Secure Transmission Design Perspective

paper_content:

This letter studies information-theoretic security without knowing the eavesdropper's channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.
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paper_title: Secrecy Capacity of Wireless Channels

paper_content:

We consider the transmission of confidential data over wireless channels with multiple communicating parties. Based on an information-theoretic problem formulation in which two legitimate partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through another independent quasi-static fading channel, we define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading information-theoretic security is achievable even when the eavesdropper has a better average signal-to-noise ratio (SNR) than the legitimate receiver ? fading thus turns out to be a friend and not a foe.
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paper_title: Secrecy capacity of SIMO and slow fading channels

paper_content:

We present a single letter characterization of the secrecy capacity of the single-input multiple-outputs (SIMO) channel under Gaussian (and possibly colored) noise. To do so, we transform the channel into a scalar Gaussian wiretap channel using standard techniques of communications theory. The result is used to study the impact of slow fading on the secrecy capacity of the channel, and how the use of multiple receive antennas could improve the performance of the system
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paper_title: Wireless Information-Theoretic Security

paper_content:

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.
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paper_title: Secrecy Outage in MISO Systems With Partial Channel Information

paper_content:

Secrecy on the physical layer is a promising technique to simplify the overall cross-layer secrecy concept. In many recent works on the multiple antenna wiretap channel, perfect channel state information to the intended receiver as well as the passive eavesdropper are assumed. In this paper, the transmitter has only partial information about the channel to the eavesdropper, but full information on the main channel to the intended receiver. The applied channel model is the flat-fading multiple-input single-output wiretap channel. We minimize the outage probability of secure transmission under single-stream beamforming and the use of artificial noise in the null space of the main channel. Furthermore, we derive a suboptimal beamforming scheme based on a Markov bound, which performs reasonably well. The results generalize the cases with perfect as well as without channel state information of the eavesdropper channel. Numerical simulations illustrate the secrecy outage probability over the degree of channel knowledge and confirm the theoretical results.
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paper_title: Minimum energy per bit for secret key acquisition over multipath wireless channels

paper_content:

We study fundamental limits on the generation of secret keys based on the randomness inherent to reciprocal wireless multipath channels. Estimates of the common channel at the two ends of a link are jointly Gaussian sources from which secret keys can be generated. The key generation problem is cast as an equivalent communication problem to characterize the secret key capacity. We analyze the low-SNR regime to quantify the minimum energy per secret key bit required for reliable key acquisition. Our results show that, in contrast to the low SNR behavior of conventional channel capacity, there is a non-zero SNR γ* that achieves the minimum energy per key bit. A time-sharing scheme is proposed to achieve the minimum energy per key bit at any SNR below γ*. We also investigate the reliability of secret key generation via error exponent analysis. In particular, our results yield a tight upper bound on the minimum energy required to generate a finite-length key with a specified probability of error in key acquisition.
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paper_title: The Gaussian interference wiretap channel when the eavesdropper channel is arbitrarily varying

paper_content:

In this work we considered the Gaussian two-user interference channel where the eavesdropper channel is arbitrarily varying, all channel matrices have rank less than or equal to 2, and the eavesdropper has 1 antenna. We identify a class of these channel models for which the secrecy degrees of freedom (s.d.o.f.) region is achieved by letting only one user transmit a time. We also provided a non-trivial example for which such a transmission strategy is sub-optimal in terms of s.d.o.f. region. The achievable scheme for this example introduces a new technique to achieve secrecy for MIMO wiretap channels, in which the transmitter-receiver pair uses linear precoding so that effectively the signals are beam-formed toward a direction that can not be attained by the eavesdropper and is at the same time orthogonal to interference from the other user.
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paper_title: Gaussian two-way wiretap channel with an arbitrarily varying eavesdropper

paper_content:

In this work, we derive the secrecy degrees of freedom (s.d.o.f.) region of the Gaussian two-way wiretap channel in which the eavesdropper channel state is arbitrarily varying and is unknown to the legitimate nodes. We prove that the s.d.o.f. region is identical to that when the eavesdropper channel is fixed and globally known. A multi-stage coding scheme that combines secret key generation and confidential message transmission is developed to prove achievability. The confidentiality guarantee provided in this work is in the sense of strong secrecy.
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paper_title: MIMO Broadcast Channel with Arbitrarily Varying Eavesdropper Channel: Secrecy Degrees of Freedom

paper_content:

A two-receiver MIMO broadcast-wiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a common-confidential message as well as a private- confidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular \emph{structured binning} across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.
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paper_title: MIMO multiple access channel with an arbitrarily varying eavesdropper

paper_content:

We investigate a two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes. The channel transfer matrices at the legitimate terminals are fixed and revealed to all the terminals, whereas the channel transfer matrix of the eavesdropper is arbitrarily varying and only revealed to the eavesdropper. We characterize the secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver and uses a single-user wiretap code is sufficient to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using an induction procedure, where at each step we combine the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.
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paper_title: MIMO Wiretap Channels with Arbitrarily Varying Eavesdropper Channel States

paper_content:

In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confidential message against any sequence of channel states experienced by the eavesdropper. This yields the conclusion that secure communication is possible regardless of the location or channel states of (potentially infinite number of) eavesdroppers. Additionally, it is observed that, the present setting renders the secrecy capacity problems for multi-terminal wiretap-type channels more tractable as compared the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access wiretap channel (MIMO MAC-WT) and the Gaussian MIMO broadcast wiretap channel (MIMO BC-WT) where the transmitter(s) and the intended receiver(s) have the same number of antennas.
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paper_title: On the Secrecy Capacity of Fading Channels

paper_content:

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 analyze the full channel state information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and eavesdropper, and the main channel CSI scenario, where only the legitimate receiver channel gain is known at the transmitter. In each scenario, the 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.
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paper_title: Rethinking the Secrecy Outage Formulation: A Secure Transmission Design Perspective

paper_content:

This letter studies information-theoretic security without knowing the eavesdropper's channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.
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paper_title: On the ergodic secrecy capacity of the wiretap channel under imperfect main channel estimation

paper_content:

The ergodic secrecy capacity of the wiretap channel is known when the main channel (between the transmitter and the legitimate receiver) state information (CSI) is perfect at the transmitter and the coherence period is sufficiently large to enable random coding arguments in each block. In a fast fading scenario, when the codeword length spans many coherence periods, the secrecy capacity is still not known. In this paper, we present a framework that characterizes this secrecy capacity under imperfect main channel estimation at the transmitter. Inner and outer bounds on the ergodic secrecy capacity are derived for a class of independent identically distributed (i.i.d.) fading channels. The achievable rate is a simple on-off scheme using a Gaussian input. The upper bound is obtained using an appropriate correlation scheme of the main and the eavesdropper channels. The upper and the lower bounds coincide with recently derived ones in the perfect main CSI extreme. Furthermore, the lower bound matches the upper bound in no main CSI extreme, where the secrecy capacity is equal to zero. Numerical results are provided for independent identically distributed (i.i.d.) Rayleigh fading channels.
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paper_title: Secure On-Off Transmission Design With Channel Estimation Errors

paper_content:

Physical layer security has recently been regarded as an emerging technique to complement and improve the communication security in future wireless networks. The current research and development in physical layer security are often based on the ideal assumption of perfect channel knowledge or the capability of variable-rate transmissions. In this paper, we study the secure transmission design in more practical scenarios by considering channel estimation errors at the receiver and investigating both fixed-rate and variable-rate transmissions. Assuming quasi-static fading channels, we design secure on-off transmission schemes to maximize the throughput subject to a constraint on secrecy outage probability. For systems with given and fixed encoding rates, we show how the optimal on-off transmission thresholds and the achievable throughput vary with the amount of knowledge on the eavesdropper's channel. In particular, our design covers the interesting case where the eavesdropper also uses the pilots sent from the transmitter to obtain imperfect channel estimation. An interesting observation is that using too much pilot power can harm the throughput of secure transmission if both the legitimate receiver and the eavesdropper have channel estimation errors, while the secure transmission always benefits from increasing pilot power when only the legitimate receiver has channel estimation errors but not the eavesdropper. When the encoding rates are controllable parameters to design, we further derive both a non-adaptive and an adaptive rate transmission schemes by jointly optimizing the encoding rates and the on-off transmission thresholds to maximize the throughput of secure transmissions.
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paper_title: Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

paper_content:

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers, without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical layer message authentication is also briefly introduced. The survey concludes with observations on potential research directions in this area.
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paper_title: Guaranteeing Secrecy using Artificial Noise

paper_content:

The broadcast nature of the wireless medium makes the communication over this medium vulnerable to eavesdropping. This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper. The assumption used is that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdropper. The transmitter ensures secrecy of communication by utilizing some of the available power to produce 'artificial noise', such that only the eavesdropper's channel is degraded. Two scenarios are considered, one where the transmitter has multiple transmit antennas, and the other where amplifying relays simulate the effect of multiple antennas. The channel state information (CSI) is assumed to be publicly known, and hence, the secrecy of communication is independent of the secrecy of CSI.
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paper_title: Secret communication using artificial noise

paper_content:

The problem of secret communication between two nodes over a wireless link is considered, where a passive eaves- dropper may overhear the communication. It is desired that the eavesdropper be unable to decode the message. We show that secrecy can be achieved by adding artificially generated noise to the information bearing signal such that it does not degrade the intended receiver's channel. We consider two different scenarios; one in which the transmitter has multiple transmit antennas and the other in which the transmitter has a single antenna but 'helper' nodes are available. In the multiple antenna scenario, the degrees of freedom provided by the multiple antennas is used to generate artificial noise intelligently so that it degrades only the eavesdropper's channel. In the multiple helper scenario, even though the transmitter does not have multiple antennas, the helper nodes simulate the effect of multiple antennas and allow the transmitter to generate artificial noise as in the previous case.
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paper_title: On secure beamforming for wiretap channels with partial channel state information at the transmitter

paper_content:

In this paper, we consider the secure transmission in ergodic fast fading multiple-input single-output single-antenna-eavesdropper (MISOSE) wiretap channels with only the statistics of eavesdropper's channel state information at the transmitter (CSIT). Two kinds of the legitimate CSIT are assumed, that is, full and statistical legitimate CSIT. With full legitimate CSIT, we generalize and optimize the previously proposed artificial noise (AN) aided secure beamforming to improve its secrecy rate performance. The AN covariance matrix in our scheme is more flexible than previous scheme and the region of non-zero secrecy rate is enlarged significantly according to our simulations. For the case with statistical legitimate CSIT, we further prove that the secure beamforming is secrecy capacity achieving for the Rayleigh faded channels. In this case, the AN is not necessary. Extensions to cases where legitimate receiver and eavesdropper have multiple antennas will also be discussed.
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paper_title: On the Design of Artificial-Noise-Aided Secure Multi-Antenna Transmission in Slow Fading Channels

paper_content:

In this paper, we investigate the design of artificial-noise-aided secure multi-antenna transmission in slow fading channels. The primary design concerns include the transmit power allocation and the rate parameters of the wiretap code. We consider two scenarios with different complexity levels: 1) the design parameters are chosen to be fixed for all transmissions; and 2) they are adaptively adjusted based on the instantaneous channel feedback from the intended receiver. In both scenarios, we provide explicit design solutions for achieving the maximal throughput subject to a secrecy constraint, given by a maximum allowable secrecy outage probability. We then derive accurate approximations for the maximal throughput in both scenarios in the high signal-to-noise ratio region, and give new insights into the additional power cost for achieving a higher security level while maintaining a specified target throughput. In the end, the throughput gain of adaptive transmission over non-adaptive transmission is also quantified and analyzed.
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paper_title: Secrecy Sum-Rates with Regularized Channel Inversion Precoding under Imperfect CSI at the Transmitter

paper_content:

In this paper, we study the performance of regularized channel inversion precoding in MISO broadcast channels with confidential messages under imperfect channel state information at the transmitter (CSIT). We obtain an approximation for the achievable secrecy sum-rate which is almost surely exact as the number of transmit antennas and the number of users grow to infinity in a fixed ratio. Simulations prove this anaylsis accurate even for finite-size systems. For FDD systems, we determine how the CSIT error must scale with the SNR, and we derive the number of feedback bits required to ensure a constant high-SNR rate gap to the case with perfect CSIT. For TDD systems, we study the optimum amount of channel training that maximizes the high-SNR secrecy sum-rate.
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paper_title: Fixed SINR solutions for the MIMO wiretap channel

paper_content:

This paper studies the use of artificial interference in reducing the likelihood that a message transmitted between two multi-antenna nodes is intercepted by an undetected eavesdropper. Unlike previous work that assumes some prior knowledge of the eavesdropper's channel and focuses on the information theoretic concept of secrecy capacity, we also consider the case where no information regarding the eavesdropper is present, and we use the relative signal-to-interference-plus-noise-ratio (SINR) of a single transmitted data stream as our performance metric. A portion of the transmit power is used to broadcast the information signal with just enough power to guarantee a certain SINR at the desired receiver, and the remainder of the power is used to broadcast artificial noise in order to mask the desired signal from a potential eavesdropper. The interference is designed to be orthogonal to the information signal when it reaches the desired receiver, and we study the resulting relative SINR of the desired receiver and the eavesdropper assuming both employ optimal beamformers.
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paper_title: On Ergodic Secrecy Rate for Gaussian MISO Wiretap Channels

paper_content:

A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper, each equipped with a single antenna. We study the problem of finding the optimal input covariance that maximizes the ergodic secrecy rate subject to a power constraint, where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper or/and legitimate channels have independent and identically distributed Gaussian entries with zero mean and unit variance, i.e., the channels have trivial covariances. This paper addresses the general case in which the eavesdropper and legitimate channels have nontrivial covariances. A set of equations describing the optimal input covariance matrix are proposed along with an algorithm to obtain the solution. Based on this framework, it is shown that when full information on the legitimate channel is available to the transmitter, the optimal input covariance has always rank one. It is also shown that when only statistical information on the legitimate channel is available to the transmitter, the legitimate channel has some general non-trivial covariance and the eavesdropper channel has trivial covariance, the optimal input covariance has the same eigenvectors as the legitimate channel covariance.
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paper_title: Robust Secure Transmission in MISO Channels Based on Worst-Case Optimization

paper_content:

This paper studies robust transmission schemes for multiple-input single-output (MISO) wiretap channels. Both the cases of direct transmission and cooperative jamming with a helper are investigated with imperfect channel state information (CSI) for the eavesdropper links. Robust transmit covariance matrices are obtained based on worst-case secrecy rate maximization, under both individual and global power constraints. For the case of an individual power constraint, we show that the non-convex maximin optimization problem can be transformed into a quasiconvex problem that can be efficiently solved with existing methods. For a global power constraint, the joint optimization of the transmit covariance matrices and power allocation between the source and the helper is studied via geometric programming. We also study the robust wiretap transmission problem for the case with a quality-of-service constraint at the legitimate receiver. Numerical results show the advantage of the proposed robust design. In particular, for the global power constraint scenario, although cooperative jamming is not necessary for optimal transmission with perfect eavesdropper's CSI, we show that robust jamming support can increase the worst-case secrecy rate and lower the signal to interference-plus-noise ratio at Eve in the presence of channel mismatches between the transmitters and the eavesdropper.
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paper_title: Robust Beamforming for Security in MIMO Wiretap Channels with Imperfect CSI

paper_content:

In this paper, we investigate methods for reducing the likelihood that a message transmitted between two multi-antenna nodes is intercepted by an undetected eavesdropper. In particular, we focus on the judicious transmission of artificial interference to mask the desired signal at the time it is broadcast. Unlike previous work that assumes some prior knowledge of the eavesdropper's channel and focuses on maximizing secrecy capacity, we consider the case where no information regarding the eavesdropper is available, and we use signal-to-interference-plus-noise-ratio (SINR) as our performance metric. Specifically, we focus on the problem of maximizing the amount of power available to broadcast a jamming signal intended to hide the desired signal from a potential eavesdropper, while maintaining a prespecified SINR at the desired receiver. The jamming signal is designed to be orthogonal to the information signal when it reaches the desired receiver, assuming both the receiver and the eavesdropper employ optimal beamformers and possess exact channel state information (CSI). In practice, the assumption of perfect CSI at the transmitter is often difficult to justify. Therefore, we also study the resulting performance degradation due to the presence of imperfect CSI, and we present robust beamforming schemes that recover a large fraction of the performance in the perfect CSI case. Numerical simulations verify our analytical performance predictions, and illustrate the benefit of the robust beamforming schemes.
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paper_title: Secrecy Outage in MISO Systems With Partial Channel Information

paper_content:

Secrecy on the physical layer is a promising technique to simplify the overall cross-layer secrecy concept. In many recent works on the multiple antenna wiretap channel, perfect channel state information to the intended receiver as well as the passive eavesdropper are assumed. In this paper, the transmitter has only partial information about the channel to the eavesdropper, but full information on the main channel to the intended receiver. The applied channel model is the flat-fading multiple-input single-output wiretap channel. We minimize the outage probability of secure transmission under single-stream beamforming and the use of artificial noise in the null space of the main channel. Furthermore, we derive a suboptimal beamforming scheme based on a Markov bound, which performs reasonably well. The results generalize the cases with perfect as well as without channel state information of the eavesdropper channel. Numerical simulations illustrate the secrecy outage probability over the degree of channel knowledge and confirm the theoretical results.
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paper_title: Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation

paper_content:

We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.
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paper_title: Impact of channel estimation errors on effectiveness of Eigenvector-based jamming for physical layer security in wireless networks

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In this paper, we present our study of an Eigenvector-based artificial noise-based jamming technique developed to provide increased wireless physical layer security in transmit-receive diversity systems and analyze the impact of channel estimation errors on system performance. Our simulation results showed that with knowledge of perfect channel state information, the technique provided secrecy capacity of approximately 7 bits/s/Hz for a normalized transmit power of 25 dB for a variety of transmit, receive, and eavesdropper configurations. We also describe a novel method to simulate generalized channel state information estimation errors. While other publications neglect the impact of these estimation errors, our simulations show that the secrecy capacity decreased rapidly as the channel estimation errors increased. For instance, at 25% error the secrecy capacity of the jamming technique was only slightly better than the non-jamming case. Our paper also outlines upcoming research efforts to further explore error sensitivity and channel state temporal stability through experimentation.
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paper_title: Resource Allocation for Secure OFDMA Networks with Imperfect CSIT

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In this paper, we formulate an optimization problem for resource allocation and scheduling in orthogonal frequency division multiple access (OFDMA) networks. Our problem formulation takes into account artificial noise generation to combat a passive multiple antenna eavesdropper and the effects of imperfect channel state information at the transmitter (CSIT) in slow fading. The optimization problem is solved by dual decomposition which results in an iterative resource allocation algorithm with a fast speed of convergence. The packet data rate, secrecy data rate, power, and subcarrier allocation policies are optimized to maximize the average secrecy outage capacity (bit/s/Hz securely and successfully delivered to the users). Simulation results illustrate that our proposed iterative algorithm converges to the optimal solution in a small number of iterations and guarantees a non-zero secrecy data rate for given target secrecy outage and channel outage probability requirements.
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paper_title: Guaranteeing Secrecy using Artificial Noise

paper_content:

The broadcast nature of the wireless medium makes the communication over this medium vulnerable to eavesdropping. This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper. The assumption used is that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdropper. The transmitter ensures secrecy of communication by utilizing some of the available power to produce 'artificial noise', such that only the eavesdropper's channel is degraded. Two scenarios are considered, one where the transmitter has multiple transmit antennas, and the other where amplifying relays simulate the effect of multiple antennas. The channel state information (CSI) is assumed to be publicly known, and hence, the secrecy of communication is independent of the secrecy of CSI.
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paper_title: Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming

paper_content:

In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.
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paper_title: On the Impact of Quantized Channel Feedback in Guaranteeing Secrecy with Artificial Noise: The Noise Leakage Problem

paper_content:

Physical-layer secrecy in wireless fading channels has been studied extensively in recent years to ensure reliable communication between the transmitter and the receiver subject to constraints on the information attainable by the eavesdropper. With multiple antennas at the transmitter, Goel and Negi proposed the use of artificial noise (AN) in the null space of the receiver's channel to corrupt the eavesdropper's reception, which helps guarantee secrecy without knowledge of the eavesdropper's channel. It has been shown that the secrecy capacity can be made arbitrarily large by increasing the transmission power, when perfect knowledge of the receiver's channel direction information (CDI) is available. However, in practice, this is not possible due to rate-limitations on the feedback channel. This paper studies the impact of quantized channel feedback on the secrecy capacity achievable with artificial noise.We show that, with imperfect CDI at the transmitter, the AN that was originally intended only for the eavesdropper may leak into the receiver's channel and limit the achievable secrecy rate. To maintain a constant performance degradation, the number of feedback bits must increase at least logarithmically with the transmission power. Moreover, we observe that the portion of power allocated to the transmission of AN should decrease as the number of quantization bits decreases to alleviate the degradation due to noise leakage.
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paper_title: QoS-Based Transmit Beamforming in the Presence of Eavesdroppers: An Optimized Artificial-Noise-Aided Approach

paper_content:

Secure transmission techniques have been receiving growing attention in recent years, as a viable, powerful alternative to blocking eavesdropping attempts in an open wireless medium. This paper proposes a secret transmit beamforming approach using a quality-of-service (QoS)-based perspective. Specifically, we establish design formulations that: i) constrain the maximum allowable signal-to-interference-and-noise ratios (SINRs) of the eavesdroppers, and that ii) provide the intended receiver with a satisfactory SINR through either a guaranteed SINR constraint or SINR maximization. The proposed designs incorporate a relatively new idea called artificial noise (AN), where a suitable amount of AN is added in the transmitted signal to confuse the eavesdroppers. Our designs advocate joint optimization of the transmit weights and AN spatial distribution in accordance with the channel state information (CSI) of the intended receiver and eavesdroppers. Our formulated design problems are shown to be NP-hard in general. We deal with this difficulty by using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Interestingly, we prove that SDR can exactly solve the design problems for a practically representative class of problem instances; e.g., when the intended receiver's instantaneous CSI is known. Extensions to the colluding-eavesdropper scenario and the multi-intended-receiver scenario are also examined. Extensive simulation results illustrate that the proposed AN-aided designs can yield significant power savings or SINR enhancement compared to some other methods.
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paper_title: Fixed-rate power allocation strategies for enhanced secrecy in MIMO wiretap channels

paper_content:

This paper studies the use of artificial interference in reducing the likelihood that a confidential message transmitted between two multi-antenna nodes is intercepted by a passive eavesdropper. A portion of the transmit power is used to broadcast the information signal with just enough power to guarantee a certain data rate for the intended receiver, and the remainder of the power is used to broadcast artificial noise in order to mask the desired signal from a potential eavesdropper. The interference is designed to be orthogonal to the multiple-stream information signal when it reaches the desired receiver. A modified water-filling algorithm is proposed that balances the required transmit power with the number of spatial dimensions available for jamming the eavesdropper. Numerical results verify the increase in secrecy capacity under the proposed transmission scheme.
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paper_title: Utility of beamforming strategies for secrecy in multiuser MIMO wiretap channels

paper_content:

This paper examines linear beamforming methods for secure communications in a multiuser wiretap channel with a single transmitter, multiple legitimate receivers, and a single eavesdropper, where all nodes are equipped with multiple antennas. No information regarding the eavesdropper is presumed at the transmitter, and we examine both the broadcast MIMO downlink with independent information, and the multicast MIMO downlink with common information for all legitimate receivers. In both cases the information signal is transmitted with just enough power to guarantee a certain SINR at the desired receivers, while the remainder of the power is used to broadcast artificial noise. The artificial interference selectively degrades the passive eavesdropper's signal while remaining orthogonal to the desired receivers. We analyze the confidentiality provided by zero-forcing and optimal minimum-power beamforming designs for the broadcast channel, and optimal minimum-MSE beamformers for the multicast channel. Numerical simulations for the relative SINR and BER performance of the eavesdropper demonstrate the effectiveness of the proposed physical-layer security schemes.
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paper_title: How much training is enough for secrecy beamforming with artificial noise

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In this paper, we consider the joint design of training and data transmission signals for wiretap channels where the transmitter is to send a secrect massage to the receiver without being intercepted by the eavesdropper. The celebrated secrecy beamforming scheme, which may or may not be assisted by artificial-noise (AN), is adopted in the data transmission phase to achieve this task. The achievable secrecy rate for practical systems with channel estimation error is first derived. Based on the achievable secrecy rate, we find the optimal tradeoff between the energy used for training and data signals. The optimal solutions in the low and high energy regimes are characterized analytically. We show that AN does not provide any advantages in the low energy regime, while it may have significant impact in the high energy regime. Numerical results are presented to verify our theoretical claims.
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paper_title: Masked Beamforming for Multiuser MIMO Wiretap Channels with Imperfect CSI

paper_content:

This letter investigates masked beamforming schemes for multiuser multiple-input multiple-output (MIMO) downlink systems in the presence of an eavesdropper. With noisy and outdated channel state information (CSI) at the base station (BS), we aim to maximize the transmit power of an artificial noise, which is broadcast to jam any potential eavesdropper, while meeting individual minimum mean square error (MMSE) constraints of the desired user links. To this end, we adopt a Bayesian approach and derive an average MSE uplink-downlink duality with imperfect CSI. Using the duality, a robust beamforming algorithm is proposed. Simulation results show the effectiveness of the proposed scheme.
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paper_title: Improving Wireless Physical Layer Security via Cooperating Relays

paper_content:

Physical (PHY) layer security approaches for wireless communications can prevent eavesdropping without upper layer data encryption. However, they are hampered by wireless channel conditions: absent feedback, they are typically feasible only when the source-destination channel is better than the source-eavesdropper channel. Node cooperation is a means to overcome this challenge and improve the performance of secure wireless communications. This paper addresses secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers. Three cooperative schemes are considered: decode-and-forward (DF), amplify-and-forward (AF), and cooperative jamming (CJ). For these schemes, the relays transmit a weighted version of a reencoded noise-free message signal (for DF), a received noisy source signal (for AF), or a common jamming signal (for CJ). Novel system designs are proposed, consisting of the determination of relay weights and the allocation of transmit power, that maximize the achievable secrecy rate subject to a transmit power constraint, or, minimize the transmit power subject to a secrecy rate constraint. For DF in the presence of one eavesdropper, closed-form optimal solutions are derived for the relay weights. For other problems, since the optimal relay weights are difficult to obtain, several criteria are considered leading to suboptimal but simple solutions, i.e., the complete nulling of the message signals at all eavesdroppers (for DF and AF), or the complete nulling of jamming signal at the destination (for CJ). Based on the designed relay weights, for DF in the presence of multiple eavesdroppers, and for CJ in the presence of one eavesdropper, the optimal power allocation is obtained in closed-form; in all other cases the optimal power allocation is obtained via iterative algorithms. Numerical evaluation of the obtained secrecy rate and transmit power results show that the proposed design can significantly improve the performance of secure wireless communications.
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paper_title: Secure Communication in Multiantenna Cognitive Radio Networks With Imperfect Channel State Information

paper_content:

In this paper, we address the issue of optimal transmitter design to achieve physical layer security for a multiple-input single-output (MISO) cognitive radio network (CRN), in which a secondary user transmitter (SU-Tx) sends confidential information to a SU receiver (SU-Rx) on the same frequency band with a primary user (PU) in the presence of an eavesdropper receiver (ED-Rx). It is assumed that all the channel state information (CSI) of the secondary, primary and eavesdropper channels is not perfectly known at the SU-Tx. The optimal transmitter design, under the restriction of Gaussian signaling without preprocessing of information, involves a nonconvex semiinfinite optimization problem which maximizes the rate of the secondary link while avoiding harmful interference to the PU and keeping the eavesdropper totally ignorant of the messages sent regardless of the uncertainties in the CSI. We propose two approaches to solve this challenging optimization problem. The first one relates the original problem to a sequence of semiinfinite capacity-achieving transmitter design problems in an auxiliary CRN without any eavesdropper, which can then be solved through transformations and using convex semidefinite programs (SDPs). The second approach explores the hidden convexity of the problem and hence transforms it into a single SDP, which significantly reduces the computational complexity. Furthermore, a few heuristic beamforming solutions for the ease of implementation are also introduced. Finally, simulation results are presented to evaluate the performance of the proposed optimal and suboptimal solutions.
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paper_title: Decode-and-forward relay beamforming for secrecy with imperfect CSI and multiple eavesdroppers

paper_content:

In this paper, we evaluate secrecy rates in cooperative relay beamforming in the presence of imperfect channel state information (CSI) and multiple eavesdroppers. A source-destination pair aided by k out of M relays, 1 ≤ k ≤ M, using decode-and-forward relay beamforming is considered. We compute the worst case secrecy rate with imperfect CSI in the presence of multiple eavesdroppers, where the number of eavesdroppers can be more than the number of relays. We solve the optimization problem for all possible relay combinations to find the secrecy rate and optimum source and relay weights subject to a total power constraint. We relax the rank-1 constraint on the complex semi-definite relay weight matrix and use S-procedure to reformulate the optimization problem that can be solved using convex semi-definite programming.
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paper_title: Guaranteeing Secrecy using Artificial Noise

paper_content:

The broadcast nature of the wireless medium makes the communication over this medium vulnerable to eavesdropping. This paper considers the problem of secret communication between two nodes, over a fading wireless medium, in the presence of a passive eavesdropper. The assumption used is that the transmitter and its helpers (amplifying relays) have more antennas than the eavesdropper. The transmitter ensures secrecy of communication by utilizing some of the available power to produce 'artificial noise', such that only the eavesdropper's channel is degraded. Two scenarios are considered, one where the transmitter has multiple transmit antennas, and the other where amplifying relays simulate the effect of multiple antennas. The channel state information (CSI) is assumed to be publicly known, and hence, the secrecy of communication is independent of the secrecy of CSI.
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paper_title: Secure MISO cognitive radio system with perfect and imperfect CSI

paper_content:

In cognitive radio (CR) systems, harmful interference from the secondary system degrades the data rate of the primary system. However, this interference may be beneficial to the primary system in terms of the secrecy rate, when unauthorized users eavesdrop on the primary link. This paper explores multiple-input single-output (MISO) CR systems where the secondary system secures the primary communication in return for permission to use the spectrum. In this context, the optimal transmission strategy has to be found which provides the best tradeoff between the useful and harmful effects of interference on the secrecy rate of the primary system. Considering the cases of perfect and imperfect channel state information of the eavesdroppers we formulate optimization problems for maximizing the primary secrecy rate under secondary data rate requirements. The resulting non-convex optimization problems are solved through a sequence of convex semidefinite programs. The simulation results reveal that the proposed schemes improve the secrecy level of the primary system while meeting the data rate requirements of the secondary system.
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paper_title: Rethinking the Secrecy Outage Formulation: A Secure Transmission Design Perspective

paper_content:

This letter studies information-theoretic security without knowing the eavesdropper's channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.
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paper_title: On the Throughput Cost of Physical Layer Security in Decentralized Wireless Networks

paper_content:

This paper studies the throughput of large-scale decentralized wireless networks with physical layer security constraints. In particular, we are interested in the question of how much throughput needs to be sacrificed for achieving a certain level of security. We consider random networks where the legitimate nodes and the eavesdroppers are distributed according to independent two-dimensional Poisson point processes. The transmission capacity framework is used to characterize the area spectral efficiency of secure transmissions with constraints on both the quality of service (QoS) and the level of security. This framework illustrates the dependence of the network throughput on key system parameters, such as the densities of legitimate nodes and eavesdroppers, as well as the QoS and security constraints. One important finding is that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network. We also study the use of a secrecy guard zone, which is shown to give a significant improvement on the throughput of networks with high security requirements.
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paper_title: Secrecy throughput of MANETs with malicious nodes

paper_content:

The secrecy throughput of mobile ad-hoc networks (MANETs) with malicious nodes is investigated. The MANET consists of n legitimate mobile nodes and m malicious nodes. Transmissions between legitimate nodes are subject to a delay constraint D. An information theoretic approach for security is applied to achieve secure communication among legitimate nodes in MANETs with transmissions being kept perfectly secure from malicious nodes. A critical threshold on the number of malicious nodes (m) is identified such that when m = o(√nD), i.e., lim n→∞ m/√nD = 0, the secrecy throughput equals the throughput of MANETs without malicious nodes, i.e., the impact of the presence of malicious nodes on the network throughput is negligible; and when m = Ω (√nDpoly(n)), i.e., lim n→∞ m/√nDpoly(n)) ≥ c for a positive constant c, the secrecy throughput is limited by the number of malicious nodes.
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paper_title: Secure Communication in Stochastic Wireless Networks—Part I: Connectivity

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The ability to exchange secret information is critical to many commercial, governmental, and military networks. Information-theoretic security-widely accepted as the strictest notion of security-relies on channel coding techniques that exploit the inherent randomness of the propagation channels to strengthen the security of digital communications systems. Motivated by recent developments in the field, we aim to characterize the fundamental secrecy limits of wireless networks. The paper is comprised of two separate parts. In Part I, we define the intrinsically secure communications graph (iS-graph), a random graph which describes the connections that can be securely established over a large-scale network. We provide conclusive results for the local connectivity of the Poisson iS-graph, in terms of node degrees and isolation probabilities. We show how the secure connectivity of the network varies with the wireless propagation effects, the secrecy rate threshold of each link, and the noise powers of legitimate nodes and eavesdroppers. We then propose sectorized transmission and eavesdropper neutralization as viable strategies for improving the secure connectivity. Our results help clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks. In Part II of the paper, we study the achievable secrecy rates and the effect of eavesdropper collusion.
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paper_title: Secure Communication in Stochastic Wireless Networks—Part II: Maximum Rate and Collusion

paper_content:

In Part I of this paper, we introduced the intrinsically secure communications graph (iS-graph)-a random graph which describes the connections that can be established with strong secrecy over a large-scale network, in the presence of eavesdroppers. We focused on the local connectivity of the iS-graph, and proposed techniques to improve it. In this second part, we characterize the maximum secrecy rate (MSR) that can be achieved between a node and its neighbors. We then consider the scenario where the eavesdroppers are allowed to collude, i.e., exchange and combine information. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncolluding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physical-layer security.
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paper_title: Secret communication in large wireless networks without eavesdropper location information

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We present achievable scaling results on the per-node secure throughput that can be realized in a large random wireless network of n legitimate nodes in the presence of m eavesdroppers of unknown location. We consider both one-dimensional and two-dimensional networks. In the one-dimensional case, we show that a per-node secure throughput of order 1/n is achievable if the number of eavesdroppers satisfies m = o(n/log n). We obtain similar results for the two-dimensional case, where a secure throughput of order 1/√n log n is achievable under the same condition. The number of eavesdroppers that can be tolerated is significantly higher than previous works that address the case of unknown eavesdropper locations. The key technique introduced in our construction to handle unknown eavesdropper locations forces adversaries to intercept a number of packets to be able to decode a single message. The whole network is divided into regions, where a certain subset of packets is protected from adversaries located in each region. In the one-dimensional case, our construction makes use of artificial noise generation by legitimate nodes to degrade the signal quality at the potential locations of eavesdroppers. In the two-dimensional case, the availability of many paths to reach a destination is utilized to handle collaborating eavesdroppers of unknown location.
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paper_title: Secure Wireless Network Connectivity with Multi-Antenna Transmission

paper_content:

Information-theoretic security constraints reduce the connectivity of wireless networks in the presence of eavesdroppers, which motivates better modeling of such networks and the development of techniques that are robust to eavesdropping. In this letter, we are concerned with the existence of secure connections from a typical transmitter to the legitimate receiver(s) over fading channels, where the legitimate nodes and eavesdroppers are all randomly located. We consider non-colluding and colluding eavesdroppers, and derive the network secure connectivity for both eavesdropper strategies. We mathematically show how nodes with multiple transmit antenna elements can improve secure connectivity by forming a directional antenna or using eigen-beamforming. Compared with single antenna transmission, a large connectivity improvement can be achieved by both multi-antenna transmission techniques even with a small number of antennas.
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paper_title: Cooperative jamming for secrecy in decentralized wireless networks

paper_content:

Cooperative jamming as a physical layer security enhancement has recently drawn considerable attention. While most existing works focus on communication systems with a small number of nodes, we investigate the use of cooperative jamming for providing secrecy in large-scale decentralized networks consisting of randomly distributed legitimate users and eavesdroppers. A modified slotted ALOHA protocol, named CJ-ALOHA, is considered where each legitimate transmitter either sends its message signal or acts as a helping jammer according to a message transmission probability p. We derive the secrecy transmission capacity to characterize the network throughput and show how the throughput is affected by the CJ-ALOHA protocol. Both analytical and numerical insights are provided on the design of the CJ-ALOHA protocol for optimal throughput performance.
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paper_title: Network coding for facilitating secrecy in large wireless networks

paper_content:

It is well known that network coding can improve the secrecy of a network that is represented by a graph with edges tapped by an eavesdropper. However, the application of such secure network coding to emerging problems in information-theoretic secrecy in wireless networks has been limited; in particular, the graph-based wiretap network approach does not readily extend to the physical wireless network. In this paper, we consider the impact of such an extension on scaling laws for wireless networks. We first employ simple examples to illustrate how an extension of the secure network coding approach can address difficult problems that have plagued wireless network security; for example, relaxing the known eavesdropper location assumption or avoiding the use of artificial noise generation. Based on this understanding, we then add secure network coding approaches to recent constructions for secrecy scaling in large wireless networks, most notably achieving secure pernode throughput in large wireless networks in the presence of an arbitrary number of non-collaborating eavesdroppers.
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paper_title: Modeling location uncertainty for eavesdroppers: A secrecy graph approach

paper_content:

In this paper, we consider end-to-end secure communication in a large wireless network, where the locations of eavesdroppers are uncertain. Our framework attempts to bridge the gap between physical layer security under uncertain channel state information of the eavesdropper and network level connectivity under security constraints, by modeling location uncertainty directly at the network level as correlated node and link failures in a secrecy graph. Bounds on the percolation threshold are obtained for square and triangular lattices, and bounds on mean degree are obtained for Poisson secrecy graphs. Both analytic and simulation results show the dramatic effect of uncertainty in location of eavesdroppers on connectivity in a secrecy graph.
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paper_title: On Secrecy Capacity Scaling in Wireless Networks

paper_content:

We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λ e = O((log n)−2), almost all of the nodes achieve a perfectly secure rate of Ω (1/√n) The achievability argument is based on a novel multi-hop forwarding scheme where randomization is added in every hop to ensure maximal ambiguity at the eavesdropper(s). Remarkable, under these assumptions, securing the transmissions of nodes does not entail a loss in the per-node throughput in terms of scaling.
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paper_title: The Secrecy Graph and Some of its Properties

paper_content:

A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The underlying point process models considered are lattices and Poisson point processes. In the lattice case, analogies to standard bond and site percolation can be exploited to determine percolation thresholds. In the Poisson case, the node degrees are determined and percolation is studied using analytical bounds and simulations. It turns out that a small density of eavesdroppers already has a drastic impact on the connectivity of the secrecy graph.
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paper_title: Secure Communication Over Fading Channels

paper_content:

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.
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paper_title: Two-way secrecy schemes for the broadcast channel with internal eavesdroppers

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The secrecy problem in a broadcast setting with one source and a number of users is considered, where the message to a given user must be kept secret from all of the other users. Multi-user diversity suggests an opportunistic approach that sends a message secretly to the user with the current best channel; however, the secrecy rate goes to zero in the limit of a large number of users. Here, channel reciprocity is exploited via a two-way secrecy scheme to provide a constant positive secrecy rate to the user with the best channel. Next, motivated by the desire to transmit to a given user (rather than opportunistically to the user with the best channel), a second scheme is developed that employs relaying from other users from whom the message is still kept secret. In this non-opportunistic case, a positive secrecy rate is again shown to be achievable in the limit of a large number of system users.
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paper_title: Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation

paper_content:

We consider the problem of secure communication with multiantenna transmission in fading channels. The transmitter simultaneously transmits an information-bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near-optimal strategy for the case of noncolluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the SNR, above which, the achievable secrecy rate is positive and shows that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained.
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paper_title: Secure On-Off Transmission Design With Channel Estimation Errors

paper_content:

Physical layer security has recently been regarded as an emerging technique to complement and improve the communication security in future wireless networks. The current research and development in physical layer security are often based on the ideal assumption of perfect channel knowledge or the capability of variable-rate transmissions. In this paper, we study the secure transmission design in more practical scenarios by considering channel estimation errors at the receiver and investigating both fixed-rate and variable-rate transmissions. Assuming quasi-static fading channels, we design secure on-off transmission schemes to maximize the throughput subject to a constraint on secrecy outage probability. For systems with given and fixed encoding rates, we show how the optimal on-off transmission thresholds and the achievable throughput vary with the amount of knowledge on the eavesdropper's channel. In particular, our design covers the interesting case where the eavesdropper also uses the pilots sent from the transmitter to obtain imperfect channel estimation. An interesting observation is that using too much pilot power can harm the throughput of secure transmission if both the legitimate receiver and the eavesdropper have channel estimation errors, while the secure transmission always benefits from increasing pilot power when only the legitimate receiver has channel estimation errors but not the eavesdropper. When the encoding rates are controllable parameters to design, we further derive both a non-adaptive and an adaptive rate transmission schemes by jointly optimizing the encoding rates and the on-off transmission thresholds to maximize the throughput of secure transmissions.
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paper_title: Secure Transmission With Multiple Antennas I: The MISOME Wiretap Channel

paper_content:

The capacity of the Gaussian wiretap channel model is analyzed when there are multiple antennas at the sender, intended receiver and eavesdropper. The associated channel matrices are fixed and known to all the terminals. A computable characterization of the secrecy capacity is established as the saddle point solution to a minimax problem. The converse is based on a Sato-type argument used in other broadcast settings, and the coding theorem is based on Gaussian wiretap codebooks. At high signal-to-noise ratio (SNR), the secrecy capacity is shown to be attained by simultaneously diagonalizing the channel matrices via the generalized singular value decomposition, and independently coding across the resulting parallel channels. The associated capacity is expressed in terms of the corresponding generalized singular values. It is shown that a semi-blind "masked" multi-input multi-output (MIMO) transmission strategy that sends information along directions in which there is gain to the intended receiver, and synthetic noise along directions in which there is not, can be arbitrarily far from capacity in this regime. Necessary and sufficient conditions for the secrecy capacity to be zero are provided, which simplify in the limit of many antennas when the entries of the channel matrices are independent and identically distributed. The resulting scaling laws establish that to prevent secure communication, the eavesdropper needs three times as many antennas as the sender and intended receiver have jointly, and that the optimum division of antennas between sender and intended receiver is in the ratio of 2:1.
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paper_title: How much training is enough for secrecy beamforming with artificial noise

paper_content:

In this paper, we consider the joint design of training and data transmission signals for wiretap channels where the transmitter is to send a secrect massage to the receiver without being intercepted by the eavesdropper. The celebrated secrecy beamforming scheme, which may or may not be assisted by artificial-noise (AN), is adopted in the data transmission phase to achieve this task. The achievable secrecy rate for practical systems with channel estimation error is first derived. Based on the achievable secrecy rate, we find the optimal tradeoff between the energy used for training and data signals. The optimal solutions in the low and high energy regimes are characterized analytically. We show that AN does not provide any advantages in the low energy regime, while it may have significant impact in the high energy regime. Numerical results are presented to verify our theoretical claims.
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Title: Wireless Physical Layer Security with Imperfect Channel State Information: A Survey

Section 1: INTRODUCTION
Description 1: Introduce the importance of secure communication over wireless fading channels and the emerging field of physical layer security. Highlight the main challenges and outline the paper's structure.

Section 2: CHARACTERIZATIONS OF THE PERFORMANCE LIMITS
Description 2: Discuss the different performance metrics used to evaluate secure transmissions with imperfect CSI, including ergodic secrecy capacity, outage-based characterizations, and secrecy degrees of freedom.

Section 3: SIGNAL PROCESSING SECRECY ENHANCEMENTS
Description 3: Review various signal processing techniques for enhancing the secrecy of wireless communications, including secure on-off transmissions, beamforming with artificial noise, and designs for relay channels and cognitive radio systems.

Section 4: SECRECY IN LARGE-SCALE DECENTRALIZED WIRELESS NETWORKS
Description 4: Explore the challenges and research developments related to achieving physical layer security in large-scale decentralized wireless networks where eavesdroppers' CSI is often unavailable.

Section 5: OPEN PROBLEMS AND DISCUSSIONS
Description 5: Identify and discuss open problems in the field, such as the impact of imperfect channel estimation at receivers and the imperfect knowledge of eavesdroppers' locations.

Section 6: CONCLUSIONS
Description 6: Summarize the key points discussed in the paper and suggest future research directions for physical layer security with imperfect CSI.