Achievable Secure Degrees Of Freedom Research Articles

Achievable Secure Degrees of Freedom of MIMO Interference Channel With a Cooperative Jammer

In this letter, the secure degrees of freedom (SDoF) of 2-user multiple-input multiple-output (MIMO) interference channel with an external N-antenna cooperative jammer (CJ) is considered. In this model, each transmitter intends to send confidential messages to the corresponding receiver and keep secret with unintended receiver. Different from the previous studies on interference channels, our model has an external cooperative jammer, which can improve the SDoF by transmitting interference signals. We derive the converse and give the corresponding achievable schemes to determine the exact SDoF, and study the influence of CJ on the SDoF of this system. We find that adding one CJ antenna has the same effect as adding one transmitting antenna, and has a better effect than adding one receiving antenna. The converse is given by using vector extensions of the role of a helper and secrecy penalty lemmas. For arbitrary values of N and M, we provide different achievable schemes for the corresponding regimes by making use of the symbol extension and spatial alignment techniques.

Achievable Secure Degrees of Freedom of ${K}$ -User MISO Broadcast Channel With Imperfect CSIT

In this letter, we derive the achievable secure degrees of freedom (SDoF) of ${K}$ -user multiple-input single-output broadcast channel with imperfect channel state information (CSI) at the transmitter. With the help of an $N_{j}$ -antenna external jammer, we propose a jamming rate splitting (J-RS) scheme to ensure the security of two wiretap models: 1) broadcast channel with confidential messages and 2) broadcast channel with an $N_{e}$ -antenna external eavesdropper, where each legal node has no CSI of wiretap channels. Our converse is based on the degrees of freedom (DoF) of the network with secrecy constraints, and the achievability is based on J-RS. By numerical analysis, it indicates that the proposed scheme can achieve more SDoF than the traditional rate splitting scheme, zero forcing scheme, and jamming scheme, which can reach to the DoF of the network.

Secure degrees of freedom of two‐user X‐channel with synergistic alternating channel state information at transmitters

In this study, a two-user single-input single-output X-channel with confidential messages is addressed. In this model, the authors assume that the transmitters have access to synergistic alternating channel state information. During different time slots, the channel state information at transmitters (CSIT) alternate between three states including perfect CSIT, delayed CSIT, and no CSIT. By using the eminent synergistic benefits of the CSIT pattern, some schemes capable of attaining the maximum achievable secure degrees of freedom (SDoF) are presented. Additionally, in devising the schemes, the minimal CSIT patterns required to achieve optimal SDoF are introduced. It is shown that for CSIT patterns which are weaker than minimal ones, using a half-duplex relay can assist the network in obtaining the optimal SDoF. Indeed, the relay alleviates the effects of the lack of knowledge at transmitters on achievable SDoF.

Secure degrees of freedom in cooperative [formula omitted]-helper MIMO cognitive radio systems

We study the achievable secure degrees of freedom (DoF) in a cooperative MIMO cognitive radio system comprised of one primary source–destination pair, multiple secondary source–destination pairs and an eavesdropper against whom the primary user intends to secure its data. In this system, multiple secondary user pairs help to secure primary user’s data against eavesdropping. In return, these secondary users are allowed to access primary user’s spectrum. All users, including primary user pair, K≥2 secondary user pairs and the eavesdropper are equipped with M antennas. We investigate the secure DoF without the knowledge of eavesdropper’s channel state information (CSI), using the interference alignment concept combined with a zero inter-user interference constraint. A beamforming design is proposed to achieve secure DoF d for the primary user and DoF d for all secondary users if Kd≤M. The case of untrusted secondary users is also investigated where the secondary users may potentially eavesdrop. Simulation examples corroborating the theoretical results are presented.

A Full-Duplex Bob in the MIMO Gaussian Wiretap Channel: Scheme and Performance

This letter considers secrecy communication from an information-theoretic perspective, and studies the secrecy capacity of a multi-input multi-output (MIMO) Gaussian wiretap channel with a source (Alice), an eavesdropper (Eve) and a Full-Duplex (FD) legitimate receiver (Bob). Bob can allocate part of his antennas to transmit jamming signals to impair Eve’s channel. Our goal is to identify the secrecy capacity behavior in the high signal-to-noise ratio (SNR) regimes, i.e., the maximal achievable secure degrees of freedom (S.D.o.F). Such S.D.o.F maximization is generally difficult to solve since it requires to face a nonlinear fractional problem. To deal with this issue, we first propose a cooperative secrecy transmission scheme, and prove its optimality in the sense of achieving the maximal S.D.o.F.. By studying this proposed transmission scheme, we obtain the maximal achievable S.D.o.F. in closed form for any given antenna allocation at Bob. Based on this closed-form result, we further analytically derive the optimal antenna allocation at Bob. To the best of our knowledge, this is the first time that the benefit brought by using the FD jamming Bob has been quantified.

Secure Degrees of Freedom in Cooperative MIMO Cognitive Radio Systems

We study the achievable secure degrees of freedom (DoF) in a cooperative MIMO cognitive radio system consisting of one primary source-destination pair, one or two secondary source-destination pairs, and one eavesdropper who is interested only in primary user's data. The cognitive radio users help to secure primary user's transmission against the eavesdropper and in return, the primary user allows the secondary users to access its licensed spectrum. All users are equipped with multiple antennas. We investigate the secure DoF using the interference alignment concept coupled with a zero inter-user interference constraint. We propose a beamforming design based only on the channel state information (CSI) between the primary and secondary user pairs which the legitimate users exchange among each other; no information data are exchanged and no eavesdropper CSI is needed. In the case of a single secondary user pair, we show that if all users have $M$ antennas, secure DoF $d_p$ and DoF $d_s$ of primary and secondary users, respectively, are achievable if they satisfy $2d_p\leq M$ and $d_s \leq M-2d_p$ . In the case of two secondary user pairs, secure DoF $d_p$ and DoFs $d_{s_1},d_{s_2}$ of primary user and two secondary users, respectively, are achievable if they satisfy $2d_p , $d_p+d_i\le M$ , $d_{s_1}+d_{s_2}\le M$ , $i\in\{s_1,s_2\}$ , or $2d_p=M$ , $d_p+d_i\le M$ , $d_{s_1}+d_{s_2} , $i\in\{s_1, s_2\}$ . Simulation examples corroborating the theoretical results are presented.

On Secrecy Capacity of Helper-Assisted Wiretap Channel with an Out-of-Band Link

We consider a physical layer security problem where there is a source, an external helper, a legitimate receiver, and an eavesdropper, each equipped with one antenna. We assume that an additional out-of-band link from the source to the helper is available to improve the transmission security rate. A two-stage cooperative scheme is proposed. The proposed scheme consists of an information sharing stage and a cooperative transmission stage. Specifically, in the information sharing stage the source informs the helper of the signal to be transmitted, while in the cooperative transmission stage the source and the helper cooperate to transmit the signal to the legitimate receiver. Under this framework, we determine the optimal weights associated with this scheme and examine the secrecy capacity of the helper-assisted wiretap channel. The optimal weight design problem is generally nonconvex. To deal with this issue, an algorithm involving a one-dimensional search is developed. On the other hand, an analytical lower bound on the secrecy capacity is derived. Based on this lower bound, we further analyze the sufficient and necessary condition to ensure a positive secrecy capacity and derive the maximal achievable secure degrees of freedom, which are shown to be exactly the same as those of the multi-input single-output (MISO) wiretap channel.

Secure MIMO Communications Under Quantized Channel Feedback in the Presence of Jamming

We consider the problem of secure communications in a MIMO setting in the presence of an adversarial jammer equipped with $n_j$ transmit antennas and an eavesdropper equipped with $n_e$ receive antennas. A multiantenna transmitter, equipped with $n_t$ antennas, desires to secretly communicate a message to a multiantenna receiver equipped with $n_r$ antennas. We propose a transmission method based on artificial noise and linear precoding and a two-stage receiver method employing beamforming. Under this strategy, we first characterize the achievable secrecy rates of communication and prove that the achievable secure degrees-of-freedom (SDoF) is given by $d_s = n_r - n_j$ in the perfect channel state information (CSI) case. Second, we consider quantized CSI feedback using Grassmannian quantization of a function of the direct channel matrix and derive sufficient conditions for the quantization bit rate scaling as a function of transmit power for maintaining the achievable SDoF $d_s$ with perfect CSI and for having asymptotically zero secrecy rate loss due to quantization. Numerical simulations are also provided to support the theory.

On the Secure Degrees of Freedom of Relaying With Half-Duplex Feedback

Secure communication protocols over a single-relay system in the presence of a multiple-antenna eavesdropper are investigated. When there is no direct link between the source and the destination, an amplify-and-forward (AF) protocol that allows both the destination and the source to jam the eavesdropper is shown to achieve secrecy rates that grow linearly with the transmit power in dB, even if all the legitimate nodes have strictly fewer antennas than the eavesdropper. The number of achievable secure degrees of freedom is quantified and shown to match an upper bound when the number of antennas at the destination is sufficiently large. However, in the presence of a direct link between source and destination, this scaling rule no longer applies. The bottleneck of the AF scheme in the presence of a direct source-destination link is identified, motivating the use of another AF scheme and a novel compress-and-forward protocol that can achieve a positive number of secure degrees of freedom using an insecure feedback link.

Secure Communications With Insecure Feedback: Breaking the High-SNR Ceiling

A multiple-antenna Gaussian wiretap channel in which the number of antennas at the source is not greater than that at the eavesdropper is considered. Without feedback, the secrecy capacity over such a channel generally converges to a constant at high signal-to-noise ratio (SNR). A half-duplex secure protocol allowing the destination to actively transfer random keys in the form of known interference is proposed. It is shown that using multiple antennas at the destination is instrumental in achieving a secrecy rate that grows linearly with logSNR. The pre-log factor of the secrecy rate, i.e., the number of secure degrees of freedom, is characterized, revealing an interesting interplay between the numbers of antennas at the three communication nodes. The relationship of the achievable secure degrees of freedom to those obtained in the case without feedback is finally discussed.