In this paper, we propose two secure multiuser multiple-input multiple-output (MIMO) transmission approaches based on interference alignment (IA) in the presence of an eavesdropper. To deal with the information leakage to the eavesdropper as well as the interference signals from undesired transmitters (Txs) at desired receivers (Rxs), our approaches aim to design the transmit precoding and receive subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals (WSs). The first proposed IA scheme focuses on aligning the WSs into proper subspaces while the second one imposes a new structure on the precoding matrices to force the WSs to zero. In each proposed IA scheme, the precoding matrices and the receive subspaces at the legitimate users are alternatively selected to minimize the cost function of a convex optimization problem for every iteration. We provide the feasible conditions and the proofs of convergence for both IA approaches. The simulation results indicate that our two IA approaches outperform the conventional IA algorithm in terms of the average secrecy sum rate.
In this paper, we propose two secure multiuser multiple-input multiple-output (MIMO) transmission approaches based on interference alignment (IA) in the presence of an eavesdropper. To deal with the information leakage to the eavesdropper as well as the interference signals from undesired transmitters (Txs) at desired receivers (Rxs), our approaches aim to design the transmit precoding and receive subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals (WSs). The first proposed IA scheme focuses on aligning the WSs into proper subspaces while the second one imposes a new structure on the precoding matrices to force the WSs to zero. In each proposed IA scheme, the precoding matrices and the receive subspaces at the legitimate users are alternatively selected to minimize the cost function of a convex optimization problem for every iteration. We provide the feasible conditions and the proofs of convergence for both IA approaches. The simulation results indicate that our two IA approaches outperform the conventional IA algorithm in terms of the average secrecy sum rate.
In this paper, interference alignment (IA) is designed for secure multiuser multiple-input multiple-output systems in the presence of an eavesdropper. The proposed IA technique designs the transmit precoding and receiving subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals. With perfect channel state information is known at the transmitters (Txs), the cost function of the optimization problem is alternatively minimized over the precoding matrices at the Txs and the receiving subspace matrices at the receivers (Rxs) and the eavesdropper. The feasible condition, the proof of convergence of the proposed IA approach are provided. Numerical results reveal a significant improvement in terms of average secrecy sum rate of our IA algorithm as compared to the conventional IA design.
In this paper, we formulate the interference alignment (IA) problem for a multiuser multiple-input multiple-output (MIMO) system in the presence of an eavesdropper as a rank constrained rank minimization (RCRM) problem. The aim of the proposed rank minimization IA schemes is to find the precoding and receiver subspace matrices to align interference and wiretapped signals into the lowest dimension subspaces while keeping the desired signal subspace spanning full available spatial dimensions. To deal with the nonconvexity of the rank function, we present two convex relaxations of the RCRM problem, namely nuclear norm (NN) and reweighted nuclear norm (RNN), and transform the rank constraints to equivalent and tractable ones. We then derive a coordinate decent approach to obtain the solutions for IA schemes. The simulation results show that our proposed IA designs outperform the conventional IA design in terms of average secrecy sum rate. On the other hand, our proposed designs perform the same or better than other secure IA schemes which account for low interference and wiretapped signal power rather than for low dimensions of interference and wiretapped signal matrices in the systems which achieve the perfect IA.
In interference alignment (IA)-based networks, interferences are constrained into certain subspaces at the unintended receivers, and the desired signal can be recovered free of interference. Due to the superposition of signals from legitimate users at the eavesdropper, the IA-based network seems to be more secure than conventional wireless networks. Nevertheless, when adequate antennas are equipped, the legitimate information can still be eavesdropped. In this paper, we analyze the performance of the external eavesdropper, and propose two anti-eavesdropping schemes for IA-based networks. When the channel state information (CSI) of eavesdropper is available, zero-forcing scheme can be utilized, in which the transmitted signals are zero-forced at the eavesdropper through the precoding of transmitters in IA-based networks. Furthermore, a more generalized artificial noise (AN) scheme is proposed for IA-based networks without the knowledge of eavesdropper's CSI. In this scheme, a single-stream AN is generated by each user, which will disrupt the eavesdropping without introducing any additional interference to the legitimate transmission of IA-based networks. In addition, the feasibility conditions, transmission rate, and eavesdropping rate are analyzed in detail, and an iterative algorithm to achieve the scheme is also designed. Extensive simulation results are provided to verify our analysis results and show the effectiveness of the proposed anti-eavesdropping schemes for IA-based networks.
To enhance physical layer security (PLS) and mitigate interference at legitimate receivers, artificial noise (AN) assisted interference alignment (IA) is explored in cooperative multiple-input multiple-output (MIMO) systems. The feasibility of traditional leakage minimization (LM) based IA is analyzed. We show that there exist two drawbacks which are not discussed in traditional LM based IA: 1) the necessary condition for the feasibility of IA is loose, and 2) the secret signal cancellation may occur at the desired receiver, which makes secure transmission infeasible. We analyze the reason and establish a condition under which either the secret signal cancellation is inevitable or IA is infeasible. Then a modified IA is proposed. Compared with the traditional LM based IA, a tighter necessary condition is established and the secret signal is protected against cancellation. Moreover, we prove that the proposed condition guarantees the properness of system, which is a rigorous characterization of necessary conditions for achieving IA. Under assumption that the modified IA is feasible, we provide a secrecy enhancing design to maximize the secrecy rate. subject to a secrecy outage constraint. We also establish a condition under which a positive secrecy rate is feasible. Numerical results validate the effectiveness of the proposed approach.
We propose a distributed artificial noise-assisted precoding scheme for secure communications over wiretap multi-input multi-output (MIMO) interference channels, where K legitimate transmitter-receiver pairs communicate in the presence of a sophisticated eavesdropper having more receive-antennas than the legitimate user. Realistic constraints are considered by imposing statistical error bounds for the channel state information of both the eavesdropping and interference channels. Based on the asynchronous distributed pricing model, the proposed scheme maximizes the total utility of all the users, where each user’s utility function is defined as the secrecy rate minus the interference cost imposed on other users. Using the weighted minimum mean square error, Schur complement and sign-definiteness techniques, the original non-concave optimization problem is approximated with high accuracy as a quasi-concave problem, which can be solved by the alternating convex search method. Simulation results consolidate our theoretical analysis and show that the proposed scheme outperforms the artificial noise-assisted interference alignment and minimum total mean-square error-based schemes.
In this paper, we consider the problem of jointly designing transmit precoding (TPC) matrix and receive filter matrix subject to both secrecy and per-transmitter power constraints in the multiple-input multiple-output (MIMO) interference channel, where K legitimate transmitter-receiver pairs communicate in the presence of an external eavesdropper. Explicitly, we jointly design the TPC and receive filter matrices based on the minimum total mean-squared error (MSE) criterion under a given and feasible information-theoretic degrees of freedom. More specifically, we formulate this problem by minimizing the total MSEs of the signals communicated between the legitimate transmitter-receiver pairs, while ensuring that the MSE of the signals decoded by the eavesdropper remains higher than a certain threshold. We demonstrate that the joint design of the TPC and receive filter matrices subject to both secrecy and transmit power constraints can be accomplished by an efficient iterative distributed algorithm. The convergence of the proposed iterative algorithm is characterized as well. Furthermore, the performance of the proposed algorithm, including both its secrecy rate and MSE, is characterized with the aid of numerical results. We demonstrate that the proposed algorithm outperforms the traditional interference alignment algorithm in terms of both the achievable secrecy rate and the MSE. As a benefit, secure communications can be guaranteed by the proposed algorithm for the MIMO interference channel even in the presence of a sophisticated/strong eavesdropper, whose number of antennas is much higher than that of each legitimate transmitter and receiver.