Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

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 introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Signal-Aligned Network Coding in K-User MIMO Interference Channels with Limited Receiver Cooperation

In this paper, we propose a signal-aligned network coding (SNC) scheme for K-user time-varying multiple-input multiple-output (MIMO) interference channels with limited receiver cooperation. We assume that the receivers are connected to a central processor via wired cooperation links with individual limited capacities. Our SNC scheme determines the precoding matrices of the transmitters so that the transmitted signals are aligned at each receiver. The aligned signals are then decoded into noiseless integer combinations of messages, also known as network-coded messages, by physical-layer network coding. The key idea of our scheme is to ensure that independent integer combinations of messages can be decoded at the receivers. Hence the central processor can recover the original messages of the transmitters by solving the linearly independent equations. We prove that our SNC scheme achieves full degrees of freedom (DoF) by utilizing signal alignment and physical-layer network coding. Simulation results show that our SNC scheme outperforms the compute-and-forward scheme in the finite SNR regime of the two-user and the three-user cases. The performance improvement of our SNC scheme mainly comes from efficient utilization of the signal subspaces for conveying independent linear equations of messages to the central processor.Comment: 12 pages, 4 figures, submitted to the IEEE Transactions on Vehicular Technolog

Generalized Signal Alignment For MIMO Two-Way X Relay Channels

We study the degrees of freedom (DoF) of MIMO two-way X relay channels. Previous work studied the case $N < 2M$, where $N$ and $M$ denote the number of antennas at the relay and each source, respectively, and showed that the maximum DoF of $2N$ is achievable when $N \leq \lfloor\frac{8M}{5}\rfloor$ by applying signal alignment (SA) for network coding and interference cancelation. This work considers the case $N>2M$ where the performance is limited by the number of antennas at each source node and conventional SA is not feasible. We propose a \textit{generalized signal alignment} (GSA) based transmission scheme. The key is to let the signals to be exchanged between every source node align in a transformed subspace, rather than the direct subspace, at the relay so as to form network-coded signals. This is realized by jointly designing the precoding matrices at all source nodes and the processing matrix at the relay. Moreover, the aligned subspaces are orthogonal to each other. By applying the GSA, we show that the DoF upper bound $4M$ is achievable when $M \leq \lfloor\frac{2N}{5}\rfloor$ ($M$ is even) or $M \leq \lfloor\frac{2N-1}{5}\rfloor$ ($M$ is odd). Numerical results also demonstrate that our proposed transmission scheme is feasible and effective.Comment: 6 pages, 6 figures, to appear in IEEE ICC 201

Compute-and-Forward: Harnessing Interference through Structured Codes

Interference is usually viewed as an obstacle to communication in wireless networks. This paper proposes a new strategy, compute-and-forward, that exploits interference to obtain significantly higher rates between users in a network. The key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise. After decoding these linear equations, the relays simply send them towards the destinations, which given enough equations, can recover their desired messages. The underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably. Encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field. This scheme is applicable even if the transmitters lack channel state information.Comment: IEEE Trans. Info Theory, to appear. 23 pages, 13 figure

A New DoF Upper Bound and Its Achievability for KK-User MIMO Y Channels

This work is to study the degrees of freedom (DoF) for the $K$-user MIMO Y channel. Previously, two transmission frameworks have been proposed for the DoF analysis when $N \geq 2M$, where $M$ and $N$ denote the number of antennas at each source node and the relay node respectively. The first method is named as signal group based alignment proposed by Hua et al. in [1]. The second is named as signal pattern approach introduced by Wang et al. in [2]. But both of them only studied certain antenna configurations. The maximum achievable DoF in the general case still remains unknown. In this work, we first derive a new upper bound of the DoF using the genie-aided approach. Then, we propose a more general transmission framework, generalized signal alignment (GSA), and show that the previous two methods are both special cases of GSA. With GSA, we prove that the new DoF upper bound is achievable when $\frac{N}{M} \in \left(0,2+\frac{4}{K(K-1)}\right] \cup \left[K-2, +\infty\right)$. The DoF analysis in this paper provides a major step forward towards the fundamental capacity limit of the $K$-user MIMO Y channel. It also offers a new approach of integrating interference alignment with physical layer network coding.Comment: 6 pages, 3 figures, submitted to IEEE ICC 2015. arXiv admin note: text overlap with arXiv:1405.071