The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential messages is studied under the assumption that delayed channel state information (CSI) is available at the transmitter. We characterize the optimal secrecy DoF (SDoF) region and show that it can be achieved by a simple artificial noise alignment scheme. The proposed scheme sends the confidential messages superposed with the artificial noise over several time slots. Exploiting delayed CSI, the transmitter aligns the transmit signal in such a way that the useful message can be extracted at the intended receiver but is completely drowned by the artificial noise at the unintended receiver. The proposed scheme can be regarded as a nontrivial extension of Maddah-Ali Tse scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secure communications.
The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential messages is studied under the assumption that delayed channel state information (CSI) is available at the transmitter. We characterize the optimal secrecy DoF (SDoF) region and show that it can be achieved by a simple artificial noise alignment scheme. The proposed scheme sends the confidential messages superposed with the artificial noise over several time slots. Exploiting delayed CSI, the transmitter aligns the transmit signal in such a way that the useful message can be extracted at the intended receiver but is completely drowned by the artificial noise at the unintended receiver. The proposed scheme can be regarded as a nontrivial extension of Maddah-Ali Tse scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secure communications.
The secrecy degrees of freedom (SDoF) of the Gaussian multiple-input and single-output (MISO) wiretap channel is studied under the assumption that delayed channel state information (CSI) is available at the transmitter and each receiver knows its own instantaneous channel. Such scenario is of practical interest since the legitimate receiver may send its channel states to the transmitter which is overheard by the eavesdropper. We first show that a strictly positive SDoF can be guaranteed whenever the transmitter has delayed CSI (either on the legitimate channel or/and the eavesdropper channel). In particular, in the case with delayed CSI on both channels, it is shown that the optimal SDoF is 2=3. We then generalize the result to the two-user Gaussian MISO broadcast channel with confidential messages and characterize the SDoF region when the transmitter has delayed CSI of both receivers. Interestingly, the artificial noise schemes are shown to provide the optimal SDoF region by masking the confidential message to the unintended receiver while aligning the interference at each receiver.
The secrecy degrees of freedom (SDOF) of the multiple-input single-output (MISO) broadcast channel with confidential messages (BCC) is studied. The network consists of a two-antenna transmitter and two single-antenna receivers, each demanding a confidential message from the transmitter. The problem is investigated with mixed channel state information at transmitter (CSIT), which is a combination of perfect delayed CSIT and inaccurate current CSIT. When the variance of the estimation error for the current CSIT scales with O(P-α), with α ∈ [0, 1], it is shown that the optimal sum SDOF of the considered BCC is 1+α. Furthermore, the optimal SDOF region of the considered MISO BCC is shown to be a polygon scaling with α. The proposed scheme is based on an artificial noise alignment that can combine the benefits of both types of delayed and current CSIT. These results can be seen as an extension of results of Yang et al. and Gou-Jafar to multiuser networks with secrecy constraints.
We study the Gaussian multiple-input multiple-output multiple-eavesdropper wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers. Each node in the network is equipped with an arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom (SDoF) for such a network has only been characterized for special cases, and is unknown in general. We completely characterize the SDoF of this network for all antenna configurations. In particular, we strictly improve the state-of-the-art achievable scheme for this network by proposing more efficient artificial noise alignment at the receivers. Furthermore, we develop a tight upper bound by utilizing three important inequalities that provide lower bounds on the received signal dimensions at receivers which supply delayed CSIT or no CSIT. These inequalities together allow for analysis of signal dimensions in networks with heterogeneous CSIT; and as a result, we present a converse proof that leads to characterization of SDoF for all possible antenna configurations.
In this letter, we study the secure degrees-of-freedom (SDoF) characterization for the multiple-input multiple-output (MIMO) X channel with confidential messages and delayed channel state information at the transmitter (CSIT). In particular, we propose a transmission scheme, which can be regarded as a generalization of the state-of-the-art scheme without security and with delayed CSIT. The key of this generalization is performing the security analysis, by which we derive the optimal duration of the artificial noise transmission phase. As a result, we derive the sum-SDoF lower bound. Furthermore, we reveal that if the number of receive antennas, denoted byN, is fixed, the minimum number of transmit antennas achieving the maximum of the lower bound is87+33N.
In this chapter, we will discuss how the quality and availability of channel state information (CSI) affects secrecy in wireless networks. In particular, we study how the delay in the availability of CSI affects secrecy in the context of the two-user broadcast channel with confidential messages. We adopt a secure degrees of freedom perspective and investigate various CSI scenarios, including cases when the availability of CSI at the transmitter varies across users and with time. We discuss how to leverage such variabilities in CSI for secrecy and highlight the differences between the optimal degrees of freedom with or without secrecy constraints. Introduction The availability of channel state information at the transmitters (CSIT) plays a crucial role in securing wireless communication at the physical layer. Various well-known physical-layer security techniques such as coding for the fading wiretap channel [1–4], coding for the multiple-antenna wiretap channel [5–8], artificial noise injection [9], cooperative jamming [10, 11], cooperation for secrecy [12–18], secure signal alignment [19–22], and other related techniques rely upon the assumption of timely availability of precise CSIT; see also a recent review article in [23]. In most practical scenarios, the channel gains are measured by the receivers and then fed back to the transmitters. The measurement and feedback process necessarily introduces imprecision and delay into the CSI. Motivated by this fact, in this chapter we explore the fundamental limits of physical layer security when the CSIT is imperfect. For concreteness, we will focus on a particular wireless network model: the multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM). This effectively models practical systems such as a cellular downlink network where each user wants not only reliability but also confidentiality of the information intended for it. The focus of this chapter is on the secure degrees of freedom (s.d.o.f.) region of the fading two-user MISO BCCM, in which the transmitter with two antennas has two confidential messages, one for each of the single antenna users (see Fig. 8.1). The secrecy capacity region of the MISO broadcast channel (BC) for the case of perfect and instantaneous CSI at all terminals (transmitter and the receivers) has been characterized in [24, 25]. Using these results, it follows that for the two-user MISO BCCM, the sum s.d.o.f. is 2 with perfect and instantaneous CSIT.
We study the Gaussian MIMOME wiretap channel where a transmitter wishes to communicate a confidential message to a legitimate receiver in the presence of eavesdroppers, while the eavesdroppers should not be able to decode the confidential message. Each node in the network is equipped with arbitrary number of antennas. Furthermore, channels are time varying, and there is no channel state information available at the transmitter (CSIT) with respect to eavesdroppers' channels; and transmitter only has access to delayed CSIT of the channel to the legitimate receiver. The secure degrees of freedom (SDoF) for such network has only been characterized for special cases, and is unknown in general. We completely characterize the SDoF of this network for all antenna configurations. In particular, we strictly improve the state-of-the-art achievable scheme for this network by proposing more efficient artificial noise alignment at the receivers. Furthermore, we develop a tight upper bound by utilizing 4 important inequalities that provide lower bounds on the received signal dimensions at receivers which supply delayed CSIT or no CSIT, or at a collection of receivers where some supply no CSIT. These inequalities together allow for analysis of signal dimensions in networks with asymmetric CSIT; and as a result, we present a converse proof that leads to characterization of SDoF for all possible antenna configurations.