Secrecy Degrees of Freedom of MIMO Broadcast Channels With Delayed CSIT

Abstract

The degrees of freedom (DoF) of the two-user Gaussian multiple-input and multiple-output (MIMO) broadcast channel with confidential message (BCC) 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 (ANA) 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 interpreted as a non-trivial extension of Maddah-Ali Tse (MAT) scheme and enables us to quantify the resource overhead, or equivalently the DoF loss, to be paid for the secrecy communications. DRAFT 3 a general CSIT assumption. In other words, if the statistics of the underlying channels seen by both receivers are symmetrical, additional side information (not necessarily instantaneous CSIT) is essential to ensure a positive SDoF, by introducing some asymmetry at the encoder. As a matter of fact, this reveals one of the major limitations of the wiretap model whose performance strongly depends on the quality of the channel state information at the transmitter side. Evidently, theoretically addressing CSI issues is of fundamental impact for secrecy systems.Recently, in the context of multi-antenna broadcast channel, the pioneering work [1] showed that completely outdated channel state information at the transmitter is still very useful and increases the degrees of freedom of the multi-user channel. Motivated by this exciting result, the new assumption, commonly referred to as delayed CSIT, has since been applied to several multi-user settings, including the MIMO broadcast channel, X channel, and interference channel [12]- [15]. Non-trivial gain of degrees of freedom have been shown in all these settings with delayed CSIT. The main idea behind the utility of delayed CSIT can be best described with the term "retrospective interference alignment" introduced in[13] and [16]. That is, the knowledge of causal channel state is used to align the interference between users into a spatial/temporal subspace with a reduced dimension at each receiver.In this paper, we study the impact of delayed CSIT on the secrecy degrees of freedom in a MIMO broadcast channel. In our setting, delayed CSI of a given receiver is available both at the transmitter and the other receiver 2 , whereas each receiver knows its own instantaneous channel. Such a scenario is of practical interest since the receivers may send their channel states to the transmitter via delayed feedback links that may be overheard by the other receivers. We first characterize the optimal SDoF of the Gaussian MIMO wiretap channel with delayed CSIT. It is shown that delayed CSIT can significantly improve the SDoF, provided that ...

Achievable secure degrees of freedom of MISO broadcast channel With alternating CSIT

“…Remark 1: The outer bound generalizes the converse proof of [2] established in the context of SDoF of MIMO wiretap channel with delayed CSIT to the case with alternating CSIT; and, also, uses elements from the converse proof of [1] established for the two-user broadcast channel with alternating CSIT by taking imposed security constraints into account. Note that, if delayed CSI of both receivers is conveyed to the transmitter, i.e., λ DD := 1, the outer bound recovers the SDoF of MISO wiretap channel with delayed CSI [2, Theorem 1].…”

“…For the two-user (2,1,1)-MISO broadcast channel the optimal SDoF is (d 1 , d 2 ) = (1, 1). Yang et al [2] study the MIMO broadcast channel in which only past or delayed CSI of both receivers is conveyed to the transmitter, and characterize the SDoF region. In [6], the authors generalized the model in [2] to the MIMO-X setting with asymmetric feedback and delayed CSIT and characterize the SDoF region.…”

“…Yang et al [2] study the MIMO broadcast channel in which only past or delayed CSI of both receivers is conveyed to the transmitter, and characterize the SDoF region. In [6], the authors generalized the model in [2] to the MIMO-X setting with asymmetric feedback and delayed CSIT and characterize the SDoF region. However, for the twouser MISO broadcast channel with partially perfect CSIT (PD state) configuration, i.e., perfect CSI of one receiver and delayed CSI of the other receiver is conveyed to the transmitter, SDoF region is unknown.…”

“…For the case in which delayed CSI of both receivers is conveyed to the transmitter, (d 1 , d 2 ) = ( 1 2 , 1 2 ) SDoF is achievable. The coding scheme in this case is established in [2] and is omitted for brevity.…”

“…First, we characterize the SDoF of the ( scheme in this case is based on an appropriate combination of schemes developed for fixed CSIT configurations, namely, PP, PD, DP and DD states. The converse proof follows by extending the proof of [2] developed in the context of SDoF of MIMO wiretap channel with delayed CSIT to the case with alternating CSIT; and, also, borrows some elements from the converse proof of [1] established for the broadcast model with alternating CSIT by taking imposed security constraints into account. Next, we study the MISO broadcast channel with alternating CSIT as shown in Figure 1 and establish an inner bound on the SDoF region.…”