The two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1; I2∈ {P;D;N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate over time between 9 possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption λI1I2= λI2I1. The results highlight the synergistic benefits of coding across CSIT states for secrecy and the interplay between various aspects of channel knowledge and its impact on s.d.o.f.
The two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1; I2∈ {P;D;N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate over time between 9 possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption λI1I2= λI2I1. The results highlight the synergistic benefits of coding across CSIT states for secrecy and the interplay between various aspects of channel knowledge and its impact on s.d.o.f.
The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form Ii, i = 1, 2 where I1, I2∈ {P, D, N}, and the forms P, D, and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of I1I2, with each state occurring for λI1I2fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where λI1I2= λI2I1. The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.
We consider the two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM), in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form P, D and N, corresponding to perfect and instantaneous, completely delayed, and no CSIT, respectively. We focus on the cases with heterogeneous CSIT from the users, that is, the states PD, PN and DN. The main contribution of this paper is to establish the exact secure degrees of freedom (s.d.o.f.) regions of the MISO BCCM in all of these three heterogeneous states. The results highlight the impact of availability of CSIT on the s.d.o.f. region.
We study the problem of secure transmission over a two-user Gaussian multi-input single-output (MISO) broadcast channel under the assumption that the channel to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting S1and S2to be the channel state information at the transmitter (CSIT) of user 1 and user 2, respectively; the overall CSIT can then alternate between four states, i.e., (S1, S2) ∈ {P,D}2. We denote λS1S2be the fraction of time the state S1S2occurs, and focus on the symmetric case such that λS1S2= λS2S1. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we generalize this model to the two-user Gaussian MISO broadcast channel and establish an inner bound on the SDoF region. This result shows the synergistic SDoF gains of alternating CSIT and illustrates that, as opposed to encoding separately over different states, an improved SDoF region is achievable by joint encoding across these states.
We study the problem of secure transmission over a two-user Gaussian multi-input single-output (MISO) broadcast channel under the assumption that the state of the channel to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting by S1 and S2 the channel state information at the transmitter (CSIT) of user 1 and user 2, respectively, the overall CSIT can then alternate between four possible states, i.e., (S1,S2)∈ {P,D} 2 . We denote by λS1S2 the fraction of time during which the state S1S2 occurs and focus on the symmetric case such that λS1S2 =λS2S1. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we generalize this model to the two-user Gaussian MISO broadcast channel and establish bounds on the SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates.
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 two-user multiple-input single-output (MISO) broadcast channel with confidential messages under the assumption of alternating channel state information at the transmitter (CSIT). We consider two alternating states: PD and DP which occur for an equal fraction of time. In state PD, the CSIT of the channel to the first receiver is available perfectly without delay (P) while that of the second receiver is available with a delay of one channel use (D); in state DP, the roles of the receivers are reversed. We characterize the exact secure degrees of freedom (s.d.o.f.) region of this system, and show as a corollary that the sum s.d.o.f. is 3/2. We observe that this sum s.d.o.f. is the same as what can be achieved by the states PP and DD occurring for equal fraction of time. Though the s.d.o.f. of the system in the states PD and DP is not known individually, we are able to establish the s.d.o.f. region when the two states alternate and occur for an equal fraction of the time.