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.
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.
This dissertation studies physical layer security in wireless networks using an information theoretic framework. The central theme of this work is exploring the effect of delayed or no channel state information (CSI) on physical layer security in various wireless channel models. We begin with the fast Rayleigh fading wiretap channel, over which a legitimate transmitter wishes to have secure communication with a legitimate receiver in the presence of an eavesdropper. Subject to an average power constraint on the input, and with no CSI at any user, we show that the input distribution that achieves the secrecy capacity for this wiretap channel is discrete with a finite number of mass points. This enables us to evaluate the exact secrecy capacity of this channel numerically. Next, we consider multi-user models, specifically, the wiretap channel with M helpers, the K-user multiple access wiretap channel, and the K-user interference channel with an external eavesdropper, when no eavesdropper's CSI is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSI at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the K-user multiple access wiretap channel reduces to a wiretap channel with (K-1) helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K-1)/(K(K-1)+1) to (K-1)/K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K-1)/(2K-1) to (K-1)/2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. We, then, study multiple-input multiple-output (MIMO) multi-user channels. We begin with the case when full CSIT is available. We consider a two-user MIMO multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum s.d.o.f. for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel. In line with the theme of this dissertation, we next consider the MIMO wiretap channel with one helper and the two-user MIMO multiple access channel when no eavesdropper CSIT is available. In each case, the eavesdropper has K antennas while the remaining terminals have N antennas. We determine the optimal sum s.d.o.f. for each channel model for the regime K<= N, and we show that in this regime, the multiple access wiretap channel reduces to the wiretap channel with a helper in the absence of eavesdropper CSIT. For the regime N<= K<= 2N, we obtain the optimal linear s.d.o.f., and show that the multiple access wiretap channel and the wiretap channel with a helper have the same optimal s.d.o.f. when restricted to linear encoding strategies. In the absence of any such restrictions, we provide an upper bound for the sum s.d.o.f. of the multiple access wiretap channel in the regime N<= K<= 2N. Our results show that unlike in the single-input single-output (SISO) case, there is loss of s.d.o.f. for even the wiretap channel with a helper due to lack of eavesdropper CSIT, when K>= N. Finally, we explore the effect of delayed CSIT on physical layer security. In particular, we consider the two user multiple-input single-output (MISO) broadcast channel with confidential messages, in which the nature of CSIT from each user can be of the form I_{i}, i=1,2 where I_{i} belongs to {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 be any of nine possible states corresponding to all possible values of (I_{1},I_{2}). While the optimal sum s.d.o.f. in the homogeneous settings corresponding to I_1=I_2 are already known in the literature, we focus on the heterogeneous settings where I_1 is not equal to I_2 and establish the optimal s.d.o.f. region in each case. We further consider the case where the CSIT state varies with time. Each state (I_1,I_2) can then occur for \lambda_{I_{1}I_{2}} fraction of the total duration. We determine the s.d.o.f. region of the MISO broadcast channel with confidential messages under such an alternating CSIT setting, with a mild symmetry assumption, where \lambda_{I_{1} I_{2}}=\lambda_{I_{2}I_{1}}.
Recent years have been marked by an enormous growth of wireless communication networks and an extensive use of wireless applications. In return, this phenomenal expansion induced more concerns about the privacy and the security of the users. Physical layer security is one of the most promising solutions that were proposed to enhance the security of next generation wireless systems. The fundamental idea behind this technique is to exploit the randomness and the fluctuations of the wireless channel to achieve security without conditional assumptions on the computational capabilities of the eavesdropper. In fact, while these elements have traditionally been associated with signal deterioration, physical layer security uses them to ensure the confidentiality of the users. Nevertheless, these technical virtues rely heavily on perhaps idealistic channel state information assumptions. In that regard, the aim of this thesis is to look at the physical layer security paradigm from the channel uncertainty perspective. In particular, we discuss the ergodic secrecy capacity of different wiretap channels when the transmitter is hampered by the imperfect knowledge of the channel state information (CSI). We consider two prevalent causes of uncertainty for the CSI at transmitter (CSIT); either an error of estimation occurs at the transmitter and he can only base his coding and the transmission strategies on a noisy version of the CSI, or the CSI feedback link has a limited capacity and the legitimate receivers can only inform the transmitter about the quantized CSI. We investigate both the single-user multiple-input multiple-output (MIMO) wiretap channel and the multi-user broadcast wiretap channel. In the latter scenario, we distinguish between two situations: multiple messages transmission and common message transmission. We also discuss the broadcast channel with confidential messages (BCCM) where the transmitter has one common message to be transmitted to two users and one secret message intended to only one of them. In all cases, we show that by appropriately designing the coding and the transmission schemes, a secure communication can still be achieved even with an imperfect knowledge of the CSIT.
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.
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 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.