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

Abstract

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 S 1 and S 2 to 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., (S 1 , S 2 ) ∈ {P, D} 2 . We denote λ S 1 S 2 be the fraction of time the state S 1 S 2 occurs, and focus on the symmetric case such that λ S 1 S 2 = λ S 2 S 1 . 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.

On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT

“…Proof: The proof of (85a)-(85f) follows along similar lines as in Lemma 1. In what follows, we now provide the proof of (85g).…”

“…As opposed to the model in [26], the model that we study in this paper as shown in Figure 2 is more general, since it allows more leverage to the transmitter to choose between four possible states, i.e., PP, PD, DP, and DD. Specializing the results in this work to the model studied in [26] reveals that the encoding scheme in [26] outperforms the scheme that we developed in [1] (SDoF of 3/2 vs. 4/3). However, the outer bound that we have established in this work is more general; and, it subsumes the outer bound in [26] and the one developed in the context of broadcast channel with delayed CSIT in [21].…”

“…Then, based on the availability of the CSIT, the model that we study (1) belongs to any of the following eight states…”

“…2014 [1]. receiver is available instantaneously at the transmitter, while the channel to the other receiver is conveyed with some delay.…”

A Survey on Robust Interference Management in Wireless Networks

“…Only recently, the impact of imperfections on the DoF was investigated from various perspectives. Those include cases in which some channels are perfectly known, while others are completely unknown [9,10], cases in which the CSIT is available however only in a delayed or outdated fashion [11][12][13][14]. In other cases the knowledge of the channel is reduced to the channel coherence patterns [15] or the topology of the network [16,17].…”