On SDoF of multi-receiver wiretap channel with alternating CSIT

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly (P) or with delay (D) to the transmitter. Denoting by S
₁
, S
₂
, and S
₃
the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., (S
₁
, S
₂
, S
₃
) ∈ {P,D}
³
. We denote by λ
_S1S2S3
the fraction of time during which the state S
₁
S
₂
S
₃
occurs. Under these assumptions, we consider the multi-receiver setup and characterize the SDoF region of fixed hybrid states PPD, PDP, and DDP. We then focus our attention on the symmetric case in which λ
_PDD
= λ
_DPD
. For this case, we 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.