Abstract
In this article, the sum secure degrees-of-freedom (SDoF) of the multiple-input multiple-output (MIMO) X channel with confidential messages (XCCM) and arbitrary antenna configurations is studied, where there is no channel state information (CSI) at two transmitters and only delayed CSI at a multiple-antenna, full-duplex, and decode-and-forward relay. We aim at establishing the sum-SDoF lower and upper bounds. For the sum-SDoF lower bound, we design three relay-aided transmission schemes, namely, the relay-aided jamming scheme, the relay-aided jamming and one-receiver interference alignment scheme, and the relay-aided jamming and two-receiver interference alignment scheme, each corresponding to one case of antenna configurations. Moreover, the security and decoding of each scheme are analyzed. The sum-SDoF upper bound is proposed by means of the existing SDoF region of two-user MIMO broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). As a result, the sum-SDoF lower and upper bounds are derived, and the sum-SDoF is characterized when the relay has sufficiently large antennas. Furthermore, even assuming no CSI at two transmitters, our results show that a multiple-antenna full-duplex relay with delayed CSI can elevate the sum-SDoF of the MIMO XCCM. This is corroborated by the fact that the derived sum-SDoF lower bound can be greater than the sum-SDoF of the MIMO XCCM with output feedback and delayed CSIT.
Highlights
The deployment of 5G and all of the connections to 6G around the world have all exacerbated the concerns for information-theoretic security in mobile communication networks [1,2,3]
For the relay-aided multiple-input multiple-output (MIMO) X channel with confidential messages (XCCM) with delayed channel state information (CSI) at the multiple-antenna full-duplex relay and no CSI at two transmitters, the sum-secure degrees-of-freedom (SDoF) lower bound under arbitrary antenna configurations is given as follows:
For the relay-aided MIMO XCCM with delayed CSI at the multiple-antenna full-duplex relay and no CSI at two transmitters, the sum-SDoF upper bound under arbitrary antenna configurations is given by the following:
Summary
The deployment of 5G and all of the connections to 6G around the world have all exacerbated the concerns for information-theoretic security in mobile communication networks [1,2,3]. In [15], under symmetric antenna configurations, a higher sum-SDoF lower bound than that in [14] was derived for MIMO XCCM with delayed CSIT, considering two more confidential messages. The second one is how to create an upper bound for the sum-SDoF in a non-trivial way We address these two problems in the following manner: We propose the relayed-aided jamming and interference alignment (IA) design for transmission scheme, which simultaneously fulfills security guarantee and transmission efficiency. Our results show that if the full-duplex relay has double antennas of the receiver, the proposed sum-SDoF lower bound is not less than the sum-SDoF in existing twouser interference networks with delayed feedback in [14,15,16,17], and can be higher than the sum-SDoF of MIMO X channel with output feedback and delayed CSIT in [17].
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