Retrospective Interference Alignment for the 3-user MIMO Interference Channel with delayed CSIT

The degrees of freedom (DoF) of the 3-user multiple input multiple output interference channel (3-user MIMO IC) are investigated where there is delayed channel state information at the transmitters (dCSIT). We generalize the ideas of Maleki et al. about {\it Retrospective Interference Alignment (RIA)} to be applied to the MIMO IC, where transmitters and receivers are equipped with $(M,N)$ antennas, respectively. We propose a two-phase transmission scheme where the number of slots per phase and number of transmitted symbols are optimized by solving a maximization problem. Finally, we review the existing achievable DoF results in the literature as a function of the ratio between transmitting and receiving antennas $\rho=M/N$. The proposed scheme improves all other strategies when $\rho \in \left(\frac{1}{2}, \frac{31}{32} \right]$.Comment: Draft version of the accepted manuscript at IEEE ICASSP 1

On the Degrees of freedom of the K-user MISO Interference Channel with imperfect delayed CSIT

This work investigates the degrees of freedom (DoF) of the K-user multiple-input single-output (MISO) interference channel (IC) with imperfect delayed channel state information at the transmitters (dCSIT). For this setting, new DoF inner bonds are provided, and benchmarked with cooperation-based outer bounds. The achievability result is based on a precoding scheme that aligns the interfering received signals through time, exploiting the concept of Retrospective Interference Alignment (RIA). The proposed approach outperforms all previous known schemes. Furthermore, we study the proposed scheme under channel estimation errors (CEE) on the reported dCSIT, and derive a closed-form expression for the achievable DoF with imperfect dCSIT.Comment: Draft version of the accepted manuscript at IEEE ICASSP 1

Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT

We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit

Degrees of Freedom Region of the MIMO Interference Channel with Output Feedback and Delayed CSIT

The two-user multiple-input multiple-output (MIMO) interference channel (IC) with arbitrary number of antennas at each terminal is considered and the degrees of freedom (DoF) region is characterized in the presence of noiseless channel output feedback from each receiver to its respective transmitter and availability of delayed channel state information at the transmitters (CSIT). It is shown that having output feedback and delayed CSIT can strictly enlarge the DoF region of the MIMO IC when compared to the case in which only delayed CSIT is present. The proposed coding schemes that achieve the corresponding DoF region with feedback and delayed CSIT utilize both resources, i.e., feedback and delayed CSIT in a non-trivial manner. It is also shown that the DoF region with local feedback and delayed CSIT is equal to the DoF region with global feedback and delayed CSIT, i.e., local feedback and delayed CSIT is equivalent to global feedback and delayed CSIT from the perspective of the degrees of freedom region. The converse is proved for a stronger setting in which the channels to the two receivers need not be statistically equivalent.Comment: Accepted for publication in IEEE Transactions on Information Theor

Retrospective Interference Alignment for Two-Cell Uplink MIMO Cellular Networks with Delayed CSIT

In this paper, we propose a new retrospective interference alignment for two-cell multiple-input multiple-output (MIMO) interfering multiple access channels (IMAC) with the delayed channel state information at the transmitters (CSIT). It is shown that having delayed CSIT can strictly increase the sum-DoF compared to the case of no CSIT. The key idea is to align multiple interfering signals from adjacent cells onto a small dimensional subspace over time by fully exploiting the previously received signals as side information with outdated CSIT in a distributed manner. Remarkably, we show that the retrospective interference alignment can achieve the optimal sum-DoF in the context of two-cell two-user scenario by providing a new outer bound.Comment: 7 pages, 2 figures, to appear in IEEE ICC 201