The degrees of freedom (DoFs) of the K-user multiple-input multiple-output (MIMO) interference channel are studied when perfect, but delayed channel state information is available at the transmitter side (delayed CSIT). Recent works have proposed schemes improving the DoF knowledge of the interference channel, but at the cost of developing transmission involving many channel uses (long delay), thus increasing the complexity at both transmitter and receiver side. This paper proposes three linear precoding strategies, limited to at most three phases, based on the concept of interference alignment, and built upon three main ingredients: delayed CSIT precoding, user scheduling, and redundancy transmission. In this respect, the interference alignment is realized by exploiting delayed CSIT to align the interference at the non-intended receivers along the space-time domain. Moreover, a new framework is proposed where the number of transmitted symbols and duration of the phases is obtained as the solution of a maximization problem, and enabling the introduction of complexity constraints, which allows deriving the achievable DoF as a function of the transmission delay, i.e., the achievable DoF-delay trade-off. Finally, the latter part of this paper settles that the assumption of time-varying channels common along all the literature on delayed CSIT is indeed unnecessary.

Retrospective Interference Alignment is a linear precoding strategy that seizes delayed channel state information at the transmitters (CSIT), improving the degrees of freedom (DoF) that can be achieved without CSIT for both the broadcast and interference channels. However, little is known for other channel configurations. This work studies the multiple-input multiple-output interference broadcast channel (IBC) with delayed CSIT, 2 cells and 2 users per cell. Although some of the schemes designed for other channels may be applied, they do not exploit the specific topology of the IBC. In this regard, we proposes a precoding strategy that includes the concept of redundancy transmission, and takes into account that users of each cell are served by a common transmitter. Assuming that transmitters and receivers are equipped with M, N antennas, respectively, state-of-the-art achievable DoF are improved for ρ = M over N > ρA, with ρA≈ 3.5414.

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 bounds 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.

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 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 ρ = M/N. The proposed scheme improves all other strategies when ρ ∈ (1/2, 31/32].

The degrees of freedom (DoF) of the 3-user multiple-input multiple-output (MIMO) interference channel (IC) with full channel state information and constant channel coefficients are investigated when (p,p+1) antennas are deployed at the transmitters and receivers, respectively. The point of departure of this paper is the work of Wang et al., which conjectured but did not prove the DoF for the antenna settings with p>1. Here the achievability of the DoF outer bound is formally proved using linear methods, thereby avoiding the use of the rational dimensions framework. The proposed transmission scheme exploits asymmetric complex signaling together with symbol extensions in time and space interference alignment concepts. While the paper deals with the p=2,3,\ldots,6 cases, providing the specific transmit and receive filters, there are also provided the tools needed for proving the achievability of the optimal DoF for p>6, whose DoF characterization is conjectured.