### Multi-User Networks with Outdated Channel State Information

The spread of ubiquitous high-speed mobile communication has changed our daily life and society significantly. Using multiple antennas at transmitters and receivers, known as multiple-input and multiple-output (MIMO) technology, is one of the key developments which allowed new advances in mobile communication. Accurate and upto-date channel state information at the transmitter (CSIT) is a necessary requirement for achieving the multiplexing gains, referred to in the literature also as degrees of freedom (DoF). Maintaining up-to-date CSIT however may become exhausting in terms of the number of resources. In case the CSIT is completely outdated, no channel time correlation can be exploited. Nevertheless, even completely outdated CSIT can be very useful for achieving DoF greater than that with completely absent CSIT. The key idea is to apply a multi-phase transmission, where in each phase, the interference terms overheard in the previous phases are retransmitted. On one hand, such terms provide the transmitters with new information about the desired symbols. On the other hand, such terms can be cancelled at the receivers which previously overheard them. In such a way, the amount of the produced interference in each consecutive phase is reduced, where in the last phase, an interference-free transmission is achieved. In this project, we design new transmission schemes to achieve more DoF in a variety of communication networks with completely outdated or simply delayed CSIT.

Firstly, a network with two transmitters and two receivers is considered, where each transmitter desires to deliver a message to each receiver. Such network is referred to in the literature as the X-channel (XC). We consider a MIMO setting, in which the transmitters have M1 and M2 antennas and the receivers have N1 and N2 antennas. In the XC, each receiver receives a superposition of two interference signals originating from different transmitters, hence the interference in its plain form cannot be reconstructed using delayed CSIT. By applying redundancy transmission (RT), each transmitter can be forced to span only a fraction of the signal space of each receiver. Then, by applying partial interference nulling (PIN), each receiver can subtract the signal of one of the interferers, where the remaining interference signal can be reconstructed at the transmitter using delayed CSIT. In case min fM1;M2g > min fN1;N2g, a more effective multi-part transmission, known as interference sensing and redundancy transmission (IS-RT), can be performed, where the interference overheard in the first part comprises the redundancy transmitted in the second part. In this project, we perform decodability analysis of the state-of-the-art transmission scheme for the MIMO XC with delayed CSIT which relies on IS-RT-PIN. Our analysis shows, that despite the fact that the receivers obtain a sufficient number of linear combinations, the transmitted information symbols are not always decodable, which is due to a linear dependence of the linear combinations. To address the identified decodability problem, a novel transmission scheme is proposed, where the parameters of the scheme are carefully selected to maximize the number of the transmitted information symbols while ensuring linear independence.

The proposed transmission scheme achieves a number of DoF greater than that of the state-of-the-art transmission scheme in which the number of the transmitted information symbols is reduced to the number of the decodable ones. Secondly, a network with three transmitters and three receivers is considered, where each transmitter wants to deliver a message to its corresponding partner receiver. Such network is referred to in the literature as the three-user interference channel (IC). We consider a symmetric MIMO setting, in which each transmitter has M antennas and each receiver has N antennas. For the three-user MIMO IC with delayed CSIT, two novel transmission schemes for M < N and M > N are proposed which achieve DoF greater than that in the literature. The first transmission scheme proposed for M < N relies on RT-PIN, where we take into account the fact that for M < N, the redundancy is naturally introduced by the channel. The proposed transmission scheme has a threephase structure, where in each phase the amount of the introduced redundancy is adjusted according to M N . The second transmission scheme proposed for M > N relies on IS-RT-PIN. As already identified for the MIMO XC with delayed CSIT, for the transmission schemes relying on IS-RT-PIN, a loss of decodability due to linear dependencies of linear combinations may occur. The transmission scheme existing in the literature uses in phase 1 a two-part IS-RT, where to avoid loss of decodability, the number of used transmit antennas is limited for suffciently large M N . In such case, the additional transmit antennas are not exploited. Our proposed transmission scheme, instead, uses in phase 1 a novel three-part IS-RT, in which the IS and RT parts of different transmitters have different durations. Such transmission allows to reduce the number of linearly dependent linear combinations, while the number of used transmit parameters of the proposed transmission scheme are carefully selected to maximize the number of the transmitted information symbols while ensuring linear independence. A number of DoF greater than that in the literature is achieved. In addition to the two proposed transmission schemes, an upper bound on the linear DoF is proposed, which turns out to be tight for 1 2 < M N _ 3 5 and 2 _ M N < 3.

Thirdly, the 2-antenna 3-user multiple-input single-output (MISO) broadcast channel (BC) with alternating CSIT is considered, in which the CSIT for each user can be either perfect (P) or delayed (D), resulting thus in total in 8 possible CSIT states I1I2I3, Ii 2 fP;Dg, i 2 f1; 2; 3g. For this scenario, we obtain two new results on the DoF characterization. The first result characterizes the DoF region for the case where the CSIT states can take the following 5 values: PPP, PPD, PDP, PDD and DDD. The second result characterizes the DoF for the case where the CSIT states can take all possible values, however the joint CSIT state probabilities are restricted to fulfil certain relationships. To achieve the optimal DoF, joint encoding over the available CSIT states is proposed, which provides DoF gains as compared to encoding over each CSIT state independently. To obtain our results, we first propose four novel constituent encoding schemes (CSs), which perform joint encoding of the CSIT state tuples (PPP; PDD), (PDD; DDD), (PDD;DPD; DDD) and (PDD;DPD; DDP). Then, after a careful assignment of the newly proposed and existing in the literature CSs to the available CSIT states, the optimal DoF are achieved.