| Summary: | Channel state information at the transmitters (CSIT) is crucial to the downlink multi-user transmissions. However, acquiring accurate and instantaneous CSIT is challenging in practical systems, due to the channel estimation error, channel quantization error, and the latency incurred in the feedback link and backhaul link. Performing techniques designed for perfect CSIT using imperfect CSIT or delayed CSIT leads to a dramatically degraded performance due to the undesirable multi-user interference. Interestingly, recent information theoretic and communication works have departed from this path by employing novel multi-user transmission strategies, Rate-Splitting (RS) and Retrospective Interference Alignment (RIA), to deal with the imperfect CSIT and the delayed CSIT, respectively. Reminiscent to the pioneering work of Han-Kobayashi scheme, RS is employed to deal with the multi-user interference caused by imperfect CSIT by splitting each user's message into a common part and a private part. Each user not only decodes its desired private message, but also decodes the common messages of both users. In this thesis, we study a set of fundamental problems that are essential to RS, with particular interests in transmission block design for various scenarios and the achievable sum rate performance with the presence of quantized CSIT. Our main results are summarized as follows. Firstly, we characterize the achievable DoF region by RS in the $K$-user MISO broadcast channel (BC) and show that the maximal sum DoF is achievable with an even power allocation for the private messages. In the MISO BC with time-varying CSIT qualities, we propose a Space-Time RS (RS-ST) by multicasting common messages via a space-time design. This strategy exploits the time-varying CSIT qualities and yields a greater sum DoF than that achieved by performing RS in each individual time slot. Moreover, focusing on a two-user scenario, we study the sum rate performance of RS and RS-ST schemes with the presence of quantized CSIT, by upper-bounding their sum rate loss relative to ZFBF with perfect CSIT. Using these upper-bounds, we show that, to maintain a constant sum rate loss, RS scheme enables a feedback overhead reduction over conventional ZFBF with quantized CSIT, and RS-ST offers a further overhead reduction over RS in the scenario with alternating feedback qualities. Besides, simulation results show that both RS and RS-ST schemes offer a significant SNR gain over conventional single-user/multiuser mode switching when the number of quantization (feedback) bits is fixed. Secondly, in the MISO interference channel (IC), we investigate the achievable DoF region by RS. More importantly, we propose a novel scheme, so called Topological RS (TRS), where each user's message is split into a private part and multiple common parts. With a ZF-precoder and a properly assigned power according to the CSIT qualities of the interference links, each common message is to be decoded by a group of users rather than all users. This feature reduces the number of common messages decoded by each user, and thus yielding a greater DoF region than RS. The maximal sum DoF achieved by TRS is derived using graph theory methodology, fractional packing of a hypergraph. We show that TRS is applicable to the homogeneous cellular deployment where each user is only connected with three dominant transmitters, and derive the sufficient condition that TRS strictly outperforms conventional ZFBF. Thirdly, in the two-user MIMO BC with asymmetric antenna configuration (and with CSIT quality not varying over time), we show that the RS transmission block should be designed to fully exploit the spatial dimension at the user with a larger number of antennas. We also find that the sum DoF is maximized with a Space-Time transmission and unequal power allocation for the private messages. In the two-user MIMO IC, we design the RS transmission block motivated by a row transformation to the channel matrices. Such an operation allows us to identify the signal space where the transmitted signals interfere with each other, so as to derive a proper power allocation policy. The achievable DoF regions are shown to be optimal for some antenna configurations. The philosophy of RIA is to employ the delayed CSIT to obtain information about the multi-user interference generated in the previous slots, and thereby create future transmissions to perform interference management. In this thesis, focusing a $K$-user MIMO IC where the number of antennas at each transmitter is greater than the number of antennas at each user, we propose two RIA schemes based on distributed overheard interference retransmission using the perfect delayed CSIT. The first scheme generalizes the scheme designed for the MISO BC by exploiting the multiple antennas at the user side. The second scheme generalizes the redundancy transmission and partial interference nulling designed for the SISO IC, by exploiting the multiple antennas at the transmitter side. With an optimal transmitter-user scheduling, these two schemes jointly yield the best known sum DoF performance so far. In the $K$-user MISO IC, the achieved sum DoF is asymptotically given by $\frac{64}?$ when $K{\to}\infty$.
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