Interference is considered to be a major obstacle to wireless communication. Popular approaches, such as the zero-forcing receiver in MIMO (multiple-input and multiple-output) multiple-access channel (MAC) and zero-forcing (ZF) beamforming in MIMO broadcast channel (BC), eliminate the interference first and decode each codeword separately using a conventional single-user decoder. Recently, a transceiver architecture called integer-forcing (IF) has been proposed in the context of the MIMO Gaussian multiple-access channel to exploit integer-linear combinations of the codewords. Instead of treating other codewords as interference, the integer-forcing approach decodes linear combinations of the codewords from different users and solves for desired codewords. Integer-forcing can closely approach the performance of the optimal joint maximum likelihood decoder. An advanced version called successive integer-forcing can achieve the sum capacity of the MIMO MAC channel. Several extensions of integer-forcing have been developed in various scenarios, such as integer-forcing for the Gaussian MIMO broadcast channel, integer-forcing for Gaussian distributed source coding and integer-forcing interference alignment for the Gaussian interference channel. This dissertation demonstrates duality relationships for integer-forcing among three different channel models. We explore in detail two distinct duality types in this thesis: uplink-downlink duality and source-channel duality. Uplink-downlink duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian MIMO broadcast channel. We show that under a total power constraint, integer-forcing can achieve the same sum rate in both cases. We further develop a dirty-paper integer-forcing scheme for the Gaussian MIMO BC and show an uplink-downlink duality with successive integer-forcing for the Gaussian MIMO MAC. The source-channel duality is established for integer-forcing between the Gaussian MIMO multiple-access channel and its dual Gaussian distributed source coding problem. We extend previous results for integer-forcing source coding to allow for successive cancellation. For integer-forcing without successive cancellation in both channel coding and source coding, we show the rates in two scenarios lie within a constant gap of one another. We further show that there exists a successive cancellation scheme such that both integer-forcing channel coding and integer-forcing source coding achieve the same rate tuple.

Next-generation wireless communication systems will need to contend with many active mobile devices, each of which will require a very high data rate. To cope with this growing demand, network deployments are becoming denser, leading to higher interference between active users. Conventional architectures aim to mitigate this interference through careful design of signaling and scheduling protocols. Unfortunately, these methods become less effective as the device density increases. One promising option is to enable cellular basestations (i.e., cell towers) to jointly process their received signals for decoding users’ data packets as well as to jointly encode their data packets to the users. This joint processing architecture is often enabled by a cloud radio access network that links the basestations to a central processing unit via dedicated connections. One of the main contributions of this thesis is a novel end-to-end communications architecture for cloud radio access networks as well as a detailed comparison to prior approaches, both via theoretical bounds and numerical simulations. Recent work has that the following high-level approach has numerous advantages: each basestation quantizes its observed signal and sends it to the central processing unit for decoding, which in turn generates signals for the basestations to transmit, and sends them quantized versions. This thesis follows an integer-forcing approach that uses the fact that, if codewords are drawn from a linear codebook, then their integer-linear combinations are themselves codewords. Overall, this architecture requires integer-forcing channel coding from the users to the central processing unit and back, which handles interference between the users’ codewords, as well as integer-forcing source coding from the basestations to the central processing unit and back, which handles correlations between the basestations’ analog signals. Prior work on integer-forcing has proposed and analyzed channel coding strategies as well as a source coding strategy for the basestations to the central processing unit, and this thesis proposes a source coding strategy for the other direction. Iterative algorithms are developed to optimize the parameters of the proposed architecture, which involve real-valued beamforming and equalization matrices and integer-valued coefficient matrices in a quadratic objective. Beyond the cloud radio setting, it is argued that the integer-forcing approach is a promising framework for interference alignment between multiple transmitter-receiver pairs. In this scenario, the goal is to align the interfering data streams so that, from the perspective of each receiver, there seems to be only a signal receiver. Integer-forcing interference alignment accomplishes this objective by having each receiver recover two linear combinations that can then be solved for the desired signal and the sum of the interference. Finally, this thesis investigates the impact of channel coherence on the integer-forcing strategy via numerical simulations.