For point-to-point communications, channel capacity is very well understood, and there are schemes that approach the capacity for most useful channel models. In contrast, the multi-user communication channels are not as well understood. The channel models are more complicated, there are more varieties, and many important problems remain open. As one well-known example, the capacity problem for discrete memoryless broadcast channel is still unsettled. As another example, the interference channel capacity region is known only in certain special cases (such as strong interference). What is clear from the recent studies of such channels is that in a multi-user wireless network, the key performance limiting factor is often the interference rather than the noise, especially at high signal-to-noise ratio.
To alleviate this difficulty, the notion of degrees of freedom has been used as a first order characterization of the system throughput as normalized by the logarithm of the signal to noise ratio. The total degrees of freedom of several interference networks have been quantified. On the other hand, the degrees of freedom region, which is more revealing than the total degrees of freedom, is much less well understood. For most of the interference networks, the regions remain unknown.
This project seeks to quantify the degree of freedom regions of a class of general interference networks with multiple transmit nodes and multiple receive nodes, possibly equipped with multiple antennas, and with general message demands. In particular, we will study the X interference network, which include interference channels, broadcast channels, multiple access channels, as special cases. Through interference alignment design based on vector and rational independence, we will bound tightly the degrees of freedom region and devise schemes that are optimal (or near-optimal) in the degree-of-freedom sense.
Broader Impact: The project will advance significantly our understanding of interference networks, and positively impact the design, architecture, and signal design and processing for next generation wireless networks. The project will also help train the next generation of researchers and engineers in the field of signal processing and communication networks.
The project is for studying fundamental limits of wireless networks. Typically, interference, rather than noise, is the main performance limiting factor for such networks. Although it is desirable to characterize the so-called capacity region of such interference networks, the problem is extremely difficult. As a first step, the degree of freedom (DoF) region is desired, which is a description of the shape of the capacity region of the network when the so called signal-to-noise ratio is large. The DoF regions of several networks with single or multiple antennas have been investigated in this project. The exact DoF regions for a number of wireless network configurations were obtained. For some other wireless networks, inner and outer bounds of such DoF regions were obtained. Novel signaling schemes that can be used to achieve higher rates than previously known were designed, based on concepts such as interference alignment and mathematical tools such as Diophantine approximation. Intellectual Merit: The research carried out in this project advanced the state-of-the-art of the study of fundamental limits of wireless networks. Previously, the studies focused mainly on the total DoF of interference networks, whereas in this project the objective and the obtained results concern DoF regions, which are more complete characterization than the total DoF. Broader Impact: Wireless networking is an integral part of the information infrastructure. Characterizing the fundamental limits and designing optimized signaling schemes, as were partially accomplished in this project, are important theoretical ventures that will have a great impact on the design of future wireless networks and the way we access and exchange information in future society.