Real Interference Alignment: Exploiting the Potential of Single Antenna Systems

In this paper, the available spatial Degrees-Of-Freedoms (DOF) in single antenna systems is exploited. A new coding scheme is proposed in which several data streams having fractional multiplexing gains are sent by transmitters and interfering streams are aligned at receivers. Viewed as a field over rational numbers, a received signal has infinite fractional DOFs, allowing simultaneous interference alignment of any finite number of signals at any finite number of receivers. The coding scheme is backed up by a recent result in the field of Diophantine approximation, which states that the convergence part of the Khintchine-Groshev theorem holds for points on non-degenerate manifolds. The proposed coding scheme is proved to be optimal for three communication channels, namely the Gaussian Interference Channel (GIC), the uplink channel in cellular systems, and the $X$ channel. It is proved that the total DOF of the $K$-user GIC is $\frac{K}{2}$ almost surely, i.e. each user enjoys half of its maximum DOF. Having $K$ cells and $M$ users within each cell in a cellular system, the total DOF of the uplink channel is proved to be $\frac{KM}{M+1}$. Finally, the total DOF of the $X$ channel with $K$ transmitters and $M$ receivers is shown to be $\frac{KM}{K+M-1}$.Comment: Submitted to IEEE Transaction on Information Theory. The first version was uploaded on arxiv on 17 Aug 2009 with the following title: Forming Pseudo-MIMO by Embedding Infinite Rational Dimensions Along a Single Real Line: Removing Barriers in Achieving the DOFs of Single Antenna System

Interference Management in a Class of Multi User Networks

Spectrum sharing is known as a key solution to accommodate the increasing number of users and the growing demand for throughput in wireless networks. Interference is the primary barrier to enhancing the overall throughput of the network, especially in the medium and high signal to noise ratios (SNRs). Managing interference to overcome this barrier has emerged as a crucial step in developing efficient wireless networks. An interference management strategy, named interference Alignment, is investigated. It is observed that a single strategy is not able to achieve the maximum throughput in all possible scenarios, and in fact, a careful design is required to fully exploit all available resources in each realization of the system. In this dissertation, the impact of interference on the capacity of X networks with multiple antennas is investigated. Degrees of freedom (DoF) are used as a figure of merit to evaluate the performance improvement due to the interference management schemes. A new interference alignment technique called layered interference alignment, which enjoys the combined benefits of both vector and real alignment is introduced in this thesis. This technique, which uses a type of Diophantine approximation theorems first introduced by the author, is deployed and was proved to enable the possibility of joint decoding among the antennas of a receiver. With a careful transmitter signal design, this method characterizes the total DoF of multiple-input multiple-output (MIMO) X channels. Then, this result is used to determine the total DoF of two families of MIMO X channels. The Diophantine approximation theorem is also extended to the field of complex numbers to accommodate the complex channel realizations as well.4 month

Multiple-Antenna Interference Channel with Receive Antenna Joint Processing and Real Interference Alignment

We consider a constant $K$-user Gaussian interference channel with $M$ antennas at each transmitter and $N$ antennas at each receiver, denoted as a $(K,M,N)$ channel. Relying on a result on simultaneous Diophantine approximation, a real interference alignment scheme with joint receive antenna processing is developed. The scheme is used to provide new proofs for two previously known results, namely 1) the total degrees of freedom (DoF) of a $(K, N, N)$ channel is $NK/2$; and 2) the total DoF of a $(K, M, N)$ channel is at least $KMN/(M+N)$. We also derive the DoF region of the $(K,N,N)$ channel, and an inner bound on the DoF region of the $(K,M,N)$ channel