Asymptotic Interference Alignment Research Articles

DoF achieving asymptotic interference alignment for two interfering 2 × 2 X channels

DoF achieving asymptotic interference alignment for two interfering 2 × 2 X channels

Degrees of Freedom of MIMO Cellular Networks: Decomposition and Linear Beamforming Design

This paper investigates the symmetric degrees of freedom (DoF) of multiple-input multiple-output (MIMO) cellular networks with $G$ cells and $K$ users per cell, having $N$ antennas at each base station and $M$ antennas at each user. In particular, we investigate techniques for achievability that are based on either decomposition with asymptotic interference alignment or linear beamforming schemes and show that there are distinct regimes of $(G,K,M,N)$ , where one outperforms the other. We first note that both one-sided and two-sided decomposition with asymptotic interference alignment achieve the same DoF. We then establish specific antenna configurations under which the DoF achieved using decomposition-based schemes is optimal by deriving a set of outer bounds on the symmetric DoF. Using these results, we completely characterize the optimal DoF of any $G$ -cell network with single-antenna users. For linear beamforming schemes, we first focus on small networks and propose a structured approach to linear beamforming based on a notion called packing ratios. Packing ratio describes the interference footprint or shadow cast by a set of transmit beamformers and enables us to identify the underlying structures for aligning interference. Such a structured beamforming design can be shown to achieve the optimal spatially normalized DoF (sDoF) of two-cell two-user/cell network and the two-cell three-user/cell network. For larger networks, we develop an unstructured approach to linear interference alignment, where transmit beamformers are designed to satisfy conditions for interference alignment without explicitly identifying the underlying structures for interference alignment. The main numerical insight of this paper is that such an approach appears to be capable of achieving the optimal sDoF for MIMO cellular networks in regimes where linear beamforming dominates asymptotic decomposition, and a significant portion of sDoF elsewhere. Remarkably, polynomial identity test appears to play a key role in identifying the boundary of the achievable sDoF region in the former case.

A Signal Subspace Interference Alignment Scheme with Sum Rate Maximization and Altruistic-Egoistic Bayesian Gaming

In this paper, we propose a distributed signal subspace interference alignment algorithm for single beam K?user (3K≥) MIMO interference channel based on sum rate maximization and game theory. A framework of game theory is provided to study relationship between interference signal subspace and altruistic-egoistic bayesian game cost function. We demonstrate that the asymptotic interference alignment under proposed scheme can be realized through a numerical algorithm using local channel state information at transmitters and receivers. Simulation results show that the proposed scheme can achieve the total degrees of freedom that is equivalent to the Cadambe-Jafar interference alignment algorithms with perfect channel state information. Furthermore, proposed scheme can effectively minimize leakage interference in desired signal subspace at each receiver and obtain a moderate average sum rate performance compared with several existing interference alignment schemes.

Asymptotic Interference Alignment for Optimal Repair of MDS Codes in Distributed Storage

The high repair bandwidth cost of (n,k) maximum distance separable (MDS) erasure codes has motivated a new class of codes that can reduce repair bandwidth over that of conventional MDS codes. In this paper, we address (n,k,d) exact repair MDS codes, which allow for any single failed node to be repaired exactly with access to any arbitrary set of d survivor nodes. We show the existence of exact repair MDS codes that achieve minimum repair bandwidth (matching the cut-set lower bound) for arbitrary admissible (n,k,d), i.e., k ≤ d ≤ n-1. Moreover, we extend our results to show the optimality of our codes for multiple-node failure scenarios in which an arbitrary set of r ≤ n-k failed nodes needs to repaired. Our approach is based on asymptotic interference alignment proposed by Cadambe and Jafar. As a byproduct, we also characterize the capacity of a class of multisource nonmulticast networks.

Degrees of Freedom of the Interference Channel with a Cognitive Helper

In this letter, we characterize the degrees of freedom (DoF) of the K≥ 3 user Gaussian interference network with a cognitive helper where each node is equipped with a single antenna. Specifically, the users send independent messages to their corresponding receiver through their own antenna and via the help of the cognitive helper. For this network, we show that the sum DoF value is upper bounded by (K+1)/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> when K is odd and K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2(K+1)</sub> when K is even, respectively. While the new DoF upper bounds are simply derived based on the fact that cooperation among users does not decrease the capacity region, we provide a new achievable scheme to obtain a total of (K+1)/ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> DoF for any K≥ 3. Thus, we establish that the exact sum DoF value of the network is given as <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(K+1)</sup> /2, whenever K is odd. The new achievable scheme is based on interference neutralization and asymptotic interference alignment.