On the Degrees of Freedom of the Symmetric Multi-Relay MIMO Y Channel

Abstract

In this paper, we study the degrees of freedom (DoF) of the symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three user nodes, each with M antennas, communicate via K geographically separated relay nodes, each with N antennas. For this model, we establish a general DoF achievability framework based on linear precoding and post-processing methods. The framework poses a nonlinear problem with respect to user precoders, user post-processors and relay precoders. To solve this problem, we adopt an uplink-downlink asymmetric strategy, where the user precoders are designed for signal alignment and the user post-processors are used for interference neutralization. With the user precoder and post-processor designs fixed as such, the original problem then reduces to a problem of relay precoder design. To address the solvability of the system, we propose a general method for solving matrix equations. Together with the techniques of antenna disablement and symbol extension, an achievable DoF of the considered model is derived for an arbitrary setup of (K, M, N ). We show that for K ≥ 2, the optimal DoF is achieved for, ∞ . We also show that the uplink-downlink asymmetric design proposed in this paper considerably outperforms the conventional approach based on uplink-downlink symmetry.

An Overview on Multiway Relay Communications: Fundamental Issues, Recent Advances, and New Challenges

“…By utilizing the above two techniques, the authors demonstrated that the optimal DoF of 3M is achieved when N ≥ ⌈ 3M 2 ⌉. In [76], the authors also investigated the DoF of the threeuser MIMO Y channel. Different from [7], [75], the authors considered using K geographically separated relay nodes to help signal forwarding.…”

Data Exchange of Relay Transmission and Information Scheduling in Shared Networks

“…Define In view of the complex information exchange scenarios in various wireless communication systems [19], we propose to use message flow graphs to characterize the information exchange among different DoF of users in MIMO multiway relay channels. Each node in the message flow graph represents a user, and each directed edge indicates that the tail node sends a message to the head node.…”

MIMO Multiway Distributed-Relay Channel with Full Data Exchange: An Achievable Rate Perspective

“…In particular, the authors in [15] and [16] considered pairwise data exchange in which users exchange messages in a pairwise manner; the works in [17] and [18] assumed a full data exchange model in which each user wants to learn the messages from all the other users. Other variants, such as X channels and Y channels, have also been studied in [19]- [21]. In these works, advanced signal alignment techniques were developed to jointly design the user precoders and the relay precoder for efficient PNC implementation.…”