On achievable rate region for decode-and-forward multi-way relay network

This paper investigates the general achievable rate region (ARR) for a wireless multi-way relay (MWR) network with full message exchange and decode-and-forward (DF) cooperative strategy. The MWR network consists of K users, each equipped with M antennas, and a single relay equipped with N antennas; and there is no user-user direct connectivity. Since different schedules would result in different ARRs, the general ARR must subsume all possible schedules; and this result is not previously known. We first present a cut set outer bound, and then derive and analyze the general ARR for DF by considering all meaningful schedules. We show that the general ARR is a convex hull expanded from a set of ARRs corresponding to special schedules. We further show that the ARR of a specific schedule can be expanded by its extreme points via the Krein-Milman theorem. In this, we have shown that the general ARR (of a MWR network using DF) is obtained by identifying and expanding these extreme points. We demonstrate the numerical results via exemplary cases.