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Abstract-In this paper, we study the degrees of freedom (DoF) of the MIMO relay networks. We start with a general Y channel, where each user has Mi antennas and aims to exchange messages with the other two users via a relay equipped with N antennas. Then, we extend our work to a general 4-user MIMO relay network. Unlike most previous work which focused on the total DoF of the network, our aim here is to characterize the achievable DoF region as well. We develop an outer bound on the DoF region based on the notion of one sided genie. Then, we define a new achievable region using the Signal Space Alignment (SSA) and the Detour Schemes. Our achievable scheme achieves the upper bound for certain conditions relating Mi's and N .

Abstract-This paper considers an interference network composed of K half-duplex single-antenna pairs of users who wish to establish bi-directional communication with the aid of a multiinput-multi-output (MIMO) half-duplex relay node. This channel is referred to as the "MIMO Wireless Switch" since, for the sake of simplicity, our model assumes no direct link between the two end nodes of each pair implying that all communication must go through the relay node (i.e., the MIMO switch). Assuming a delay-limited scenario, the fundamental limits in the high signal-to-noise ratio (SNR) regime is analyzed using the diversitymultiplexing tradeoff (DMT) framework. Our results sheds light on the structure of optimal transmission schemes and the gain offered by the relay node in two distinct cases, namely reciprocal and non-reciprocal channels (between the relay and end-users). In particular, the existence of a relay node, equipped with a sufficient number of antennas, is shown to increase the multiplexing gain; as compared with the traditional fully connected K-pair interference channel. To the best of our knowledge, this is the first known example where adding a relay node results in enlarging the pre-log factor of the sum rate. Moreover, for the case of reciprocal channels, it is shown that, when the relay has a number of antennas at least equal to the sum of antennas of all the users, static time allocation of decode and forward (DF) type schemes is optimal. On the other hand, in the non-reciprocal scenario, we establish the optimality of dynamic decode and forward in certain relevant scenarios.

In this paper, we completely characterize the deterministic capacity region of a four-node relay network with no direct links between the nodes, where each node communicates with the three other nodes via a relay. Towards this end, we develop an upper bound on the deterministic capacity region, based on the notion of a one-sided genie. To establish achievability, we use the detour schemes that achieve the upper bound by routing specific bits via indirect paths instead of sending them directly.

We study the capacity region of a deterministic 4node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.