The degrees of freedom of the MIMO Y-channel

Abstract

The degrees of freedom (DoF) of the MIMO Ychannel, a multi-way communication network consisting of 3 users and a relay, are characterized for arbitrary number of antennas. The converse is provided by cut-set bounds and novel genie-aided bounds. The achievability is shown by a scheme that uses beamforming to establish network coding on-the-fly at the relay in the uplink, and zero-forcing pre-coding in the downlink. It is shown that the network has min{2M2+2M3, M1+ M 2 + M3, 2N } DoF, where Mj and N represent the number of antennas at user j and the relay, respectively. Thus, in the extreme case where M1 +M2 +M3 dominates the DoF expression and is smaller than N , the network has the same DoF as the MAC between the 3 users and the relay. In this case, a decode and forward strategy is optimal. In the other extreme where 2N dominates, the DoF of the network is twice that of the aforementioned MAC, and hence network coding is necessary. As a byproduct of this work, it is shown that channel output feedback from the relay to the users has no impact on the DoF of this channel.

Optimal DoF Region for the Asymmetric Two-Pair MIMO Two-Way Relay Channel

“…We now prove the bound (8e) by using the genie-aided message approach as in [11], [24], [26], [27]. By the converse assumption, each user i can decode its intended message {Wī ,i } with its own transmitted messages {W i,ī } as side information.…”

“…This is realized through the joint design of relay compression matrix and source precoding matrices. In [24], the optimal sum DoF of the MIMO Y channel with asymmetric antenna setting is characterized by using signal alignment and antenna deactivation techniques. It is pointed out that symmetric data exchange, where the two users in each pair communicate the same number of data streams, can achieve the optimal sum DoF.…”

“…But the analysis is limited to symmetric data exchange. In contrast with the scheme in [24] and [29], we need not only to construct network-coded symbols but also to process the additional asymmetric data streams at the relay, which enables us to obtain the DoF region rather than just the sum DoF. In [31], the optimal DoF region of the K-user MIMO Y channel with symmetric antenna setting is studied by using channel diagonalization and cyclic communication techniques.…”

Optimal Degrees of Freedom Region for the Asymmetric MIMO Y Channel

“…Note that PDE pattern have been introduced in [1], [2] and CDE pattern have been introduced in [12], [13].…”

Efficient message exchange protocols exploiting state-of-the-art PHY layer

“…Secondly, the paper considers the extension to three terminals, which is sometimes named in the literature as the Y-channel [9,10], and in this paper will be referred to as the Y-network. It comprises three terminals communicating with each other with the help of a relay and can be regarded as a generalized network model of the TWRC for three different users, when the terminals cannot physically establish direct connections among them and where each terminal has some information that wants to transmit to the other two.…”