Generalized signal alignment for arbitrary MIMO two-way relay channels

Abstract

Abstract-In this paper, we consider the arbitrary MIMO two-way relay channels, where there are K source nodes, each equipped with Mi antennas, for i = 1, 2, · · · , K, and one relay node, equipped with N antennas. Each source node can exchange independent messages with arbitrary other source nodes assisted by the relay. We extend our newly-proposed transmission scheme, generalized signal alignment (GSA) in [1], to arbitrary MIMO two-way relay channels when N > Mi + Mj, ∀i = j. The key idea of GSA is to cancel the interference for each data pair in its specific subspace by two steps. This is realized by jointly designing the precoding matrices at all source nodes and the processing matrix at the relay node. Moreover, the aligned subspaces are orthogonal to each other. By applying the GSA, we show that a necessary condition on the antenna configuration to achieve the DoF upper bound min{Mi − Ms − Mt + ds,t | ∀s, t}. Here, ds,t denotes the DoF of the message exchanged between source node s and t. In the special case when the arbitrary MIMO two-way relay channel reduces to the K-user MIMO Y channel, we show that our achievable region of DoF upper bound is larger than the previous work.

Generalized Signal Alignment: On the Achievable DoF for Multi-User MIMO Two-Way Relay Channels

“…In this case, we use the idea of the symbol extension [35] together with GSA to prove the achievability of the DoF upper bound K M. We consider the (K − 1)-symbol extension of the channel model, where the channel coefficients do not necessarily vary over time. The received signal at the relay can be written as (2) . .…”

“…By allowing arbitrary information exchange pattern, our considered multi-user MIMO two-way relay channel is a unified channel model. 2 It includes several existing channel models as special cases, namely, K -user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized MIMO two-way X relay channel and L-cluster K = K L -user MIMO multiway channel.…”

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

“…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. In [29], the sum DoF of an arbitrary MU-MIMO TWRC is analyzed under an asymmetric antenna setting. But the analysis is limited to symmetric data exchange.…”

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

“…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. In [29], the sum DoF of an arbitrary MU-MIMO TWRC is analyzed under an 4 asymmetric antenna setting. But the analysis is limited to symmetric data exchange.…”