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This paper studies and analyzes a multi-pair MIMO two-way relay (TWR) system from a principal-angle perspective. In this system, users are grouped into pairs and two users in each pair exchange information through a common relay. The transmission scheme consists of two phases. In the uplink phase, the relay’s receive signal space is divided into two subspaces for each pair: in one subspace, the signals of the two users are near-parallel, and physical-layer network coding (PNC) decoding is applied to retrieve network-coded messages; in the other subspace, the two user signals are near-orthogonal, and complete decoding (CD) is applied to retrieve individual user messages. In the downlink phase, the relay’s transmit signal space is split into orthogonal subspaces for each pair, and in each subspace a common message is broadcasted to the two users. Our main contribution is to establish a critical link between the transmission scheme and the concept of principal angle in linear algebra. In particular, principal angle quantizes the degree of orthogonality between the user signals and helps determining how to partition the relay’s receive signal space into PNC decoding subspace and CD decoding subspace. Building on that, we discuss the optimal design of user/relay precoders for both uplink and downlink phases to maximize the asymptotic sum-rate of the proposed scheme at high signal-to-noise ratio (SNR). The analysis and numerical results indicate that our scheme performs close to the cut-set outer bound and significantly outperforms the existing schemes in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a generalized construction of distributed network codes for a network consisting of M users sending independent information to a common base station through independent block fading channels. The aim is to increase the diversity order of the system without reducing its throughput. The proposed scheme, called generalized dynamic-network codes (GDNC), is a generalization of the dynamic-network codes (DNC) recently proposed by Xiao and Skoglund. The design of the network codes that maximize the diversity order is recognized as equivalent to the design of linear block codes over a nonbinary finite field under the Hamming metric. We prove that adopting a systematic generator matrix of a maximum distance separable block code over a sufficiently large finite field as the network transfer matrix is a sufficient condition for full diversity order under link failure model. The proposed generalization offers a much better tradeoff between rate and diversity order compared to the DNC. An outage probability analysis showing the improved performance is carried out, and computer simulations results are shown to agree with the analytical results. [ABSTRACT FROM PUBLISHER]