Generalized Signal-Space Alignment Based Physical-Layer Network Coding for Distributed MIMO Systems

We study an uplink distributed multiple-input-multiple-output (D-MIMO) system, where multiple users are served by multiple base stations (BSs) connected to a common central unit (CU). We propose a generalized signal-space alignment (SSA)-based physical-layer network coding (PNC) scheme, termed G-SSA-PNC. In G-SSA-PNC, the multi-antenna users encode their messages by using nested lattice coding, linearly precode the nested lattice codewords for SSA, and then broadcast to the multi-antenna BSs. The BSs linearly post-process the received signals to extract signals at certain aligned directions. PNC decoding is applied to those extracted signals to generate network-coded message combinations, and the decoded message combinations are then forwarded to the CU for user messages decoding. Compared with the original SSA-PNC scheme, our scheme is different in the following three aspects. First, the G-SSA-PNC employs an individual shaping lattice for nested lattice coding at each source, as in contrast to the use of a common shaping lattice in original SSA-PNC. Second, we derive the feasibility condition of PNC decoding under the new nested lattice coding scheme and show that the SSA precoding and the nested lattice coding needs to be jointly designed to meet the feasibility condition. Third, we formulate a sum rate maximization problem and propose a suboptimal solution to the problem. The numerical results demonstrate the superiority of the G-SSA-PNC in performance over the benchmark schemes, including original SSA-PNC, compress-and-forward, and interference alignment.