Interference alignment with physical-layer network coding in MIMO relay channels

This paper proposes the ideas of interference alignment with physical-layer network coding (IAPNC). While conventional interference alignment (IA) aligns interfering signals and then treats them as noise, IAPNC treats the aligned signals as combined signals and utilizes them to convey data streams to receivers. We show the ideas of IAPNC in multi-hop multiple-input multiple-output (MIMO) channels consisting of 3 transmitter-receiver pairs and 2 half-duplex decode-and-forward (DF) relays in each intermediate layer, i.e., 3-2 ... 2-3 MIMO channels. We consider three users want to convey independent data streams to distinct destinations with the aid of relays. Simulation results show that IAPNC scheme in the 3-2-3 MIMO channel achieves the same degrees of freedom (DoF) as conventional IA scheme in the 3-3-3 MIMO channel which has one more relay. The results also show that the end-to-end sum-rate of IAPNC scheme outperforms that of zero-forcing (ZF) filtering scheme in medium-to-high signal-to-noise ratio (SNR) regime for the 3-2-3 MIMO channel. The performance improvement of IAPNC scheme mainly comes from efficient utilization of signals in interfering signal subspaces.