IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION 1 Signal Alignment: Enabling Physical Layer Network Coding for MIMO Networking

Abstract—We apply signal alignment (SA), a wireless commu-nication technique that enables physical layer network coding (PNC) in multi-input multi-output (MIMO) wireless networks. Through calculated precoding, SA contracts the perceived signal space at a node to match its receive capability, and hence facilitates the demodulation of linearly combined data packets. PNC coupled with SA (PNC-SA) has the potential of fully exploiting the precoding space at the senders, and can better utilize the spatial diversity of a MIMO network for higher system degrees-of-freedom (DoF). PNC-SA adopts the idea of ‘demodulating a linear combination ’ from PNC. The design of PNC-SA is also inspired by recent advances in IA, though SA aligns signals not interferences. We study the optimal precoding and power allocation problem of PNC-SA, for SNR (singal-to-noise-ratio) maximization at the receiver. The mapping from SNR to BER is then analyzed, revealing that the DoF gain of PNC-SA does not come with a sacrifice in BER. We then design a general PNC-SA algorithm in larger systems, and demonstrate general applications of PNC-SA, and show via network level simulations that it can substantially increase the throughput of unicast and multicast sessions, by opening previously unexplored solution spaces in multi-hop MIMO routing. Index Terms—Network coding; physical layer letwork coding; interference alignment; signal alignment; MIMO networks. I