The two-phase MIMO NC (network coding) scheme can be used to boost the throughput in a two-way relay channel in which nodes are equipped with multiple antennas. The obvious strategy is for the relay node to extract the individual packets from the two end nodes and mix the two packets to form a network-coded packet. In this paper, we propose a new scheme called MIMO PNC (physical network coding), in which the relay extracts the summation and difference of the two end packets and then converts them to the network-coded form. MIMO PNC is a natural combination of the single-antenna PNC scheme and the linear MIMO detection scheme. The advantages of MIMO PNC are many. First, it removes the stringent carrier-phase requirement in single-antenna PNC. Second, it is linear in complexity with respect to the constellation size and the number of simultaneous data streams in MIMO. Simulation shows that MIMO PNC outperforms the straightforward MIMO NC significantly under random Rayleigh fading channel. Based on our analysis, we further conjecture that MIMO PNC outperforms MIMO NC under all possible realizations of the channel.
I. INTRODUCIONIn wireless networks, the use of relay has many advantages. It can lead to better coverage and connectivity. With a smaller distance for node-to-node transmissions, the power consumption can be reduced. At the same time, the detrimental effects of the interferences from other transmissions can be alleviated, leading to higher capacity per unit area.Consider the simple two-way relay channel (TWRC) shown in Fig. 1. In [1], the authors introduced network coding into TWRC: the two end nodes transmit their packets to the relay in two different time slots; the relay then forms a network-coded packet out of the two packets and broadcast it to the end nodes. The number of time slots needed to exchange one packet is 3. Subsequent to [1], we proposed physical layer network coding (PNC) [2]. PNC allows the two end nodes to transmit their packets in the same time slot. The superimposed packets received simultaneously are then directly transformed to a network-coded packet at the physical layer of the relay. As a result, the number of time slots needed to exchange one packet is reduced to 2.PNC is attracting increasing attention. At the communication level, variants of PNC have been proposed [3,4,5] to improve performance or to ease implementation. At the network level, PNC has also been shown to be able to increase network capacity by a fixed factor [6,7]. In addition, information-theoretic studies indicate that PNC can allow the capacity of TWRC to be approached in both low SNR and high SNR regions [8,9,10].