  Physical layer network coding (PNC) has been studied to serve wireless
network MIMO systems with much lower backhaul load than approaches such as
Cloud Radio Access Network (Cloud-RAN) and coordinated multipoint (CoMP). In
this paper, we present a design guideline of engineering applicable PNC to
fulfil the request of high user densities in 5G wireless RAN infrastructure.
Unlike compute-and-forward and PNC design criteria for two-way relay channels,
the proposed guideline is designed for uplink of network MIMO (N-MIMO) systems.
We show that the proposed design criteria guarantee that 1) the whole system
operates over binary system; 2) the PNC functions utilised at each access point
overcome all singular fade states; 3) the destination can unambiguously recover
all source messages while the overall backhaul load remains at the lowest
level. We then develop a two-stage search algorithm to identify the optimum PNC
mapping functions which greatly reduces the real-time computational complexity.
The impact of estimated channel information and reduced number of singular fade
states in different QAM modulation schemes is studied in this paper. In
addition, a sub-optimal search method based on lookup table mechanism to
achieve further reduced computational complexity with limited performance loss
is presented. Numerical results show that the proposed schemes achieve low
outage probability with reduced backhaul load.
