Performance Analysis of Physical Layer Network Coding in Massive MIMO Systems with M-QAM Modulations

In this paper, we develop a practical approach for deploying Physical Layer Network Coding (PNC) in multi-user M-Ary Quadrature Amplitude Modulation (M-QAM) Massive Multiple-Input Multiple-Output (MIMO) systems. We formulate a PNC mapping scheme as a function of clusters of estimated summation and difference (SD) of the transmitted symbols from user pairs. Utilizing existing linear detection schemes, such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE), a cluster of SD symbols are detected using an SD linearly transformed channel matrix. Furthermore, utilizing Maximum a Posteriori (MAP) soft decoding, the SD symbols are mapped to the PNC symbols, leveraging on the PNC symbol that maximizes the likelihood function. For each variant of M-QAM, we derive and simplify a specialization of the generalized PNC mapping function. The error performance results, through simulation, reveal that the proposed PNC scheme achieves twice the spectral efficiency in Massive MIMO, without changing the latter's underlying framework and without any degradation in the bit-error-rate (BER). In fact, our investigation has proved that the BER of the proposed Massive MIMO and PNC is slightly better than that of the conventional Massive MIMO. The feasibility of deploying our proposed PNC scheme in Massive MIMO systems paves way for NC applications to be realized in cellular systems.