A two-way full-duplex multiple-input multiple-output (MIMO) relay provides effective spectral efficiency and system capacity improvement. However, self-interference (SI) as a serious problem limits the development of a full-duplex relay. In this paper, the novel SI suppression schemes based on the Dempster-Shafer (DS) evidence theory are proposed to suppress SI in the two-way full-duplex MIMO relay. DS evidence theory can appropriately characterize uncertainty and make full use of multiple evidence source information by DS combination rule to obtain reliable decisions. The first proposed DS network coding (DS-NC) scheme adopts DS evidence theory to detect the signal of each source node, considering SI suppression in the basic probability assignment computation in the multiple access phase. Moreover, different from the DS-NC scheme, the further proposed DS physical-layer network coding (DS-PNC) scheme considers SI suppression from the vector space perspective and combines the PNC mapping rule with the DS theory to obtain a network-coded signal without estimating each source node signal. In the broadcast phase, antenna selection is adopted at the relay and DS evidence theory is also applied at each source node for SI suppression. Meanwhile, the effects of imperfect SI channel estimation and the intended channel estimation on the proposed schemes are also studied. Finally, the proposed DS-PNC scheme is studied with the SI signal model which considers analog radio frequency cancellation, the effects of I/Q modulator imbalances, and power amplifier nonlinearity of the transmitter. Simulation results reveal that the proposed DS-PNC scheme is a little more sensitive to the channel estimation errors than the traditional spatial-domain schemes. However, with the perfect channel state information, the proposed DS-NC with one iteration and DS-PNC schemes outperform traditional spatial-domain schemes. Furthermore, considering the SI signal model with nonlinear distortion and radio frequency cancellation, the DS-PNC scheme is also superior to the traditional schemes. Meanwhile, the DS-PNC scheme is more robust to the SI and achieves the same diversity gain as the ideal cancellation.
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