We consider a multi-user multiple-input multipleoutput setup, where full-duplex multi-antenna nodes apply linear beamformers to simultaneously transmit and receive multiple streams over Rician fading channels. The exact first and second positive moments of the residual self-interference (SI), involving the squared norm of a sum of non-identically distributed random variables, are derived in closed-form. The method of moments is hence invoked to provide a Gamma approximation for the residual SI distribution. The proposed theorem holds under arbitrary linear precoder/decoder design, antenna array size, number of information streams, and SI cancellation capability. Index Terms-Multiple-input multiple-output (MIMO), full-duplex (FD), self-interference (SI), Rician fading model. T O DATE, wireless systems, have been designed and dimensioned under a complete separation of the transmit and receive functions, a.k.a., half-duplex (HD) mode. This is typically achieved via orthogonal radio frequency (RF) partitioning, e.g., in time-division duplex (TDD) and frequencydivision duplex (FDD) systems. The motivation behind this trend has been to avoid the overwhelming self-interference (SI) arising from the bi-directional operation. The rapid increase in traffic, under limited RF resources, however, has driven the incentive for an overhaul in the wireless system design. A candidate solution involves transceiving information over the same RF resources, i.e., full-duplex (FD) mode [1] . There is a growing surge of interest in this topic, as in theory, FD has the potential to double the spectral efficiency versus HD. Several point-to-point prototypes of FD radio nodes have been shown in practice recently [2] . Despite pioneering efforts, FD operation in the context of multi-user multiple-input multiple-output (MIMO) setups is not well understood. A long-standing limitation is in the modeling of the residual SI using the Rayleigh distribution [3] .
The residual SI is also characterized in REF for a multi-user multiple-input multiple-output (MIMO) setup considering FDX multi-antenna nodes and assuming the availability of perfect channel state information.
Self-Interference in Full-Duplex Multi-User MIMO Channels
IEEE Communications Letters
IEEE Communications Letters
Mathematics Computer Science