Oblique projection: An interference mitigation for MIMO multihop full‐duplex relay

Full‐duplex (FD) assisted multiple‐input–multiple‐output relaying increases the spectral efficiency through efficient spectrum utilization. The major concerns for the FD assisted relay system are the cancellation of inter‐relay interference (IRI) and relay self‐interference (RSI). Previous works were idealized only on the basis of either RSI or IRI; hence, all other realistic models to overcome the RSI or IRI were unappreciated. This paper aims to reduce the interference‐to‐signal ratio. We propose the joint relay's receive beamforming based on oblique projection to mitigate the RSI and IRI in multihop environments. Applying first orthogonal projectors to the relay's received signal, the relay's received signals are divided into interference subspace and signal subspace. Then, the desired signal is recovered from signal subspace by using oblique projection that cancels out the RSI and IRI. The geometric interpretation of oblique projection is analyzed to understand its properties. The major merit of this method is that it can be adopted even when the RSI and IRI channels are unknown. In comparison to the existing interference cancellation methods, the signal‐to‐interference ratio of our proposed method does not deteriorate even when the transmit power is high. Additionally, we demonstrate that the oblique projection output is equivalent to an orthogonal projection using geometrical interpretation, simulation, and theoretical derivation.