  In this paper, a novel full-duplex non-coherent (FD-NC) transmission scheme
is developed for massive multiple-input multiple-output (mMIMO) systems using
analog beamforming (ABF). We propose to use a structured Grassmannian
constellation for the non-coherent communications that does not require channel
estimation. Then, we design the transmit and receive ABF via the slow
time-varying angle-of-departure (AoD) and angle-of-arrival (AoA) information,
respectively. The ABF design targets maximizing the intended signal power while
suppressing the strong self-interference (SI) occurred in the FD transmission.
Also, the proposed ABF technique only needs a single transmit and receive RF
chain to support large antenna arrays, thus, it reduces hardware
cost/complexity in the mMIMO systems. It is shown that the proposed FD-NC
offers a great improvement in bit error rate (BER) in comparison to both
half-duplex non-coherent (HD-NC) and HD coherent schemes. We also observe that
the proposed FD-NC both reduces the error floor resulted from the residual SI
in FD transmission, and provides lower BER compared to the FD coherent
transmission.
