  We study distributed algorithms for adjusting beamforming vectors and
receiver filters in multiple-input multiple-output (MIMO) interference
networks, with the assumption that each user uses a single beam and a linear
filter at the receiver. In such a setting there have been several distributed
algorithms studied for maximizing the sum-rate or sum-utility assuming perfect
channel state information (CSI) at the transmitters and receivers. The focus of
this paper is to study adaptive algorithms for time-varying channels, without
assuming any CSI at the transmitters or receivers. Specifically, we consider an
adaptive version of the recent Max-SINR algorithm for a time-division duplex
system. This algorithm uses a period of bi-directional training followed by a
block of data transmission. Training in the forward direction is sent using the
current beam-formers and used to adapt the receive filters. Training in the
reverse direction is sent using the current receive filters as beams and used
to adapt the transmit beamformers. The adaptation of both receive filters and
beamformers is done using a least-squares objective for the current block. In
order to improve the performance when the training data is limited, we also
consider using exponentially weighted data from previous blocks. Numerical
results are presented that compare the performance of the algorithms in
different settings.
