  We present distributed methods for jointly optimizing Intelligent Reflecting
Surface (IRS) phase-shifts and beamformers in a cellular network. The proposed
schemes require knowledge of only the intra-cell training sequences and
corresponding received signals without explicit channel estimation. Instead, an
SINR objective is estimated via sample means and maximized directly. This
automatically includes and mitigates both intra- and inter-cell interference
provided that the uplink training is synchronized across cells. Different
schemes are considered that limit the set of known training sequences from
interferers. With MIMO links an iterative synchronous bi-directional training
scheme jointly optimizes the IRS parameters with the beamformers and combiners.
Simulation results show that the proposed distributed methods show a modest
performance degradation compared to centralized channel estimation schemes,
which estimate and exchange all cross-channels between cells, and perform
significantly better than channel estimation schemes which ignore the
inter-cell interference.
