  We consider a cell-free massive multiple-input multiple-output system with
multi-antenna access points (APs) and user equipments (UEs), where the UEs can
be served in both the downlink (DL) and uplink (UL) within a resource block. We
tackle the combined optimization of the DL precoders and combiners at the APs
and DL UEs, respectively, together with the UL combiners and precoders at the
APs and UL UEs, respectively. To this end, we propose distributed beamforming
designs enabled by iterative bi-directional training (IBT) and based on the
minimum mean squared error criterion. To reduce the IBT overhead and thus
enhance the effective DL and UL rates, we carry out the distributed beamforming
design by assuming that all the UEs are served solely in the DL and then
utilize the obtained beamformers for the DL and UL data transmissions after
proper scaling. Numerical results show the superiority of the proposed combined
DL-UL distributed beamforming design over separate DL and UL designs,
especially with short resource blocks.
