  In the cell-free massive multiple-input multiple-output (CF mMIMO) system,
the centralized transmission scheme is widely adopted to manage the inter-user
interference. Unfortunately, its implementation is limited by the extensive
signaling overhead between the central process unit (CPU) and the access points
(APs). To solve this problem, we propose a distributed downlink transmission
scheme in this letter. First, the null space-based precoding is used to cancel
the interference to partial users, where only a portion of channel state
information (CSI) needs to be shared among the AP cluster. Based on this, the
dual decomposition method is adopted to jointly optimize the precoder and power
control, where the calculation can be performed independently by each AP
cluster with closed-form expression. With very few iterations, our distributed
scheme achieves the same performance as the centralized one. Moreover, it
significantly reduces the information exchange to the CPU.
