of the transmitted/received signals is performed at the , while the operations are carried out at the . Each is equipped with an array of $N > K$ antennas and $L \leq N$ chains. A fully-connected architecture is considered where each chain is connected to the whole set of antenna elements using $N$ analog phase shifters. Without loss of essential generality, it is assumed in this paper that the number of active chains at each of the in the network is equal to $L_A=\min\{K,L\}$. That is, if $K \leq L$, all in the cell-free network provide service to the whole set of and if $K > L$, instead, each can only provide service to $L$ out of the $K$ in the network and, thus, an algorithm must be devised to decide which are the to be beamformed by each of the .

![Allocation of the samples in large-scale and short-scale coherence intervals.[]{data-label="fig:TDD_frame"}](TDD_frame){width="7.8cm"}

The propagation channels linking the to the are typically characterized by small-scale parameters that are (almost) static over a coherence time-frequency interval of $\tau_c$ time-frequency samples (see [@Marzetta16 Chapter 2]), and large-scale parameters (i.e., path loss propagation losses and covariance matrices) that can be safely assumed to be 