  In this paper, we introduce a Deep Neural Network (DNN) to maximize the
Proportional Fairness (PF) of the Spectral Efficiency (SE) of uplinks in
Cell-Free (CF) massive Multiple-Input Multiple-Output (MIMO) systems. The
problem of maximizing the PF of the SE is a non-convex optimization problem in
the design variables. We will develop a DNN which takes pilot sequences and
large-scale fading coefficients of the users as inputs and produces the outputs
of optimal transmit powers. By consisting of densely residual connections
between layers, the proposed DNN can efficiently exploit the hierarchical
features of the input and motivates the feed-forward nature of DNN
architecture. Experimental results showed that, compared to the conventional
iterative optimization algorithm, the proposed DNN has excessively lower
computational complexity with the trade-off of approximately only 1% loss in
the sum rate and the fairness performance. This demonstrated that our proposed
DNN is reasonably suitable for real-time signal processing in CF massive MIMO
systems.
