Uncertainty propagation in neural network enabled multi-channel optimisation

Multi-channel optimisation relies on accurate channel state information (CSI) estimation. Error distributions in CSI can propagate through optimisation algorithms to cause undesirable uncertainty in the solution space. The transformation of uncertainty distributions differs between classic heuristic and Neural Network (NN) algorithms. Here, we investigate how CSI uncertainty transforms from an additive Gaussian error in CSI into different power allocation distributions in a multi-channel system. We offer theoretical insight into the uncertainty propagation for both Water-filling (WF) power allocation in comparison to diverse NN algorithms. We use the Kullback-Leibler divergence to quantify uncertainty deviation from the trusted WF algorithm and offer some insight into the role of NN structure and activation functions on the uncertainty divergence, where we found that the activation function choice is more important than the size of the neural network