Message Passing GNN for Graph Based Wireless Communication Models

This paper presents a message passing Graph Neural Networks (GNN) for symbol estimation in different communication scenarios presented under a unique system model. Even if the properties such as the correlations or sparsity of the channel matrix may vary, the use of the underlying graph representation enables a generic definition of learned or non-learned message-passing algorithm for different communication types. We highlight how the prepossessing of the channel matrix brings changes in the graph and how this impacts the definition of GNN. To this end, we compare Factor Graph Neural Network (FGNN) which are directly based on the adjacency of the channel matrix to GNN defined on a transformed graph. The resulting neural networks may be used alone to estimate the symbol distribution or may be helped by a Soft-Input Soft-Output (SISO) detector which provide prior information to the GNN. Our results show that depending on the scenario FGNN may not always converge and estimate the transmitted symbols. Yet we show that they can outperform non-learned receivers such as Linear Minimum Mean Square Error (LMMSE) or Vector Expectation Propagation (VEP).