Learning and Analysis of Damping Factor in Massive MIMO Detection Using BP Algorithm with Node Selection

In a massive multiple-input multiple-output (MIMO) system, belief propagation (BP) detection is known as a method to separate and detect received signals. In BP detection, a MIMO channel is represented by a factor graph and the transmitted symbols are estimated by message passing. However, the convergence property of BP deteriorates due to multiple loops included in the MIMO channel. As a method to improve the convergence property and the detection performance, the damped BP that averages two successive messages with a weighing factor (called damping factor) is known. To train the damping factors off-line for each antenna configuration, deep neural network-based damped BP (DNN-dBP) has been reported. The problem with DNN-dBP is that the detection performance deteriorates when there is a difference of the channel correlation between training and test. This is because the optimal damping factors vary with the channel correlation. In this paper, to solve this issue, we derive the damping factors of BP with the node selection (NS) method that selects nodes to be updated to lower spatial correlation using DNN-dBP. By applying the NS method, the channel correlation among the selected nodes in BP detection is lowered. Therefore, the proposed method can improve the detection performance deterioration due to the mismatches of the channel correlations between training and test in DNN-dBP. In addition, the convergence property of BP is improved by applying the NS method. Therefore, the proposed method has the same detection performance with low computational complexity as the conventional DNN-dBP. By computer simulation, it is shown that the proposed method significantly improves the bit error rate (BER) performance deterioration due to the mismatches of the channel correlations between training and test in DNN-dBP. The results also show that the proposed method can show the same BER performance with low computational complexity as the conventional DNN-dBP. We also investigate the distribution of the trained damping factors and evaluate the tendency of that.