Graph Neural Networks and Learned Approximate Message Passing Algorithms for Massive MIMO Detection

Abstract: Massive multiple-input and multiple-output (MIMO) is a method to improvethe performance of wireless communication systems by having a large numberof antennas at both the transmitter and the receiver. In the fifth-generation(5G) mobile communication system, Massive MIMO is a key technology toface the increasing number of mobile users and satisfy user demands. At thesame time, recovering the transmitted information in a massive MIMO uplinkreceiver requires more computational complexity when the number of transmittersincreases. Indeed, the optimal maximum likelihood (ML) detector hasa complexity exponentially increasing with the number of transmitters. Therefore,one of the main challenges in the field is to find the best sub-optimalMIMO detection algorithm according to the performance/complexity tradeoff.In this work, all the algorithms are empirically evaluated for large MIMOsystems and higher-order modulations.Firstly, we show how MIMO detection can be represented by a MarkovRandom Field (MRF) and addressed by the loopy belief propagation (LBP)algorithm to approximately solve the equivalent MAP (maximum a posteriori)inference problem. Then, we propose a novel algorithm (BP-MMSE) thatstarts from the minimum mean square error (MMSE) solution and updates theprior in each iteration with the LBP belief. To avoid the complexity of computingMMSE, we use Graph Neural Networks (GNNs) to learn a messagepassingalgorithm that solves the inference task on the same graph.To further reduce the complexity of message-passing algorithms, we recallhow in the large system limit, approximate message passing (AMP), a lowcomplexity iterative algorithm, can be derived from LBP to solve MIMO detectionfor i.i.d. Gaussian channels. Then, we show numerically how AMPwith damping (DAMP) can be robust to low/medium correlation among thechannels. To conclude, we propose a low complexity deep neural iterativescheme (Pseudo-MMNet) for solvingMIMOdetection in the presence of highlycorrelated channels at the expense of online training for each channel realization.Pseudo-MMNet is based on MMNet algorithm presented in [24] (in turnbased on AMP) and it significantly reduces the online training complexity thatmakes MMNet far from realistic implementations.