Design of adaptively scaled belief in large MIMO detection for higher-order modulation

This paper proposes a new design criterion of adaptively scaled belief (ASB) in Gaussian belief propagation (GaBP), especially for large multi-user multi-input multi-output (MU-MIMO) detection with higher-order modulation. The most vital issue with regard to improving the convergence property of GaBP iterative detection is how to deal with the soft symbol outliers, which are induced by modeling errors of prior beliefs due to a lack of channel hardening effects. Unfortunately, the modeling errors become more severe in the presence of higher correlation among typical bit-wise prior beliefs while utilizing higher-order quadrature amplitude modulation (QAM) schemes. To avoid impairments of the inter-bit correlation, symbol-wise beliefs are defined for GaBP self-iterative detection. Moreover, as a simplest way to mitigate the harmful impacts of soft symbol outliers, a novel adaptive belief scaling is proposed while stabilizing dynamics of random MIMO channels. Finally, the validity of ASB for symbol-wise iterative detection is confirmed regarding suppression of the bit error rate (BER) floor level.