Design of Adaptively Scaled Belief in Multi-Dimensional Signal Detection for Higher-Order Modulation

This paper proposes an adaptively scaled belief (ASB) in Gaussian belief propagation (GaBP) designed for use in large multi-user multi-input multi-output (MU-MIMO) detection under higher order modulation schemes. In practical MU-MIMO systems, the dominant factor in the poor convergence of GaBP iterative detection is approximation errors arising from the fact that the law of large numbers does not work well in many such applications as a result of physical system limitations. Unfortunately, the approximation errors become more severe when there is higher correlation among typical bit-wise prior beliefs when higher order quadrature amplitude modulation schemes are used. To cope with the impairments arising from inter-bit correlation, symbol-wise beliefs can be defined for GaBP self-iterative detection, although this still does not remove approximation errors. As a simple method for mitigating the harmful effects of approximation error, this paper proposes a novel method for adaptive belief scaling while stabilizing the dynamics of random MIMO channels. Based on the functionality of ASB, we also propose a method for approximately calculating conditional expectations with lower computational complexity without sacrificing detection capability. Finally, the validity of using ASB for symbol-wise iterative detection in suppressing the bit-error-rate floor level is confirmed.