Bilinear Gaussian Belief Propagation for Large MIMO Channel and Data Estimation

Grant-Free Access via Bilinear Inference for Cell-Free MIMO With Low-Coherence Pilots

“…The damping steps [3], [7] introduced with damping factor η ∈ [0, 1] in lines 13, 15, 17 and 18 aims to prevent the algorithm from converging to local minima by forcing a slow update of soft-replicas, whereas belief scaling with parameter γ(t) is adopted in line 16, in order to adjust the reliability of beliefs (i.e., harnessing harmful outliers). The scaling parameter is designed to be a linear function of the number of iterations, that is,…”

“…assuming a fixed pilot length K p = 14. As for methods to compare, we have adopted not only MMV-AMP but also minimum norm solution (MNS) that is known to be a method to seek a closed-form unique CE solution in case of a non-orthogonal pilot sequence [7], while employing the minimum mean square error (MMSE) performance with perfect knowledge of AUD and MUD at the receiver as reference. Please note that since the non-Bayesian approach, which takes advantage of the sample covariance of the received signals in order to detect user activity patterns, aims at only AUD, the resultant performance in terms of CE can be lower-bounded by MNS with perfect AUD.…”

“…It has, however, been recently shown in [6] that the estimation performance of BiGAMP severely deteriorates when non-orthogonal pilot sequences are exploited, even if adaptive damping is employed, because the derivation of BiGAMP relies heavily on the assumption of very large systems, although shortening the pilot sequence is the very aim of the method itself. In order to circumvent this issue, the authors in [7] proposed a novel bilinear message passing algorithm, referred to as bilinear Gaussian belief propagation (BiGaBP), with the aim of generalizing BiGAMP on the basis of belief propagation (BP) [8] for robust recovery subject to nonorthogonal piloting. Despite the aforementioned progresses, many existing works including the ones mentioned above, focus only on joint CE and MUD while assuming that perfect AUD is available at the receiver.…”

“…Compounding on the above, a fundamental challenge of grant-free approaches from a system viewpoint is the spatial correlation of the massive MIMO channel, which has been argued in [18] to be a limiting factor of centralized massive MIMO, although most of the existing work in the area, including e.g. [6], [7], [11], [12], [19]- [21], make use of the assumption that channels are subjected to ideal (uncorrelated) Rayleigh fading. In order to iron out this issue, the cell-free massive MIMO concept -studied in [22], [23], which virtually configures a massive MIMO setup by spatially distributing access points (APs) connected through wired fronthaul links to a common central computing unit (CCU) -has recently emerged, offering an architecture capable of decorrelating the spatial dependence between APs, leading to an ideal independently distributed channel structure.…”

Grant-Free Access via Bilinear Inference for Cell-Free MIMO with Low-Coherent Pilots

“…It has, however, been recently shown in the literature [14] that the estimation performance of BiGAMP severely deteriorates when non-orthogonal pilot sequences are exploited, even if adaptive damping is employed, due to the fact that the derivation of BiGAMP relies heavily on the assumption of very large systems, although shortening the pilot sequence is the very aim of the method itself. In order to circumvent this issue, the authors in [15] proposed a novel bilinear message passing algorithm, referred to as bilinear Gaussian belief propagation (BiGaBP), with the aim of generalizing BiGAMP on the basis of belief propagation (BP) [16] for robust recovery subject to non-orthogonal piloting. Despite the aforementioned progresses, many existing works including the ones mentioned above, focus only on joint CE and MUD while assuming that perfect AUD is available at the receiver.…”