Bayesian ensemble refinement by replica simulations and reweighting

We describe different Bayesian ensemble refinement methods, examine their interrelation, and discuss their practical application. With ensemble refinement, the properties of dynamic and partially disordered (bio)molecular structures can be characterized by integrating a wide range of experimental data, including measurements of ensemble-averaged observables. We start from a Bayesian formulation in which the posterior is a functional that ranks different configuration space distributions. By maximizing this posterior, we derive an optimal Bayesian ensemble distribution. For discrete configurations, this optimal distribution is identical to that obtained by the maximum entropy "ensemble refinement of SAXS" (EROS) formulation. Bayesian replica ensemble refinement enhances the sampling of relevant configurations by imposing restraints on averages of observables in coupled replica molecular dynamics simulations. We show that the strength of the restraint should scale linearly with the number of replicas to ensure convergence to the optimal Bayesian result in the limit of infinitely many replicas. In the "Bayesian inference of ensembles" (BioEn) method, we combine the replica and EROS approaches to accelerate the convergence. An adaptive algorithm can be used to sample directly from the optimal ensemble, without replicas. We discuss the incorporation of single-molecule measurements and dynamic observables such as relaxation parameters. The theoretical analysis of different Bayesian ensemble refinement approaches provides a basis for practical applications and a starting point for further investigations.Comment: Paper submitted to The Journal of Chemical Physics (15 pages, 4 figures); updated references; expanded discussions of related formalisms, error treatment, and ensemble refinement with and without replicas; appendi

1-Bit Massive MIMO Downlink Based on Constructive Interference

In this paper, we focus on the multiuser massive multiple-input single-output (MISO) downlink with low-cost 1-bit digital-to-analog converters (DACs) for PSK modulation, and propose a low-complexity refinement process that is applicable to any existing 1-bit precoding approaches based on the constructive interference (CI) formulation. With the decomposition of the signals along the detection thresholds, we first formulate a simple symbol-scaling method as the performance metric. The low-complexity refinement approach is subsequently introduced, where we aim to improve the introduced symbol-scaling performance metric by modifying the transmit signal on one antenna at a time. Numerical results validate the effectiveness of the proposed refinement method on existing approaches for massive MIMO with 1-bit DACs, and the performance improvements are most significant for the low-complexity quantized zero-forcing (ZF) method.Comment: 5 pages, EUSIPCO 201

An odyssey into local refinement and multilevel preconditioning III: Implementation and numerical experiments

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform refinement-based discretizations of elliptic equations, they tend to be less effective for algebraic systems, which arise from discretizations on locally refined meshes, losing their optimal behavior in both storage and computational complexity. Our primary focus here is on Bramble, Pasciak, and Xu (BPX)-style additive and multiplicative multilevel preconditioners, and on various stabilizations of the additive and multiplicative hierarchical basis (HB) method, and their use in the local mesh refinement setting. In parts I and II of this trilogy, it was shown that both BPX and wavelet stabilizations of HB have uniformly bounded condition numbers on several classes of locally refined two- and three-dimensional meshes based on fairly standard (and easily implementable) red and red-green mesh refinement algorithms. In this third part of the trilogy, we describe in detail the implementation of these types of algorithms, including detailed discussions of the data structures and traversal algorithms we employ for obtaining optimal storage and computational complexity in our implementations. We show how each of the algorithms can be implemented using standard data types, available in languages such as C and FORTRAN, so that the resulting algorithms have optimal (linear) storage requirements, and so that the resulting multilevel method or preconditioner can be applied with optimal (linear) computational costs. We have successfully used these data structure ideas for both MATLAB and C implementations using the FEtk, an open source finite element software package. We finish the paper with a sequence of numerical experiments illustrating the effectiveness of a number of BPX and stabilized HB variants for several examples requiring local refinement

Efficient Downlink Channel Reconstruction for FDD Multi-Antenna Systems

In this paper, we propose an efficient downlink channel reconstruction scheme for a frequency-division-duplex multi-antenna system by utilizing uplink channel state information combined with limited feedback. Based on the spatial reciprocity in a wireless channel, the downlink channel is reconstructed by using frequency-independent parameters. We first estimate the gains, delays, and angles during uplink sounding. The gains are then refined through downlink training and sent back to the base station (BS). With limited overhead, the refinement can substantially improve the accuracy of the downlink channel reconstruction. The BS can then reconstruct the downlink channel with the uplink-estimated delays and angles and the downlink-refined gains. We also introduce and extend the Newtonized orthogonal matching pursuit (NOMP) algorithm to detect the delays and gains in a multi-antenna multi-subcarrier condition. The results of our analysis show that the extended NOMP algorithm achieves high estimation accuracy. Simulations and over-the-air tests are performed to assess the performance of the efficient downlink channel reconstruction scheme. The results show that the reconstructed channel is close to the practical channel and that the accuracy is enhanced when the number of BS antennas increases, thereby highlighting that the promising application of the proposed scheme in large-scale antenna array systems