A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels

Abstract

Recently, a two-stage beamforming concept under the name of Joint Spatial Division and Multiplexing (JSDM), a kind of divide-and-conquer approach based on statistical user-grouping, has been proposed to enable simplified system operations in massive MIMO. In this study, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive MIMO systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies (which is often characterized with limited scattering and hence correlatedness in the spatial domain). The main contribution of this work is threefold. First, by an inspiration from the user-grouping idea (in the JSDM framework), the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator, based on generic subspace projection taking the joint angle-delay power profile into account, is derived for spatially correlated wideband MIMO channels. Second, the statistical prebeamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. The generalized eigenvector beamspace (GEB) appears to be a nearly optimal pre-beamformer when the eigenspaces of different resolvable multi-path components are assumed to be nearly orthogonal. Finally, a spatio-temporal domain correlator type reduced rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead thanks to the subspace projection. Index TermsThe authors are with the Center for Pervasive Communications and Computing (CPCC),

An Efficient Interference-Aware Constrained Massive MIMO Beamforming for mm-Wave JSDM

“…In [20], a weighted minimum mean square error (WMMSE) type digital beamformer is proposed to suppress residual interference. A near-optimal generalized eigenbeamformer (GEB), which has strong interference suppression capability, is proposed for SC transmission at mmwave bands in [18], [19]. However, none of these analog beamformers obey constant-modulus constraint.…”

Joint design of digital and analog processing for downlink C-RAN with large-scale antenna arrays

“…We assume that the signal processing strategies of the BBU, the RRHs and the UEs are jointly managed by the BBU based on the global channel state information (CSI) reported from the RRHs by means of the fronthaul links. Each RRH can obtain its local CSI via feedback on the uplink in a frequency division duplexing system [12] or uplink channel training in a timedivision duplexing (TDD) system [13]. In this work, we focus on the perfect CSI case such that the CSI reported to the BBU is accurate.…”

Beamspace aware adaptive channel estimation for single-carrier time-varying massive MIMO channels

“…The new subspace S H D will be different than the Wiener filter formulation earlier [13]. In particular, it will also be timevarying, or evolving in time.…”

“…In this section, our goal is to find a good subspace (spanned by the columns of S (g) D matrix) on which the reduced dimensional instantaneous Kalman estimator can be realized as accurately as possible, so that a minimal performance compromise in the subsequent statistical signal processing operations after beamforming is provided. Different criteria can be used to design beam pattern as similar to one in [13]. In this paper, we adopt error volume as the optimization criterion, namely, the minimization of det P (g) n|n , and S (g) D is designed to minimize the error volume at each signaling interval for a given prediction error covariance P (g) n|n−1 that is a function of all previous training signals.…”

“…(33) Proposition: Given all previous training signals, the pre-beamformer S [13]. Under this pre-beamformer design, all three matrices SNR l,(g) n|n , SNR l,(g) n|n−M and SNR l,(g) 0|−m are simultaneously diagonalizable, i.e., given these generalized eigenvectors that diagonalize SNR l,(g) 0|−m initially, the SNR l,(g) n|n and SNR l,(g) n|n−M are also diagonalizable for every n from the recursive relation in (32).…”