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

In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output 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. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. 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

Optimal low-rank approximations of Bayesian linear inverse problems

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to characterize and approximate the posterior distribution of the parameters. We first investigate approximation of the posterior covariance matrix as a low-rank update of the prior covariance matrix. We prove optimality of a particular update, based on the leading eigendirections of the matrix pencil defined by the Hessian of the negative log-likelihood and the prior precision, for a broad class of loss functions. This class includes the F\"{o}rstner metric for symmetric positive definite matrices, as well as the Kullback-Leibler divergence and the Hellinger distance between the associated distributions. We also propose two fast approximations of the posterior mean and prove their optimality with respect to a weighted Bayes risk under squared-error loss. These approximations are deployed in an offline-online manner, where a more costly but data-independent offline calculation is followed by fast online evaluations. As a result, these approximations are particularly useful when repeated posterior mean evaluations are required for multiple data sets. We demonstrate our theoretical results with several numerical examples, including high-dimensional X-ray tomography and an inverse heat conduction problem. In both of these examples, the intrinsic low-dimensional structure of the inference problem can be exploited while producing results that are essentially indistinguishable from solutions computed in the full space

Signal Processing in Large Systems: a New Paradigm

For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to \infty$. Modern technological and societal advances now demand the study of sometimes extremely large populations and simultaneously require fast signal processing due to accelerated system dynamics. This results in not-so-large practical ratios $n/N$, sometimes even smaller than one. A disruptive change in classical signal processing methods has therefore been initiated in the past ten years, mostly spurred by the field of large dimensional random matrix theory. The early works in random matrix theory for signal processing applications are however scarce and highly technical. This tutorial provides an accessible methodological introduction to the modern tools of random matrix theory and to the signal processing methods derived from them, with an emphasis on simple illustrative examples

Beamspace Aware Adaptive Channel Estimation for Single-Carrier Time-varying Massive MIMO Channels

In this paper, the problem of sequential beam construction and adaptive channel estimation based on reduced rank (RR) Kalman filtering for frequency-selective massive multiple-input multiple-output (MIMO) systems employing single-carrier (SC) in time division duplex (TDD) mode are considered. In two-stage beamforming, a new algorithm for statistical pre-beamformer design is proposed for spatially correlated time-varying wideband MIMO channels under the assumption that the channel is a stationary Gauss-Markov random process. The proposed algorithm yields a nearly optimal pre-beamformer whose beam pattern is designed sequentially with low complexity by taking the user-grouping into account, and exploiting the properties of Kalman filtering and associated prediction error covariance matrices. The resulting design, based on the second order statistical properties of the channel, generates beamspace on which the RR Kalman estimator can be realized as accurately as possible. It is observed that the adaptive channel estimation technique together with the proposed sequential beamspace construction shows remarkable robustness to the pilot interference. This comes with significant reduction in both pilot overhead and dimension of the pre-beamformer lowering both hardware complexity and power consumption.Comment: 7 pages, 3 figures, accepted by IEEE ICC 2017 Wireless Communications Symposiu