Low-complexity optimization for Two-Dimensional Direction-of-arrival Estimation via Decoupled Atomic Norm Minimization

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows gridless angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by 1D angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANM in terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy

Matrix and Tensor-based ESPRIT Algorithm for Joint Angle and Delay Estimation in 2D Active Broadband Massive MIMO Systems and Analysis of Direction of Arrival Estimation Algorithms for Basal Ice Sheet Tomography

In this thesis, we apply and analyze three direction of arrival algorithms (DoA) to tackle two distinct problems: one belongs to wireless communication, the other to radar signal processing. Though the essence of these two problems is DoA estimation, their formulation, underlying assumptions, application scenario, etc. are totally different. Hence, we write them separately, with ESPRIT algorithm the focus of Part I and MUSIC and MLE detailed in Part II. For wireless communication scenario, mobile data traffic is expected to have an exponential growth in the future. In order to meet the challenge as well as the form factor limitation on the base station, 2D "massive MIMO" has been proposed as one of the enabling technologies to significantly increase the spectral efficiency of a wireless system. In "massive MIMO" systems, a base station will rely on the uplink sounding signals from mobile stations to figure out the spatial information to perform MIMO beamforming. Accordingly, multi-dimensional parameter estimation of a ray-based multi-path wireless channel becomes crucial for such systems to realize the predicted capacity gains. In the first Part, we study joint angle and delay estimation for 2D "massive MIMO" systems in mobile wireless communications. To be specific, we first introduce a low complexity time delay and 2D DoA estimation algorithm based on unitary transformation. Some closed-form results and capacity analysis are involved. Furthermore, the matrix and tensor-based 3D ESPRIT-like algorithms are applied to jointly estimate angles and delay. Significant improvements of the performance can be observed in our communication scheme. Finally, we found that azimuth estimation is more vulnerable compared to elevation estimation. Results suggest that the dimension of the antenna array at the base station plays an important role in determining the estimation performance. These insights will be useful for designing practical "massive MIMO" systems in future mobile wireless communications. For the problem of radar remote sensing of ice sheet topography, one of the key requirements for deriving more realistic ice sheet models is to obtain a good set of basal measurements that enables accurate estimation of bed roughness and conditions. For this purpose, 3D tomography of the ice bed has been successfully implemented with the help of DoA algorithms such as MUSIC and MLE techniques. These methods have enabled fine resolution in the cross-track dimension using synthetic aperture radar (SAR) images obtained from single pass multichannel data. In Part II, we analyze and compare the results obtained from the spectral MUSIC algorithm and an alternating projection (AP) based MLE technique. While the MUSIC algorithm is more attractive computationally compared to MLE, the performance of the latter is known to be superior in most situations. The SAR focused datasets provide a good case study to explore the performance of these two techniques to the application of ice sheet bed elevation estimation. For the antenna array geometry and sample support used in our tomographic application, MUSIC performs better originally using a cross-over analysis where the estimated topography from crossing flightlines are compared for consistency. However, after several improvements applied to MLE, i.e., replacing ideal steering vector generation with measured steering vectors, automatic determination of the number of scatter sources, smoothing the 3D tomography in order to get a more accurate height estimation and introducing a quality metric for the estimated signals, etc., MLE outperforms MUSIC. It confirms that MLE is indeed the optimal estimator for our particular ice bed tomographic application. We observe that, the spatial bottom smoothing, aiming to remove the artifacts made by MLE algorithm, is the most essential step in the post-processing procedure. The 3D tomography we obtained lays a good foundation for further analysis and modeling of ice sheets

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