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We propose a novel sensing approach for the beam alignment problem in millimeter wave systems using a single Radio Frequency (RF) chain. Conventionally, beam alignment using a single phased array involves comparing beamformer output power across different spatial regions. This incurs large training overhead due to the need to perform the beam scan operation. The proposed Synthesis of Virtual Array Manifold (SVAM) sensing methodology is inspired from synthetic aperture radar systems and realizes a virtual array geometry over temporal measurements. We demonstrate the benefits of SVAM using Cramer-Rao bound (CRB) analysis over schemes that repeat beam pattern to boost signal-to-noise (SNR) ratio. We also showcase versatile applicability of the proposed SVAM sensing by incorporating it within existing beam alignment procedures that assume perfect knowledge of the small-scale fading coefficient. We further consider the practical scenario wherein we estimate the fading coefficient and propose a novel beam alignment procedure based on efficient computation of an approximate posterior density on dominant path angle. We provide numerical experiments to study the impact of parameters involved in the procedure. The performance of the proposed sensing and beam alignment algorithm is empirically observed to approach the fading coefficient-perfectly known performance, even at low SNR. 

A novel sensing approach for the single radio frequency (RF) chain millimeter wave systems is proposed. The sensing strategy is inspired from synthetic aperture radar systems, and synthesizes a virtual array manifold vector using a single phased array over temporal measurements. The geometry of the virtual array can be controlled enabling synthesis of both a virtual uniform linear array (ULA) and a virtual sparse linear array starting from a large physical array. Moreover, the proposed sensing can be realized using conventional phased array/analog combiner. Several design parameters of the sensing scheme provide flexibility and are discussed including their impact on initial alignment. The proposed sensing approach allows for a rich set of options for inference. Candidate detection and estimation algorithms are presented and their performance is evaluated. 

We present a Light-Weight Sequential Sparse Bayesian Learning (LWS-SBL) algorithm as an alternative to the orthogonal matching pursuit (OMP) algorithm for the general sparse signal recovery problem. The proposed approach formulates the recovery problem under the Type-II estimation framework and the stochastic maximum likelihood objective. We compare the computational complexity for the proposed algorithm with OMP and highlight the main differences. For the case of parametric dictionaries, a gridless version is developed by extending the proposed sequential SBL algorithm to locally optimize grid points near potential source locations and it is empirically shown that the performance approaches Cramer-Rao bound.´ Numerical results using the proposed approach demonstrate the support recovery performance improvements in different scenarios at a small computational price when compared to the OMP algorithm. 

In this paper, we revisit the framework for maximum likelihood estimation (MLE) as applied to parametric models with an aim to estimate the parameter of interest in a gridless manner. The approach has inherent connections to the sparse Bayesian learning (SBL) formulation, and naturally leads to the problem of structured matrix recovery (SMR). We therefore pose the parameter estimation problem as a SMR problem, and recover the parameter of interest by appealing to the Carathéodory-Fejér result on decomposition of positive semi-definite Toeplitz matrices. We propose an iterative algorithm to estimate the structured covariance matrix; each iteration solves a semi-definite program. We numerically compare the performance with other gridless schemes in literature and demonstrate the superior performance of the proposed technique