Novel Active Sensing and Inference for mmWave Beam Alignment Using Single RF Chain Systems

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 Cram\'er-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.

Maximum Likelihood-based Gridless DoA Estimation Using Structured Covariance Matrix Recovery and SBL with Grid Refinement

We consider the parametric data model employed in applications such as line spectral estimation and direction-of-arrival estimation. We focus on the stochastic maximum likelihood estimation (MLE) framework and offer approaches to estimate the parameter of interest in a gridless manner, overcoming the model complexities of the past. This progress is enabled by the modern trend of reparameterization of the objective and exploiting the sparse Bayesian learning (SBL) approach. The latter is shown to be a correlation-aware method, and for the underlying problem it is identified as a grid-based technique for recovering a structured covariance matrix of the measurements. For the case when the structured matrix is expressible as a sampled Toeplitz matrix, such as when measurements are sampled in time or space at regular intervals, additional constraints and reparameterization of the SBL objective leads to the proposed structured matrix recovery technique based on MLE. The proposed optimization problem is non-convex, and we propose a majorization-minimization based iterative procedure to estimate the structured matrix; each iteration solves a semidefinite program. We recover the parameter of interest in a gridless manner by appealing to the Caratheodory-Fejer result on decomposition of PSD Toeplitz matrices. For the general case of irregularly spaced time or spatial samples, we propose an iterative SBL procedure that refines grid points to increase resolution near potential source locations, while maintaining a low per iteration complexity. We provide numerical results to evaluate and compare the performance of the proposed techniques with other gridless techniques, and the CRB. The proposed correlation-aware approach is more robust to environmental/system effects such as low number of snapshots, correlated sources, small separation between source locations and improves sources identifiability.

A Novel Bayesian Approach for the Two-Dimensional Harmonic Retrieval Problem

Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two dimensional harmonic retrieval problem, through remodeling and reparameterization of the standard data model. This new model allows us to introduce a block sparsity structure in a manner that enables a natural pairing of the parameters in the two dimensions. The numerical simulations demonstrate that the inference algorithm developed (H-MSBL) does not suffer from source identifiability issues and is capable of estimating the harmonic components in challenging scenarios, while maintaining a low computational complexity.