Hybrid SMI Realization via Matrix Completion and Riemannian Manifold Optimization on Narrowband Sub-Array Based Architectures

TL;DR

This paper introduces RR2D, a structured covariance completion framework that enables hybrid SMI to approximate full array observations, improving beamforming performance in hardware-constrained architectures.

Contribution

The paper proposes a novel covariance completion method, RR2D, that reconstructs unobservable covariance matrices for hybrid beamforming arrays, bridging the gap between theory and practical hardware constraints.

Findings

RR2D effectively reconstructs covariance matrices from partial observations.

Hybrid SMI with RR2D outperforms previous hybrid SMI methods.

Performance approaches that of full digital MVDR in experiments.

Abstract

Hybrid beamforming architectures reduce hardware complexity but restrict access to full array observations, rendering direct implementation of classical covariance based methods such as minimum variance distortionless response (MVDR) and sample matrix inversion (SMI) infeasible. This work introduces a structured covariance completion framework, termed Rock Road to Dublin (RR2D), which estimates the unobservable analytical covariance matrix (ACM) from a partially observed sample covariance matrix (SCM). RR2D exploits signal stationarity across the array and enforces physical measurement consistency using Dykstra's alternating projection algorithm with positive semidefinite, Toeplitz, and block constraints. The reconstructed virtual ACM enables a realizable hybrid SMI (HSMI) formulation that remains fully compatible with existing hybrid MVDR optimization frameworks. Empirical results for a 32 element hybrid array demonstrate both the expected degradation of HSMI implemented directly under prior HMVDR formulations and the performance gains achieved through RR2D. The proposed HSMI consistently outperforms previous hybrid SMI and partial digital baselines, achieving performance close to the HMVDR reference. Overall, RR2D bridges the gap between theoretical HMVDR formulations and practical hybrid hardware by enabling structured covariance reconstruction from incomplete observations.