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

Researchers from Virginia Tech and Raytheon have developed **RR2D (Rock Road to Dublin)**, a breakthrough algorithm that solves a core challenge in hybrid beamforming architectures. These systems reduce hardware complexity by using partial digital arrays, but this restriction makes classical covariance-based methods like Sample Matrix Inversion (SMI) infeasible. RR2D introduces a structured covariance completion framework that reconstructs the missing analytical covariance matrix from limited observations using stationarity assumptions and Dykstra's alternating projection algorithm with physical constraints.

In empirical tests on a 32-element hybrid array, the team demonstrated that direct HSMI implementations suffer performance degradation compared to theoretical HMVDR baselines. However, RR2D consistently outperformed both previous hybrid SMI approaches and partial digital baselines, achieving results nearly identical to the ideal HMVDR reference. The algorithm enforces Toeplitz structure and positive semidefinite constraints to ensure measurement consistency, effectively bridging the gap between theoretical optimization frameworks and practical hardware limitations.