Optimal dimensionality reduction for multi-sensor fusion in the presence of fading and noise

We derive linear estimators of stationary random signals based on reduced-dimensionality observations collected at distributed sensors and communicated over wireless fading links to a fusion center, where additive noise is also present. Dimensionality reduction compresses sensor data to meet low-power and bandwidth constraints, while linearity in compression and estimation are well motivated by the limited computing capabilities wireless sensor networks are envisioned to operate with. For uncorrelated sensor data, we develop mean-square error (MSB) optimal estimators in closed-form; while for correlated sensor data, we derive sub-optimal iterative estimators which guarantee convergence at least to a stationary point. Performance analysis and corroborating simulations demonstrate the merits of the novel distributed estimators relative to existing alternatives.