[3] He derived an analytic model for the eigenfunctions of linear time-varying systems and introduced the product high-order ambiguity function, an algorithm useful to estimate the parameters of multi-component polynomial-phase signals.

[4] Barbarossa invented new ways to estimate the instantaneous frequency of continuous-phase signals embedded in noise, based on pattern analysis of their time-frequency representation.

[9] Together with Fasano, Barbarossa introduced an optimal space-time coding technique, named Trace-Orthogonal Design, for MIMO systems with no channel information.

[11][12] He was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2012[13] for contributions to signal processing, sensor networks, and wireless communications.

He was named Fellow of the European Association for Signal Processing (EURASIP) in 2015 for contributions to radar remote sensing, sensor and communication networks.