Power spectra separation aims at extracting the individual power spectra of multiple emitters from the received mixtures. Traditional spectrum sensing for dynamic spectrum sharing is mostly concerned with detecting or estimating the aggregate spectrum. Spectra separation can be considered as a further step towards full awareness of the radio frequency (RF) environment, which may enable judicious routing, scheduling and beamforming with more effective interference avoidance. In other applications such as geoscience, astronomy, and chemometrics, separating the spectra of the objects/analytes from the sensed mixtures is also of great interest. Our prior work tackled this problem from a tensor decomposition point of view, but this requires delicate and careful receiver setups, and the algorithms are computationally heavy and difficult to decentralize. In this work, we propose to solve the power spectra separation problem using a structured matrix factorization model, where the columns of one of the two factor matrices live in the unit simplex. The salient features of this new framework are that 1) the receivers can be far simpler in terms of hardware, 2) an algebraically very simple algorithm can be employed for the centralized case, 3) and that effective decentralized algorithms can be devised under this framework. Numerical simulations and a laboratory experiment using real software-defined radios are presented to demonstrate the effectiveness of the proposed algorithms.
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- Spectrum estimation
- cognitive radio
- nonnegative matrix factorization
- sparse optimization
- spectra separation