Tensor-based power spectra separation and emitter localization for cognitive radio

This paper considers the problem of separating the power spectra and mapping the locations of co-channel transmitters using compound measurements from multiple sensors. This kind of situational awareness is important in cognitive radio practice, for spatial spectrum interpolation, transmission opportunity mining, and interference avoidance. Using temporal auto- and cross-correlations of the sensor outputs, it is shown that the power spectra separation task can be cast as a tensor decomposition problem in the Fourier domain. In particular, a joint diagonalization or (symmetric) parallel factor analysis (PARAFAC) model emerges, with one loading matrix containing the sought power spectra - hence being nonnegative, and locally sparse. Exploiting the latter two properties, it is shown that a very simple algebraic algorithm can be used to speed up the factorization. Assuming a path loss model, it is then possible to identify the transmitter locations by focusing on exclusively used (e.g., carrier) frequencies. The proposed approaches offer identifiability guarantees, and simplicity of implementation. Simulations show that the proposed approaches are effective in separating the spectra and localizing the transmitters.