Stochastic semiparametric regression for spectrum cartography

An online spectrum cartography algorithm is proposed to reconstruct power spectral density (PSD) maps in space and frequency based on compressed and quantized sensor measurements. The emerging regression task is addressed by decomposing the PSD at every location into a linear combination of the power spectra (due to individual transmitters and background noise) scaled by attenuation functions capturing propagation effects. The attenuation functions are, in turn, postulated to be a sum of two terms: the first is a linear combination of a collection of basis functions whereas the second is an element of a reproducing kernel Hilbert space (RKHS) of vector-valued functions. A novel stochastic gradient descent algorithm is proposed to compute both components in an online fashion. Numerical tests verify the map estimation performance of the proposed technique.