Radio scene analysis using trilinear decomposition

We consider a scenario with multiple radio sources performing packet based transmissions. The sources belong to heterogeneous networks and their signals may overlap in time and frequency. Each source is characterized by its power spectral density and an on/off activity sequence. A network of sensors performs measurements, where each sensor computes spectrogram of the received signal with certain time and frequency resolution. Spectrograms from different sensors are collected and arraigned in a three-way array, whose three dimensions correspond to space, time, and frequency indices. We show that, under certain rank conditions of the three-way array, it is possible to recover sources to sensors channel gain coefficients, power spectral densities and on/off activity sequences of the sources by decomposing the three-way array into rank-one components. The recovery process is illustrated with simulation examples involving 802.11b/g and Bluetooth sources whose signals overlap in time and frequency.