Radio scene analysis using trilinear decomposition

Abstract

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. I. INTRODUCTIONIn this work we consider a scenario with multiple radio sources operating in the same frequency band. Such a scenario happens in the 2.4 GHz ISM band which is used by WLAN radios, Bluetooth devices, cordless phones, Zig-bee radios, microwave ovens etc. The sources from different systems operate in this frequency band without any coordination and hence, they transmit signals that may overlap in time and frequency. These signals are received by a network of sensors. Each radio source is characterized by its power spectral density(PSD) and on/off activity in time. In order to capture this nonstationary behavior, each sensor computes spectrogram with certain time and frequency resolution. The spectrograms from different locations are collected and processed using a centralized scheme. Collected spectrograms form a three-way array, whose three dimensions correspond to space, time, and frequency indices. The key observation is that under certain rank conditions, sources to sensors channel gain coefficients, PSDs and on/off activity sequences of the sources can be recovered uniquely by decomposing the received 3-way array into rank-one components [1]. In general, the decomposition process happens in two steps. In the first step we perform block decomposition, which separates heterogeneous groups of sources. The block decomposition requires a non-trivial generalization of the basic uniqueness condition [2]. In the second step we recover individual contributions of sources within each group(rank-one components) by assuming nonoverlapping transmissions in time. This step reduces to a clustering problem. The proposed algorithm can identify multiple interfering signals, which may overlap in time and frequency.