Channel Gain Cartography for Cognitive Radios Leveraging Low Rank and Sparsity

Channel gain cartography aims at inferring the channel gains between two arbitrary points in space based on the measurements (samples) of the gains collected by a set of radios deployed in the area. Channel gain maps are useful for various sensing and resource allocation tasks essential for the operation of cognitive radio networks. In this paper, the channel gains are modeled as the tomographic accumulations of an underlying spatial loss field (SLF), which captures the attenuation in the signal strength due to the obstacles in the propagation path. In order to estimate the map accurately with a relatively small number of measurements, the SLF is postulated to have a low-rank structure possibly with sparse deviations. Efficient batch and online algorithms are derived for the resulting map reconstruction problem. Comprehensive tests with both synthetic and real data sets corroborate that the algorithms can accurately reveal the structure of the propagation medium, and produce the desired channel gain maps.