Shadow fading correlations with compressive sensing: Prediction accuracy

The cross-correlation between shadowing components in wireless communications has important implications for wireless systems. The new cooperative and cognitive communications methods can exploit these correlations, if the statistical properties of shadowing correlations were known in particular radio environment under the consideration. The statistical large scale models have higher uncertainty compared to locally provided models. In this paper we study the question how much uncertainty for shadow models is generated by sparsely sampling shadowing coefficients in a locality to build Radio Environment Maps that include shadowing models. The spatial correlations induce redundancy in these "shadowing maps", and potentially enable them to be reconstructed based on small number of measurements. We quantify this redundancy for commonly used models of correlated shadowing by applying compressive sensing techniques. We show that shadowing maps are indeed highly compressible, and can be potentially predicted by taking only a small number of random samples. We also present a small case study in which these techniques are used to estimate the coverage area of a wireless transmission system.