Energy-modified Leverage Sampling for Radio Map Construction via Matrix Completion

This paper explores an energy-modified leverage sampling strategy for matrix completion in radio map construction. The main goal is to address potential identifiability issues in matrix completion with sparse observations by using a probabilistic sampling approach. Although conventional leverage sampling is commonly employed for designing sampling patterns, it often assigns high sampling probability to locations with low received signal strength (RSS) values, leading to a low sampling efficiency. Theoretical analysis demonstrates that the leverage score produces pseudo images of sources, and in the regions around the source locations, the leverage probability is asymptotically consistent with the RSS. Based on this finding, an energy-modified leverage probability-based sampling strategy is investigated for efficient sampling. Numerical demonstrations indicate that the proposed sampling strategy can decrease the normalized mean squared error (NMSE) of radio map construction by more than 10% for both matrix completion and interpolation-assisted matrix completion schemes, compared to conventional methods.