We study Waze-inspired spectrum discovery, where the cloud collects the spectrum sensing results from many smartphones and predicts location-specific spectrum availability based on information fusion. Observe that with limited sensing capability, each smartphone can sense only a limited number of channels; and further, the more channels each smartphone senses, the less accurate the sensing results would be. To develop a comprehensive understanding, we cast the spectrum discovery problem as a matrix recovery problem, which is different from the classical matrix completion problem, in the sense that it suffices to determine only part of the matrix entries in the matrix recovery formulation. It is shown that the widely-used similarity-based collaborative filtering method would not work well because it requires each smartphone to sense too many channels. With this motivation, we propose a location-aided smartphone data fusion method and show that the channel numbers each smartphone needs to sense could be dramatically reduced. Moreover, we analyze the partial matrix recovery performance by using the location-aided data fusion method, and numerical results corroborate the intuition that with each smartphone sensing more channels, the recovery performance improves at first but then degrades beyond some point because of the decreasing sensing accuracy.