There is need to develop better models and characterization methods for spectrum usage and radio environments of cognitive radios. Currently different theoretical and simulation based approaches towards enabling dynamic spectrum access would greatly benefit from the possibility to generate synthetic data for testing purposes. Such Radio Environment Maps must statistically exhibit the characteristics of realistic environments. Previous and on-going spectrum measurement campaigns are generating a vast amount of such data. In this paper we provide a partial answer to the spectrum modelling problem by showing how one can characterize and model spectrum maps with spatial statistics and random fields. We present the basic mathematical premises for building models and also through examples outline how one can generate useful statistics from real measurement data.
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