A method comprises receiving power information transmitted by a plurality of mobile devices in a wireless communication system; processing the received power information to be a result of unknown power information multiplied by a measurement matrix relating to positions of the plurality of mobile devices, wherein a number of columns of the measurement matrix is larger than a number of rows of the measurement matrix; generating an amendment matrix satisfying restricted isometry property (RIP), for processing the measurement matrix, and obtaining a modified measurement matrix satisfying the RIP according to the amendment matrix and the measurement matrix; obtaining estimated power information according to the received power information by using L1 norm and the modified measurement matrix; and constructing at least one spectrum map of at least one frequency band according to the estimated power information.