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In this paper, we propose a novel method for estimating the rain rate at any given point within a two-dimensional plain using measurements of the received signal level extracted from power control records of an existing deployed fixed wireless communication network. The path-average rainfall intensity along each microwave radio link is estimated from the rainfall-induced attenuation using an empirical relationship. The proposed algorithm consists of appropriate preprocessing of the links data, followed by a modified weighted least squares algorithm to infer on the rain level at any given point in space. The algorithm can be used to interpolate measurements onto a regular grid to construct a two-dimensional rainfall intensity field. The novelty of the proposed estimation method comes from its ability to be applied on an arbitrary geometry network comprising different microwave links lengths and frequencies and allowing easy integration of rain gauge observations into the model to improve estimation accuracy. The technique has been applied to an existing fixed wireless communication network comprising 22 microwave links covering an area of about 15times15 km2 and operating at carrier frequencies of about 20 GHz. The resulting rainfall field estimates have been compared to rain gauge stations in the vicinity and to weather radar data, showing good agreement.