At the airports, fast-scanning phased array radars are used to detect point-like targets, e.g., birds and drones. However, these radars do not possess Doppler processing and thus are not used for observation of the weather targets like precipitation events. A series of steps need to be performed, such as beamforming in elevation, target masking for weather-like targets, and Doppler processing to complete the signal processing chain for this kind of radar for weather-like targets. This paper focuses only on beamforming in elevation which is the first step in the direction of 3D wind field estimation for a fast-scanning phased array radar. The reiterative Minimum Mean Square Error (rMMSE) beamforming technique is proposed in this paper and has been used on real radar observations. The performance is analysed for the first time when noise is under or overestimated. The rMMSE beamformer has been compared with the Fourier (FR) and Capon (CP) beamformers.