A radar with a phased array antenna conducts a search using a 1500-beam search raster. That is, it steps through 1500 beam positions that span a certain angular area. It transmits one pulse per beam. The radar uses range gates separated by \(10 \mathrm{~m}\). The output of each range gate is sent to a bank of Doppler filters with a width of \(1000 \mathrm{~Hz}\) each. Thus, the signal processor consists of a set of range gates with a bank of Doppler filters connected to each range gate output. The output of the signal processor consists of a range-Doppler array of signals that consists of \(\mathrm{MN}\) elements where \(\mathrm{M}\) is the number of range gates and \(\mathrm{N}\) is the number of Doppler filter outputs. During the particular search of interest, the detection processor covers a range extent of \(10 \mathrm{~km}\) and a Doppler extent of \(25 \mathrm{~km}\). The design specifications state that, in this mode, the radar must have less than one false alarm every 10 scans through the search raster. What is the required \(P_{f a}\) in each range-Doppler-beam cell needed to support this requirement?