# How to obtain Peak and Average Power in Radar Detection?

I have a problem solving a RADAR exercise.

The specifications of the 2D radar antenna are the following ones:

• Dimensions: Horizontal Lh=5m ; Vertical Lv=0.8m
• Turn rate: 12 rpm
• Max range of operation: 80 NM (1NM=1852m) being able to detect a constant RCS target of 10m^2 in uniform rain conditions with intensity I = 16mm/hour
• Pulse Repetition Frequency: PRF=850Hz (Rectangular pulse transmitted)
• Integration Efficiency in the receiver: Ei=0.9
• Noise factor of the receiver: F=4dB
• 2 operation frequencies: 2.7GHz (S Band) and 5.4GHz (C Band)
• Attenuation caused by rain with intensity I: 1.6dB (@2.7GHz) and 12dB (@5.4GHz)
• Minimum SNR required at the detector input : SNRmin=17dB
• Probability of detection: Pd=0.85
• Probability of false alarm: Pfa=10^(-6)
• The beamwidth of a typical electrically large antenna is 1.2*wavelength/dimension (horizontal or vertical) [rad]

I don't know how to compute: The peak (Pt) and average power (Pm) required to satisfy the detection requirements for the 2 proposed frequencies of operation

Result:

• Pt = 129.7 kW = 51.13 dBW / Pm = 146.8 W = 21.67 dBW @2.7 GHz
• Pt = 712.8 kW = 58.53 dBW / Pm = 807.2 W = 29.07 dBW @5.4 GHz

I will appreciate all your suggestions. Thank you!