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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)
  • Radar Blind Distance: Rc=200m
  • Integration Efficiency in the receiver: Ei=0.9
  • Internal Radar Losses: L=6dB
  • 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!

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The classic radar range equation can be used to solve this problem. Just google "radar range equation" if you are not familiar with it (although you should be if you are asking this question). All of the information given in your question can be used to deduce the variables in the range equation, one of which is your unknown, the peak power. Once the peak power is known the average power can be calculated from it, the pulse repetition rate and the pulse width.

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