4.15. A certain radar has the following specifications: single pulse SNR corresponding to a reference range is . The probability of detection at this range is . Assume a Swerling I type target. Use the radar equation to compute the required pulse widths at ranges so that the probability of detection is maintained.

10–10W PD = 0.95 Tfa = 8 minutes τ = 2μs B = 2MHz f0 = 10GHz R = 100Km Pfa 0.9 Pfa 15dB Pm = 0.15 Pfa VT 1.5° 35°

τ = 2μs fr = 400Hz Pfa 10 –6 =

PD 1 e –SNR I0( –4SNRlnu)du Pfa 1

= – ∫

PD SNR = 10dB Pfa = 0.01 PD = 0.8 Pfa 10 –5 =

R0 = 200Km 10dB PD = 0.95 R = 220Km