3-5] DETECTION PROBABILITY FOR A PULSED DOPPLER RADAR 163 



cycles specifically incorporated. For a gated pulse doppler system the noise 

 is gated with the same duty factor as the signal so that dg = ds in Equation 

 6-39. 



Detecting only the fundamental doppler signal in a filter output corre- 

 sponds to the case of detecting a single pulse in Paragraph 3-3. Thus the 

 basic single-scan probability of detecting a fluctuating target should be 

 given by the expression in Equation 3-31 with the factor K correspond- 

 ing to the integration of a single pulse. 



In order to account for certain features of the pulsed doppler system, 

 this basic probability must be modified somewhat. This modification is due 

 to the straddling of a pulse by contiguous range gates and the eclipsing of 

 part of the received pulse by the transmitted pulse. These effects act to 

 decrease the single-scan probability of detection from its basic value. This 

 reduction is denoted by the factor F(R). Thus the probability of detection 

 of a fluctuating target by a pulsed doppler radar can be represented by 



Prf = F(/?)e-^'(«/«o)4. (3_47) 



The Straddling and Eclipsing Factor. Range gate straddling refers 

 to the situation when the received signal simultaneously falls within two 

 range channels. This situation is illustrated in Fig. 3-13, where the received 



n 



I I I I I I ^ I I I I I I I I I I Ml I 



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I 



n 



Transmitted Pulses 



Received Pulses 



Fig. 3-13 Range Gate Straddling. 



pulse lies partly in channel 2 and partly in channel 3. Since the gating of 

 only a fraction of the received pulse into a given channel is equivalent to 

 decreasing the duty ratio by this factor and since the noise in that channel 

 is undiminished, the signal power in the channel will be proportional to the 

 square of the fraction of the pulse within the channel gate. Thus, if a 

 fraction a of the received pulse falls within gate k and the fraction 1 — a 

 falls within gate ^ + 1, the signal power in the first gate will be proportional 

 to a^ while that in the second channel will be proportional to (1 — a)^. 

 When half the pulse lies in each gate, there will be a loss of 6 db in each 



