5-11] DETERMINATION OF SIGNAL'S TIME OF ARRIVAL 281 



and the radio frequency of a magnetron oscillator normally varies randomly 

 from pulse to pulse by a small amount. The statistics of signal parameter 

 distributions would have to be considered in a more realistic optimum 

 receiver, and the result would be somewhat different from that derived 

 in this paragraph. 



One should not make the mistake of thinking that great gains over 

 current practice can be attained through some complicated optimizing 

 scheme. Actually, most radar systems are tuned up in this respect about 

 as far as they can be when consideraton is taken of limitations in the 

 state of the art and fluctuations in the parameters of the input signals 

 with which the systems must contend. For instance, a pulse radar employ- 

 ing a self-excited magnetron oscillator is not coherent because it is not 

 normally feasible to control the frequency of the power oscillator to a 

 sufficient degree. Because of pulse-to-pulse frequency fluctuations, the 

 receiver must operate upon the envelope of the signal, and it will normally 

 employ a non-linear device to generate it. In this case, the best that can 

 be done is to match the low-pass equivalent of the IF amplifier to the 

 pulse envelope, and this is quite normally done as a matter of course. 

 When there are a number of pulses available in an echo, some provision 

 is usually made to integrate them. Most commonly, this is accomplished 

 on the display where the decay time of the phosphor may be matched to 

 the signal duration. The point is that insofar as is possible receivers are 

 normally matched to the signal waveform, and most radar systems can 

 be quite legitimately regarded as correlation or matched filter radars, 

 although possibly somewhat degraded from the optimum type. 



5-11 APPLICATION TO THE DETERMINATION OF A 

 SIGNAL'S TIME OF ARRIVAL 



An important function of radar systems is the measurement of a target's 

 parameters such as its range, velocity, size, and location. In this paragraph 

 we shall develop some characteristics of a receiver which provides optimum 

 target tracking in a manner similar to that used in the preceding paragraph 

 to develop the properties of matched filter receivers for optimum target 

 detection. We shall restrict our analysis to the problem of measuring the 

 time of arrival of the signal. Since both angle and range are measured by 

 comparing the return signal with angle and range reference signals which 

 are generated as functions of time, the following discussion can be applied 

 to both types of tracking. As in Paragraph 5-10, the receiver will be sup- 

 posed to be a linear filter, and where applicable, the notation introduced in 

 that paragraph will be adopted. 



Various operational definitions might be used to fix the arrival time of a 

 signal. The mean, the median, or the mode of the distribution of the signal 



