1-5] THE MODULATION OF RADAR SIGNALS 25 



A = A^{\ ■\- 771 COS co„/) (1-24) 



where aj„ = modulating frequency (aj^ ^ w) and m — modulation ratio 

 {m < 1), then, each of the terms of the product (Ei X Er) would contain 

 modulation sidebands. For example, the d-c term would now become 



Ao . mAo n nc\ 

 1 cos co,„/ (1-25) 



T IT 



and the fundamental frequency term would become 



'-y sin w/ H ^ [sin(co -(- w™)/ — sin(w — w™)/] (1-26) 



and so on for the higher harmonics. 



If this (Ei X Er) product were then passed through a filter, F(ju), 

 which eliminated the d-c term and the fundamental frequency u and all 

 its harmonics, the final output would be 



(Ei X Er) X F(jc^) = '-^ cos co„,/. (1-27) 



TT 



Thus, we observe, the frequency and the magnitude of the modulation 

 intelligence are recovered from the incoming wave by the product-taking 

 procedures. The procedures just described are often referred to as de- 

 modulation or detection. 



A third type of product-taking device closely resembles the basic model 

 of Fig. 1-17. The incoming signal is multipled by a reference signal gener- 

 ated within the radar receiver. One form of this process is known as 

 7nixing or heterodyning. In this process, a cross-product is taken between 

 the incoming signal and a locally generated signal. This process converts 

 the microwave signal to a much lower frequency, which may be filtered 

 and amplified by relatively simple electronic techniques. 



Two general forms of microwave mixing are commonly used, noncoherent 

 mixing and coherent mixing. In coherent mixing, the phase of the locally 

 generated signal is made to have a known relationship to the phase of the 

 transmitted signal. This type of mixing makes it possible to detect the 

 phase and frequency modulations introduced by target motion. 



The extraction of angle and range information from the received signals 

 is almost always accomplished by a cross-product of the received intel- 

 ligence and an internally generated reference signal. 



The detailed analysis of the various means for extracting target intel- 

 ligence from radar signals — and the problems that arise in these processes 

 — forms a major portion of this book. Chapter 3 and Chapters 5 through 9 

 are all concerned with various phases of these problems. 



