Application to Binary Communications and Pulsed Radar Vacuum Channel

8 Application to Binary Communications and Pulsed Radar (Vacuum Channel) 

The previous subsections were primarily concerned with the behavior of the three-frequency nonlinear heterodyne system for applications in cw radar and analog communications. As such, a determination of the output signal-to-noise ratio (SNR)q was adequate to characterize the system. In this subsection, we investigate applications in digital communications and pulsed radar, and therefore examine system performance in terms of the error probability P. Evaluation of the probability of error under various conditions requires a decision criterion as well as a knowledge of the signal statistics we now investigate operation of the three-frequency nonlinear heterodyne scheme in the time domain rather than in the frequency domain. 

We begin with an investigation of binary communications and pulsed radar for both nonorthogonal and orthogonal signaling formats in the vacuum channel. In Section 7.3.9, we examine envelope probability distributions and 

We assume here, as previously, that when a signal is present the fields incident on the mixer are parallel, plane polarized, and spatially first-order coherent over the detector aperture. In general, therefore, the input to the square-law device, as previously [see (7.51)], will be two narrowband signals plus white Gaussian noise with zero mean resulting from the LO, over the band [0,/J. Thus 

In the time domain, the white Gaussian noise, which arises from the LO, can be expressed as [7.65] 

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