## Sophisticated Signals and the Uncertainty Principle in RadarThis book is devoted to some of the problems encountered in the theory of sophisticated signals used in radar. The term sophisticated signal is under stood to mean a signal for which the product of the signal duration by the spectrum width substantially exceeds unity. Although it is impossible to draw an exact borderline between simple and sophisticated signals, the term "sophisticated signal" is sufficient to define one of the principal characteristics of modern radar. Recently, various sophisticated signals (frequency-modulated pulses, coded groups, phase-modulated signals, etc.) have found use in radar. This makes it possible to improve the resolution, to ensure simultaneous measurements of the range and range rate of a target, to elecrically scan over finite angular dimensions, etc. Although the realization of such potentialities is associated with substantial difficulties, one can say with certainty that "classical" radar technology, which uses simple signals at constant frequency and duty cycle, yields to more complex methods based on the use of wide-band signals of the sophisticated structure. The properties of radar signals, which characterize the measurement of a target's range and range rate, are described by the Woodward ambiguity function. The role of this function is similar to that of the antenna pattern, i.e., the ambiguity function defines the accuracy and resolution of the range and range rate measurements to the same extent as the antenna pattern de fines the accuracy and resolution of the azimuth and elevation measurements. |

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### Contents

Pulse Compression Signals 1 Optimal Reception of SignalsMatched Filter | 1 |

2 Response of a Pulsed Signal to a Matched Filter Correlation Method | 6 |

3 Optimal Reception of FrequencyModulated Pulse Signals | 10 |

Copyright | |

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accuracy and resolution Af-sequences ambiguity function amplitude antenna pattern approximation arbitrary assumed autocorrelation function Barker codes circuit coefficients complex components compression ratio condition considered coordinates correlation function correlation integral corresponds criterion cross section defined depends determined eigenvalue envelope equation estimate expression factor finite FM signal Fourier transform frequency band frequency characteristic frequency modulation func function R(rj Gaussian given input signal instantaneous frequency integral interval linear magnitude matched filter matrix maximum negentropy noise obtain optimal receiver parameters particle phase errors polynomial possible power spectrum properties pulse duration quantum physics quasi-optimal radar range and range realizable received signal rectangular reflected signal result shown side lobes side-lobe level signal energy signal form signal s(t signal spectrum signal-to-noise ratio solution sophisticated signals spectra spectral density spectrum width spheroidal functions stationary phase method substantially target theorem tion uncertainty principle uncertainty relationship values vector wave function