This 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.