On the optimum range resolution of radar signals in noise

Optimum radar resolution is recognized to be a problem in distinguisltmg between different possible target configurations. Radar reception systems which perform optimum range resolution are then designed using the principles of statistical decision theory. In particular, the design of the optimum resolution system is carried out for a squared-error loss function, modified to provide extra penalties for wrong guesses about the number of targets present. Such a system is capable of simultaneously deciding the number of targets present, their spatial positions (ranges) and their relative amplitudes. The analysis also includes a discussion of an optimum device for the resolution of distributed (clutter-like) targets. HE ability to resolve multiple-echo signals in time determines the range resolution of radar systems. The resolution rule-of-thumb for pulse radars is that echo pulses separated by a pulse length can be resolved, but echo pulses which overlap to any significant extent appear as only one target. Woodward' has developed a generalization of this rule which is applicable even for radar (sounding) signals whose time-bandwidth products are larger than unity. After defining the so-called Radar Ambiguit,y Function, Woodward infers that the time resolution cell for any signal is equal to the reciprocal of the (sounding) signal bandwidth. However, this classical definition of resolution takes only qualitative account of the fact that the signals are embedded in noise. Even very narrow-band signals should be resolvable for arbitrarily small time separations in the complete absence of noise. We intuitively expect, then, that our ability to resolve two or more known signals in noise should depend, not only on the signal bandwidth, but on the echo-to-noise power ratio. In this paper, we shall treat the resolution problem as a problem of combined signal detection and signal estimation. Systems which achieve optimum range resolution will be derived, and their characteristics compared with those systems which are optimum only in the single-target detection sense. Various authors have recognized the need for treating the general signal resolution problem in a more precise fashion than can be done by appeals to Woodward's ambiguity function alone. Swerling' has analyzed the problem of resolving two radar targets at the same range, but at (slightly) different angles within the antenna beamwidth. Helstrom3*4 discusses the problem of distinguishing between two noise-corrupted signals whose form and location are known exactly. In this paper, we shall attempt first to formulate a suitable definition of radar resolution and then to apply …