New calculation methods for echo-ranging ambiguity

In correlation echo ranging the ambiguity, or square of the signal autocorrelation envelope, is important, and two new approaches are presented that speed up general ambiguity calculations. Some signals such as linear FM can be represented by lines in a frequency-time plot, and for two such lines the cross ambiguity is associated with the point of crossing and depends on the angle of crossing. This method is extended to curved lines, including lines that touch rather than cross. Other signals have a noiselike modulation, and may be conveniently described by a distribution of spectral intensity in the frequency-time plot. For two such noise signals the mean value of the cross ambiguity depends very simply on the overlap of the two distributions. In the limit the two approaches are shown to give answers consistent with one another. In one illustrative application it is shown that, with symmetrical pulse forms, a high ambiguity at the extremes of the ambiguity diagram is always accompanied by an ambiguity concentration near the origin. In another example the ambiguity diagrams and general behavior are calculated for straight and slightly curved lines (FM pulses), for both the narrowband and wideband cases.