System for Algorithmic Construction of Signal Waveforms with Optimal Autocovariance Properties Available to Purchase

A system for sorting and representing all possible waveforms has been developed for those classed as finite duration, balanced, constant amplitude, and frequency modulated. They are first categorized according to their frequency‐time schedules into subclasses that are ranked in terms of the ratio between average and midrange frequencies. By representing successive intervals between time‐axis crossings as elements of isosum integer partitions, it is then possible through primitively recursive relations to enumerate and generate in a well‐ordered manner all possible waveforms in unambiguously defined subclassses. The waveforms can then be examined in sequence for optimal attainment of desired signal‐processing properties. Furthermore, the subclasses themselves have a natural order that permits the entire parent class to be surveyed. The technique is applied to the problem of measuring an unknown clustered multipath distribution by replica cross‐correlation. In each category of waveforms, an optimal subset is found which occupies a limited area of the map of isosum integer partitions. Relationships are developed among multipath distribution extent, waveform autocovariance features, and the computation time required for the resolution process. One example is to seek waveforms whose autocovariance has maximum lag in which it does not vary more than a specified amount. In a particular class, this yields waveforms whose autocovariance has essentially only one isolated sidelobe in addition to the central peak. This permits an explicit resolution of the multipath structure using Rank 3 sets of linear equations. As measured by the number of digital computer cycles required in the calculation, these optimal waveforms are 10 times more effective than linear FM or pseudorandom noise pulses of equal time‐bandwidth product.