Non-Overlapping Identical Division of Integer Set

This paper develops a systematic approach to identically dividing a consecutive integer set into two or more non-overlapping subsets, where each subset generates consecutive difference lags with reduced redundancy. Unlike the identical nested partitioning scheme which assigns every element in the integer set to a subset, the proposed identical division scheme allows some integers to remain unassigned. This flexibility enables more effective subset formation with reduced redundancy. A general expression for selecting subset elements is devised to facilitate systematic design, and the resulting difference lags are analyzed. Compared to identical nested partitioning schemes, the proposed division method achieves higher difference lags for the same number of elements used in each subset. As an example of practical applications, the proposed identical division scheme is employed to efficiently design sparse step-frequency radar waveforms for interference-free multi-radar operation, with its effectiveness demonstrated through target range estimation.