Identical Partitioning of Consecutive Integer Set

In this paper, we develop a scheme to partition a one- or multi-dimensional consecutive integer number set into multiple identical, possibly rotated, subsets. The proposed technique first exploits one-dimensional nested subsets, and the results are extended to achieve two- and multi-subset partitioning as well as in two- and multi-dimensional spaces. The number of consecutive lags in each case is examined. The results are useful to various sensing and communication applications, and sparse step-frequency waveform design for range estimation in automotive radar is demonstrated as an example.