An expanding and shift scheme for constructing fourth-order difference coarrays

An expanding and shift scheme for efficient fourth-order difference coarray construction is proposed. It consists of two sparse subarrays, where one of them is modified and shifted according to the analysis provided. The number of consecutive lags of the proposed structure at the fourth order is consistently larger than two previously proposed methods. Two effective construction examples are provided with the second sparse subarray chosen to be a two-level nested array, as such a choice can increase the number of consecutive lags further. Simulations are performed to show the improved performance by the proposed method in comparison with existing structures.