Generalized Dilated Array Scheme Exploiting High-Order Virtual Co-Array for a Moving Platform

Recently, array motion, as an approach to improve the uniform degrees-of-freedom (uDOFs) of sparse linear arrays (SLAs), has received increasing attention. By applying the dilation method to the array geometry, the maximum uDOFs of a dilated array on a moving platform can be tripled through the synthetic array resulting from array motion. Furthermore, through multiple uniform shifts and synthesis, the dilation coefficient can be further increased, as well as the number of uDOFs. However, the existing dilation scheme is only applicable to the second-order statistics based models and does not consider those designed based on high-order cumulants. Besides, in scenarios with multiple shifts, the shift interval is uniform, which actually includes redundancy. In this work, the concept of shift sequence is introduced, which has no uniformity constraint and can be any sparse set. On this basis, a generalized array dilation scheme adapted to arbitrary order cumulants and shift sequence is proposed, which is an extended version of the dilation scheme for second-order statistics based models with uniform shift sequence, and the optimal value of the dilation coefficient is derived based on symmetrically defined 2q-th-order cumulants and asymmetrically definedr-th-order cumulants, respectively. It is revealed that, by increasing the order to cumulants and using sparse shift sequences, a much higher number of uDOFs is achieved. Simulation results are provided to demonstrate the effectiveness of the proposed generalized array dilation scheme.