Novel Sparse Linear Array Based on a New Suboptimal Number Sequence with a Hole-Free Difference Co-Array

In this paper, we propose a new sparse linear array (SLA) that enjoys a hole-free difference co-array (DCA) and closed-form expressions for its sensor positions. The proposed configuration is valid for arrays containing seven or more sensors (N >= 7). Exact expressions for the array aperture and achievable degrees of freedom (DOFs) have been derived. Numerical simulations were performed using MATLAB to reinforce the theoretical understanding. The main aim of this study is not to claim superiority over any existing SLA design, but to report that we have found a new number sequence that can act as an SLA. Except for being highly susceptible to mutual coupling, the proposed array has all the desirable features of a good SLA. We observed that the proposed array is on par with other SLAs for N < 20. However, for 20 or more sensors, the array aperture does not scale rapidly in proportion to the added sensors and fails to match the resolution and/or DOFs offered by other sparse arrays. Nevertheless, the proposed sparse array is based on a unique and previously unknown number sequence.