Optimized Sparse Array Design Based on the Sum Coarray

The number of elements of a uniform linear array (ULA) is the main bottleneck in many applications in array processing in terms of cost and power consumption. This motivates the use of sparse arrays where some of the elements are removed. However, designing a sparse array configuration with the smallest number of elements that preserves the full array beam pattern is generally NP hard. In this paper we adopt work in multiple-input-multiple-output (MIMO) radar to study a sparse array composed of two sub apertures. We derive the minimal number of elements required using this design, showing that in general there are two optimal solutions. Next, we present an extension of this approach beyond two sub apertures. By optimizing the number of sub apertures, we prove that the optimal array configuration is related to the notion of prime factorization. This allows to achieve a significant reduction in the number of elements.