Half-Inverted Array Design Scheme for Large Hole-Free Fourth-Order Difference Co-Arrays

Linear sparse arrays with fourth-order cumulantprocessing can resolveO(N4)directions-of-arrival (DOAs) usingNphysical sensors, provided that the fourth-order differenceco-array Delta 4contains a contiguous segment of sizeO(N4).Furthermore, if Delta 4has no holes, then the received data can befully exploited in subspace-based DOA estimators. However, fewexisting arrays attain large hole-free Delta 4. Many existing arraysdesigned for Delta 4are constructed from two smaller arrays, calledthe basis arrays. Nevertheless, such arrays either restrict the basisarrays to certain types or have no guarantee of hole-free Delta 4.Thispaper proposes the half-inverted (HI) arrays, parameterized bytwo basis arraysS(1)andS(2), the shifting parameterM,andthescaling parameter sigma.AnHIarrayconsistsofS(1)and an inverted,scaled, and shifted version ofS(2). HI arrays are guaranteedwith hole-free Delta 4over a range of(M,sigma)pairs. This propertyunifies several existing arrays with hole-free Delta 4and admitsan optimization problem over(M,sigma). The half-inverted generalhole-free (HIGH) scheme is defined as the HI array with a closed-form and optimized(M,sigma)pair determined by the second-orderco-arrays of the basis arrays. The HIGH scheme enjoys a largehole-free Delta 4. The shift-scale representation (SSR) is presentedto study Delta 4of HI arrays visually. From these results, the half-inverted array based on second-order optimization and extendedshift (HI-SOES) is proposed. For a fixedN, HI-SOES synthesizesa hole-free Delta 4larger than an existing array. Numerical examplesdemonstrate the DOA estimation performance of HI arrays andexisting arrays.

Automated summary

This paper introduces a new array structure (HI array) that achieves a large hole-free Delta 4 through optimized design, improving the performance of DOA estimation.