1-Bit Sparse Gridless Super-Resolution Doa Estimation For Coprime Arrays

Direction of Arrival (DOA) estimation using 1-bit analog-to-digital converters (ADCs) offers significant cost, power, and hardware complexity reduction for sensor arrays. We propose a 1-bit sparse super-resolution DOA method for coprime arrays to achieve search-free DOA estimation, under the assumption of uncorrelated sources. The approach extends gridless DOA estimation for coprime arrays based on sparse super-resolution (SR) theory to 1-bit measurements. Using the arcsine law, a scaled version of the full precision covariance matrix can be recovered from the 1-bit data. The vectorized covariance matrix becomes the effective measurements from the coprime virtual array, and then the DOA estimation problem is expressed as an infinite-dimensional atomic norm minimization problem in the continuous angle domain. The corresponding dual problem is converted to a finite semidefinite program with linear matrix inequality constraints, that is solvable in polynomial time. Finally, the search-free DOA estimates are obtained using the unit-circle zeros of a nonnegative polynomial formed from the dual polynomial, followed by an ℓ1 norm minimization. The angular resolution and accuracy of the proposed method is compared to state-of-the-art approaches such as 1-bit and full-precision versions of spatially smoothed MUSIC and a discrete offgrid method, as well as the full-precision gridless SR method.