Virtual array interpolation for coprime arrays: a signal reconstruction perspective

Coprime arrays can highly increase degree-of-freedom by operating the second-order virtual signal. However, the corresponding virtual array is discontiguous, and thus most existing direction-of-arrival estimation approaches fail to utilise all received information. To avoid performance loss, the authors intend to convert the discontiguous array into a contiguous one in this Letter and propose two virtual array interpolation algorithms for the coprime array from the perspective of signal reconstruction. By promoting the sparsity of the signal via simplified atomic norm minimisation and enhanced matrix completion, respectively, the two algorithms can effectively reconstruct the signal of the interpolated virtual array in a gridless manner. Simulation results are presented to demonstrate the performance advantage of the two proposed approaches.