Order Estimation via Matrix Completion for Multi-Switch Antenna Selection

This letter addresses the problem of order estimation for uniform linear arrays (ULAs) with multi-switch antenna selection in the small-sample regime. Multi-switch antenna selection results in a data matrix with missing entries, a scenario for which existing order estimation methods that build on the eigenvalues of the sample covariance matrix do not perform well. A direct application of the Davis-Kahan theorem allows us to show that the signal subspace is quite robust in the presence of missing entries. Based on this finding, this letter proposes a matrix completion (MC) subspace-based order estimation criterion that exploits the shift-invariance property of ULAs. A recently proposed shift-invariant matrix completion (SIMC) method is used for reconstructing the data matrix, and the proposed order estimation criterion is based on the chordal subspace distance between two submatrices extracted from the reconstructed matrix for increasing values of the dimension of the signal subspace. Our simulation results show that the method provides accurate order estimates with percentages of missing entries higher than 50
$\%$
.