Sparse Subspace Averaging for Order Estimation

This paper addresses the problem of source enumeration for arbitrary geometry arrays in the presence of spatially correlated noise. The method combines a sparse reconstruction (SR) step with a sub-space averaging (SA) approach, and hence it is named sparse sub-space averaging (SSA). In the first step, each received snapshot is approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the ` 0 -norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which ap-proximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. Our simulation results show that SSA provides robust order estimates under a variety of noise models.