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 subspace averaging (SA) approach, and hence it is named sparse subspace 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 l0-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 approximately 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.

This work was supported by the Ministerio de Ciencia, Innovación y Universidades under grant TEC2017-92552-EXP (aMBITION), by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under grants TEC2017-86921-C2-2-R (CAIMAN), PID2019-104958RB-C43 (ADELE), and BES-2017-080542, and by The Comunidad de Madrid under grant Y2018/TCS-4705 (PRACTICO-CM)