Section: New Results
Application of the Continuous Exact relaxation to Channel and DOA sparse estimation problems
Participants : Emmanuel Soubies, Laure Blanc-Féraud.
This work is made in collaboration with Adilson Chinatto, Cynthia Junqueira, João M. T. Romano (University of Campinas, Brazil) and Pascal Larzabal, Jean-Pierre Barbot (ENS Cachan, SATIE Lab).
This work is devoted to two classical sparse problems in array processing: Channel estimation and DOA (Direction Of Arrivals) estimation. We show how our results on optimization [1] , [14] , [17] can be used, at the same computational cost, in order to obtain improvement in comparison with optimization (usually used) for sparse estimation. Moreover, for the DOA case, we show that our analysis conducted in the Single Measurement Vector (SMV) case [1] can be generalized to the Multiple Measurement Vectors (MMV) case. In that case, the variable is not a vector of but a matrix of where is the signal length and the number of snapshots. Hence, one wants to apply sparsity to the rows of , i.e. must have a small number of nonzero rows, instead of applying the sparsity on all the components of . This results in a row-structured sparsity penalty which is modelled using a mixed - norm.
Finally, numerical experiments demonstrate the efficiency of the proposed approach compared to classical methods as relaxation, Iterative Hard Thresholding or MUSIC algorithms and that it can reach the Cramer Rao Bound in some cases [4] .