Adaptive algorithm for sparse system identification using projections onto weighted ℓ1 balls

This paper presents a novel projection-based adaptive algorithm for sparse system identification. Sequentially observed data are used to generate an equivalent number of closed convex sets, namely hyperslabs, which quantify an associated cost criterion. Sparsity is exploited by the introduction of appropriately designed weighted ℓ₁ balls. The algorithm uses only projections onto hyperslabs and weighted ℓ₁ balls, and results into a computational complexity of order O(L) multiplications/additions and O(Llog₂ L) sorting operations, where L is the length of the system to be estimated. Numerical results are also given to validate the proposed method against very recently developed sparse LMS and RLS type of algorithms, which are considered to belong to the same type of algorithmic family.