This paper presents a novel projection-based adaptive algorithm for sparsesignal and system identification. The sequentially observed data are used togenerate an equivalent sequence of closed convex sets, namely hyperslabs. Eachhyperslab is the geometric equivalent of a cost criterion, that quantifies"data mismatch". Sparsity is imposed by the introduction of appropriatelydesigned weighted $\ell_1$ balls. The algorithm develops around projectionsonto the sequence of the generated hyperslabs as well as the weighted $\ell_1$balls. The resulting scheme exhibits linear dependence, with respect to theunknown system's order, on the number of multiplications/additions and an$\mathcal{O}(L\log_2L)$ dependence on sorting operations, where $L$ is thelength of the system/signal to be estimated. Numerical results are also givento validate the performance of the proposed method against the LASSO algorithmand two very recently developed adaptive sparse LMS and LS-type of adaptivealgorithms, which are considered to belong to the same algorithmic family.
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