A novel adaptive algorithm is derived for sparse channel identification in the presence of Symmetric α-Stable (SαS) noise. The algorithm is based on the minimization of a new cost function, which is the sum of two terms. The first term is the distance between the previous and the current channel estimate. The distance metric is Riemannian, the same as in the improved-proportionate normalized least-mean-square (IPNLMS) algorithm, so that the sparse nature of the filter taps is taken into account. The second term depends on an appropriately defined 1-norm of the a posteriori estimation error and ensures robustness under SαS noise. The resulting algorithm, the so-called sign-IPNLMS (sIPNLMS), has linear computational complexity with respect to its filter coefficients. The superior performance of the sIPNLMS algorithm over the original IPNLMS, the recursive least-squares (RLS), and the normalized least-mean-square (NLMS) is shown by identifying two measured, sparse, underwater acoustic channels under the presence of recorded snapping shrimp ambient noise and simulated SαS noise. In addition, our proposed algorithm shows similar performance with IPNLMS under Gaussian noise and hence it becomes promising for either impulsive or non-impulsive noise environments.
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