DCD-RLS Adaptive Filters With Penalties for Sparse Identification

In this paper, we propose a family of low-complexity adaptive filtering algorithms based on dichotomous coordinate descent (DCD) iterations for identification of sparse systems. The proposed algorithms are appealing for practical designs as they operate at the bit level, resulting in stable hardware implementations. We introduce a general approach for developing adaptive filters with different penalties and specify it for exponential and sliding window RLS. We then propose low-complexity DCD-based RLS adaptive filters with the lasso, ridge-regression, elastic net, and l(0) penalties that attract sparsity. We also propose a simple recursive reweighting of the penalties and incorporate the reweighting into the proposed adaptive algorithms to further improve the performance. For general regressors, the proposed algorithms have a complexity of O(N-2) operations per sample, where N is the filter length. For transversal adaptive filters, the algorithms require only O(N) operations per sample. A unique feature of the proposed algorithms is that they are well suited for implementation in finite precision, e.g., on FPGAs. We demonstrate by simulation that the proposed algorithms have performance close to the oracle RLS performance.