DCD-RLS Adaptive Filters With Penalties for Sparse Identification

• Published in: IEEE transactions on signal processing Vol. 61; no. 12; pp. 3198 - 3213
• Main Authors: Zakharov, Yuriy V., Nascimento, Vitor H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithms; Adaptive filter; Adaptive filters; Algorithms; Applied sciences; Complexity theory; Cost function; DCD algorithm; Design engineering; Detection, estimation, filtering, equalization, prediction; dichotomous coordinate descent (DCD); Exact sciences and technology; Field programmable gate arrays; Fines & penalties; FPGA; Hardware; Information, signal and communications theory; Mathematical analysis; Microsoft Windows; penalty function; Recursive; reweighting; RLS; Signal and communications theory; Signal processing algorithms; Signal, noise; sparse representation; Studies; Telecommunications and information theory; Transaction processing; Performance evaluation; Adaptive algorithm; FPGA; Adaptive filtering; Iterative method; Field programmable gate array; Adaptive filter; Recursive algorithm; Implementation; reweighting; Penalty function; dichotomous coordinate descent (DCD); Algorithm performance; Simulation; Least squares method; Algorithm complexity; Transverse filter; Recursive method; Signal processing; RLS; Sparse representation; Oracle; DCD algorithm
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2013.2258340

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 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 operations per sample, where is the filter length. For transversal adaptive filters, the algorithms require only 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.