Adaptive filters for sparse system identification

Sparse system identification has attracted much attention in the field of adaptive algorithms, and the adaptive filters for sparse system identification are studied. Firstly, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed ℓ2,1 norm of the adaptive filter\u27s coefficients. A block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Meanwhile, the proposed block-sparse proportionate idea has been extended to both the proportionate affine projection algorithm (PAPA) and the proportionate affine projection sign algorithm (PAPSA). Secondly, a generalized scheme for a family of proportionate algorithms is also presented based on convex optimization. Then a novel low-complexity reweighted PAPA is derived from this generalized scheme which could achieve both better performance and lower complexity than previous ones. The sparseness of the channel is taken into account to improve the performance for dispersive system identification. Meanwhile, the memory of the filter\u27s coefficients is combined with row action projections (RAP) to significantly reduce the computational complexity. Finally, two variable step-size zero-point attracting projection (VSS-ZAP) algorithms for sparse system identification are proposed. The proposed VSS-ZAPs are based on the approximations of the difference between the sparseness measure of current filter coefficients and the real channel, which could gain lower steady-state misalignment and also track the change in the sparse system --Abstract, page iv

Frequency Controlled Noise Cancellation for Audio and Hearing Purposes

Methods for hearing aids sought to compensate for loss in hearing by amplifying signals of interest in the audio band. In real-world, audio signals are prone to outdoor noise which can be destructive for hearing aid.  Eliminating interfering noise at high speed and low power consumption became a target for recent researches. Modern hearing compensation technologies use digital signal processing which requires minimum implementation costs to reduce power consumption, as well as avoiding delay in real time processing. In this paper, frequency controlled noise cancellation (FCNC) strategy for hearing aid and audio communication is developed with low complexity and least time delay. The contribution of the current work is made by offering a method that is capable of removing inherent distortion due filter-bank insertion and assigning adaptive filtering to a particular sub-band to remove external noise. The performance of the proposed FCNC was examined under frequency-limited noise, which corrupts particular parts of the audio spectrum. Results showed that the FCNC renders noise-immune audio signals with minimal number of computations and least delay. Mean square error (MSE) plots of the proposed FCNC method reached below -30 dB compared to -25 dB using conventional sub-band method and to -10 dB using standard full-band noise canceller. The proposed FCNC approach gave the lowest number of computations compared to other methods with a total of 346 computations per sample compared to 860 and 512 by conventional sub-band and full-band methods respectively. The time delay using FCNC is the least compared to the other methods

Proportionate Recursive Maximum Correntropy Criterion Adaptive Filtering Algorithms and their Performance Analysis

The maximum correntropy criterion (MCC) has been employed to design outlier-robust adaptive filtering algorithms, among which the recursive MCC (RMCC) algorithm is a typical one. Motivated by the success of our recently proposed proportionate recursive least squares (PRLS) algorithm for sparse system identification, we propose to introduce the proportionate updating (PU) mechanism into the RMCC, leading to two sparsity-aware RMCC algorithms: the proportionate recursive MCC (PRMCC) algorithm and the combinational PRMCC (CPRMCC) algorithm. The CPRMCC is implemented as an adaptive convex combination of two PRMCC filters. For PRMCC, its stability condition and mean-square performance were analyzed. Based on the analysis, optimal parameter selection in nonstationary environments was obtained. Performance study of CPRMCC was also provided and showed that the CPRMCC performs at least as well as the better component PRMCC filter in steady state. Numerical simulations of sparse system identification corroborate the advantage of proposed algorithms as well as the validity of theoretical analysis