A survey on active noise control in the past decade–Part II: Nonlinear systems

Robust and sparsity-aware adaptive filters: A Review

Recently, the logarithmic hyperbolic cosine adaptive filter (LHCAF) was proposed and was seen to demonstrate excellent robustness against impulsive interference. However, for the modelling of sparse systems, it may not provide optimal performance as it does not take into account the sparse nature of the system. To improve the modelling accuracy and convergence performance, a sparsity aware zero attraction LHCAF (ZA-LHCAF) and a reweighted zero attraction LHCAF (RZA-LHCAF) is proposed. To further improve the performance for modelling of sparse systems in impulsive environments, a joint logarithmic hyperbolic cosine function (JLHCF) is proposed as the cost function. The corresponding update rule, called the joint logarithmic hyperbolic cosine adaptive filter (JLHCAF) is deduced and the bound on learning rate is derived. A room equalization scenario is also considered and an improved sparsity aware robust algorithm based on JLHCF, namely the filtered-x JLHCAF (Fx-JLHCAF) is proposed for the same. Extensive simulation studies carried out for different system identification scenarios, under Gaussian and non-Gaussian disturbances and a room equalization scenario, demonstrate the superior performance achieved by JLHCAF over existing sparsity aware robust adaptive filters.

Joint Logarithmic Hyperbolic Cosine Robust Sparse Adaptive Algorithms

An Optimistic Design of 16-Tap FIR Filter with Radix-4 Booth Multiplier Using Improved Booth Recoding Algorithm

Low complexity and ease of implementation provided by zero-attraction-based least mean square (LMS) algorithms have made them popular candidates for sparse system identification. In this brief, a new sparsity aware norm based on a modified Versoria function is proposed, and utilized to develop a novel Versoria zero-attraction LMS (VZA-LMS) algorithm. Moreover, to make the proposed algorithm independent of the zero-attraction parameter, an adaptive zero attractor VZA-LMS (A-VZA-LMS) algorithm is also derived. The bound on learning rate, which ensures convergence in the mean and mean square sense, is derived. Computational complexity of the proposed algorithms are also compared with the existing zero-attraction-based LMS algorithms. Simulation results show that the proposed algorithms provide improved performance over the state-of-the-art algorithms.

Adaptive Modified Versoria Zero Attraction Least Mean Square Algorithms

Single constant multiplication (SCM) and multiple constant multiplications (MCM) are among the most popular schemes used for low-complexity shift-add implementation of finite impulse response (FIR) filters. While SCM is used in the direct form realization of FIR filters, MCM is used in the transposed direct form structures. Very often, the hybrid form FIR filters where the sub-sections are implemented by fixed-size MCM blocks provide better area, time, and power efficiency than those of traditional MCM and SCM based implementations. To have an efficient hybrid form filter, in this paper, we have performed a detailed complexity analysis in terms of the hardware and time consumed by the hybrid form structures. We find that the existing hybrid form structures lead to an undesirable increase of complexity in the structural-adder block. Therefore, to have a more efficient implementation, a variable size partitioning approach is proposed in this paper. It is shown that the proposed approach consumes less area and provides nearly 11% reduction of critical path delay, 40% reduction of power consumption, 15% reduction of area-delay product, 52% reduction of energy-delay product, and 42% reduction of power-area product, on an average, over the state-of-the-art methods.

Efficient Shift-Add Implementation of FIR Filters Using Variable Partition Hybrid Form Structures

Adaptive exponential functional link network (AEFLN) is a recently developed linear-in-the-parameters nonlinear adaptive filter. It has been observed that the convergence performance of the AEFLN filter deteriorates in the presence of colored and/or correlated inputs. To overcome this issue, an affine projection algorithm (APA) based AEFLN (AEFLN-APA) filter is proposed in this brief. To reduce the hardware complexity of the proposed filter, an approximate AEFLN-APA filter is also developed. The proposed APA-based filters are found to provide improved modeling accuracy in nonlinear system identification scenarios. In this brief, the proposed nonlinear filters are also applied to active noise control (ANC) systems. An adaptive exponential filtered-s APA (AEFsAPA) is developed to enhance the noise mitigation capability of an ANC system. In addition, an approximate AEFsAPA is also formulated to achieve reduced-complexity implementation of AEFsAPA. Simulation results demonstrate the improved convergence behavior of the proposed schemes in nonlinear active noise mitigation scenarios.

Design of Nonlinear Filters Using Affine Projection Algorithm Based Exact and Approximate Adaptive Exponential Functional Link Networks

Zero-attraction-based adaptive filters are widely used for sparse system identification, where a suitable penalty function is integrated with the least mean square (LMS) framework to improve the convergence behavior of the identification process. In this brief, we have made an attempt to implement some of the most popular zero-attracting algorithms in hardware. The complexity of realization associated with these algorithms is investigated in detail. Following the above analysis, several architectural simplifications are proposed for the reduced-complexity implementation of their penalty functions. We then use these realizations to develop a set of novel design strategies for the efficient implementation of these algorithms. Simulation results show that the performance loss for the proposed algorithms is minimal compared to their standard versions. A detailed synthesis study is also carried out to validate the proposed structures, which demonstrates that the hardware overhead in the proposed designs is marginal compared to the existing delayed LMS architecture.

Analysis and Design of Unified Architectures for Zero-Attraction-Based Sparse Adaptive Filters

Distributed arithmetic (DA)-based approximate structures are used for efficient implementation of inner-products in various error-resilient applications. In the existing literature, most of these approximate architectures are developed by truncating the least significant bits (LSBs) of the inputs and/or the multiplying coefficients. The existing works do not provide any analytical study to evaluate and design an approximate structure. To address this issue, an analytical framework is proposed in this paper. It is shown that the analytical results match very closely with the Monte Carlo simulation results. The proposed framework reveals that the truncation of the LSBs of partial inner-products is a promising alternative to design more efficient DA architectures with less error. Following these observations, a novel approach to truncate the LSBs of partial inner-products, namely, a weight-dependent truncation strategy and its two variants with a suitable error compensation function are presented in this paper. Synthesis results, accuracy analysis, and evaluation in two commonly used error-tolerant applications demonstrate the superiority of the proposed architectures over the state-of-the-art DA-based approximate structures.

Dwaipayan Ray

Papers

Adaptive Modified Versoria Zero Attraction Least Mean Square Algorithms

Efficient Shift-Add Implementation of FIR Filters Using Variable Partition Hybrid Form Structures

Design of Nonlinear Filters Using Affine Projection Algorithm Based Exact and Approximate Adaptive Exponential Functional Link Networks

Analysis and Design of Unified Architectures for Zero-Attraction-Based Sparse Adaptive Filters

An Analytical Framework and Approximation Strategy for Efficient Implementation of Distributed Arithmetic-Based Inner-Product Architectures