Set-membership NLMS Research Articles

ReAdapt: A Reconfigurable Datapath for Runtime Energy-Quality Scalable Adaptive Filters

This paper proposes ReAdapt–a reconfigurable datapath architecture for scaling the energy-quality trade-off of adaptive filtering at runtime. The ReAdapt can dynamically select four adaptive filtering algorithms for gradating complexity levels during runtime by reconfiguring the processing flow in its datapath and by blocking the switching activity (e.g., reducing the CMOS dynamic power) of unused modules with data-gating. The ReAdapt proposal can scale the energy-quality trade-off by choosing the following four different levels of filter algorithms complexity: 1) least mean square (LMS); 2) partial update normalized LMS (PU-NLMS); 3) set-membership normalized LMS (SM-NLMS); 4) normalized LMS (NLMS). The ReAdapt architecture reuses common modules of each adaptive filter, resulting in a compact VLSI hardware implementation. The ReAdapt architecture operation is implemented in a case-study for interference mitigation for electroencephalogram (EEG) signal processing. The hardware synthesis results show an increase of 6.80 times in throughput and at least a reduction of 2.84 times in energy per operation compared with the state-of-the-art adaptive filters. This paper also investigates the benefits of dynamically reconfiguring the four ReAdapt operating modes at runtime for different levels of signal-to-noise ratio (SNR) for the processed signals. We also demonstrate that dynamically reconfiguring the ReAdapt operating modes during runtime results in an optimal energy-quality trade-off which is advantageous over the conventional single static mode.

Narrowband Interference Cancellation using Set-membership Adaptive Predictor for GPS Receiver

The global positioning system (GPS) provides accurate positioning and timing information that is useful in various civil and military applications. The adaptive filtering predictor for GPS jamming suppression applications is proposed. This research uses the gLab-G software to substitute for the hardware receiver to record the GPS signal waveform. The normalized least-mean-square (NLMS) and set-membership NLMS (SM-NLMS) filtering methods are employed for continuous wave interference suppression. Simulation results reveal that our proposed methods can provide the better performances when the interference-to-noise ratios (INR) are varied from 20 to 50 dB. The anti-jamming performances are evaluated via extensive simulation by computing mean squared prediction error (MSPE) and signal-to-noise ratio (SNR) improvements.

New symmetric decorrelating set-membership NLMS adaptive algorithms for blind speech intelligibility enhancement

This paper addresses the problem of speech enhancement and acoustic noise reduction by partial and set-membership adaptive algorithms combined with the symmetric decorrelating adaptive (SAD) algorithm structure. In this paper, we propose two new adaptive algorithms based on set-membership principle that improve the original set-membership algorithm behavior in speech enhancement applications. The first proposed algorithm (called Proposed 1), is based on the combination of the SAD algorithm structure with a smart control that uses decorrelating properties between the output and the mixing signal to control and update the SAD adaptive filters. The second proposed algorithm (called Proposed 2) is a modification of Proposed 1 and based on a new regularization relations of the SAD adaptive filters that use a combination between the variance of the mixing and the output signals of the SAD structures. These two proposed algorithms (Proposed 1 and Proposed 2) aim to improve the convergence speed performance and the output signal-to-noise-ratio of the original SAD algorithm when no smart control of the adaptive filters is used. The proposed algorithms have very interesting properties with non-stationary signal like speech when the SAD algorithm is, used alone, fails. The simulation results that are obtained by the comparison between the proposed algorithms (Proposed 1 and Proposed 2) and the original two-channel set-membership NLMS algorithm have shown the best performances of Proposed 1 and Proposed 2 in terms of the following criteria: systems mismatch, segmental SNR and segmental men square error.

A Novel Approach of 2D Adaptive Filter Based on MPSO Technique for Biomedical Image

In this paper, extension of the 1-D adaptive filter schemes to 2D formation and the new 2D adaptive filters are designed. The results of proposed scheme are compared with 2D variable step-size normalized least mean squares, the 2D VSS affine projection algorithms, the 2D set-membership NLMS, and 2D SM APA. The performance of proposed scheme is compared with other reported methods for 2D adaptive filter design. Based on simulation results, it is demonstrated that the proposed method can achieve 85% and 90% reduction in normalized mean square error and normalized maximum error mean, respectively. Moreover, the proposed 2D-ANC filter applied for reconstruction of a biomedical image shows 6 dB signal-to-noise ratio improved as compared to recently reported algorithm.

A flexible sparse set-membership NLMS algorithm for multi-path and acoustic echo channel estimations

A highly improved set-membership normalized least mean square (SM-NLMS) algorithm is carried out to further strengthen the estimation behavior of previously presented SM-NLMS algorithm for estimating sparse multi-path and acoustic echo channels. The newly developed sparse SM-NLMS algorithm utilizes an approximating l0 function (AL0) to modify the SM-NLMS’s cost function to devise a zero attractor. Then, a zero attractor is realized to provide a quick zero attraction for estimating the sparse signals. The proposed soft parameter functioned SM-NLMS (SPFSM-NLMS) algorithm is derived by means of the unconstrained stochastic gradient minimization method to form the finalized SPFSM-NLMS (FSPFSM-NLMS) algorithm. The FSPFSM-NLMS algorithm is derived mathematically, and whose estimation behavior is considered and analyzed on a multi-path sparse channel as well as an acoustic echo channel. Moreover, our presented FSPFSM-NLMS algorithm is also studied under various sparsity levels. The simulated results illustrate that the developed FSPFSM-NLMS algorithm provides a superior sparse channel estimation behavior compared to the zero-attracting SM-NLMS (ZASM-NLMS), reweighting ZASM-NLMS (RZASM-NLMS) and NLMS in terms of the steady-state performance and convergence speed.

Author’s response to comment on ‘application of noise guidance to the assessment of industrial noise with character on residential dwellings in the UK’, D. Baker 93 (2015) 88–96

A highly improved set-membership normalized least mean square (SM-NLMS) algorithm is carried out to further strengthen the estimation behavior of previously presented SM-NLMS algorithm for estimating sparse multi-path and acoustic echo channels. The newly developed sparse SM-NLMS algorithm utilizes an approximating l0 function (AL0) to modify the SM-NLMS’s cost function to devise a zero attractor. Then, a zero attractor is realized to provide a quick zero attraction for estimating the sparse signals. The proposed soft parameter functioned SM-NLMS (SPFSM-NLMS) algorithm is derived by means of the unconstrained stochastic gradient minimization method to form the finalized SPFSM-NLMS (FSPFSM-NLMS) algorithm. The FSPFSM-NLMS algorithm is derived mathematically, and whose estimation behavior is considered and analyzed on a multi-path sparse channel as well as an acoustic echo channel. Moreover, our presented FSPFSM-NLMS algorithm is also studied under various sparsity levels. The simulated results illustrate that the developed FSPFSM-NLMS algorithm provides a superior sparse channel estimation behavior compared to the zero-attracting SM-NLMS (ZASM-NLMS), reweighting ZASM-NLMS (RZASM-NLMS) and NLMS in terms of the steady-state performance and convergence speed.

New efficient two channel forward set-membership partial-update NLMS algorithms for blind speech enhancement and acoustic noise reduction

This paper addresses the problem of speech enhancement by partial adaptive algorithms combined with the forward blind source separation (FBSS) structure. We propose three new two-channel forward partial update algorithms: (i) The first algorithm is based on the use of the correlation properties to adapt and control the variable step-size parameter of adaptive cross-filters of the FBSS structure, this algorithm is called the two channel correlated set membership partial update NLMS (TC-SM-PU-NLMScor). (ii) The second algorithm is based on the use of a new coefficients update relations to control the normalization energy of the adaptive NLMS cross filters of the FBSS structure. This algorithm is called the two channel set member ship partial update regularized NLMS (TC-SM-PU-RNLMS). (iii) The third algorithm is a combination of proposed 1 (TC-SM-PU-NLMScor) and proposed 2 (TC-SM-PU-RNLMS), this algorithm is called the two channel correlated set membership partial update regularized NLMS (TC-SM-PU-RNLMScor). In this paper, we show the obtained results of the comparison between the three proposed algorithms and the original two channel correlated set membership partial NLMS (TC-SM-PU-NLMS) algorithm. This comparison is expressed in terms of objective criteria as the System Mismatch (SM), the Segmental Mean Square Error (SegMSE) and the Segmental SNR (SegSNR).

On the robustness of set-membership adaptive filtering algorithms

In this paper, we address the robustness, in the sense of l2-stability, of the set-membership normalized least-mean-square (SM-NLMS) and the set-membership affine projection (SM-AP) algorithms. For the SM-NLMS algorithm, we demonstrate that it is robust regardless of the choice of its parameters and that the SM-NLMS enhances the parameter estimation in most of the iterations in which an update occurs, two advantages over the classical NLMS algorithm. Moreover, we also prove that if the noise bound is known, then we can set the SM-NLMS so that it never degrades the estimate. As for the SM-AP algorithm, we demonstrate that its robustness depends on a judicious choice of one of its parameters: the constraint vector (CV). We prove the existence of CVs satisfying the robustness condition, but practical choices remain unknown. We also demonstrate that both the SM-AP and SM-NLMS algorithms do not diverge, even when their parameters are selected naively, provided the additional noise is bounded. Numerical results that corroborate our analyses are presented.

Adaptive Channel Estimation Based on an Improved Norm-Constrained Set-Membership Normalized Least Mean Square Algorithm

An improved norm-constrained set-membership normalized least mean square (INCSM-NLMS) algorithm is proposed for adaptive sparse channel estimation (ASCE). The proposed INCSM-NLMS algorithm is implemented by incorporating an lp-norm penalty into the cost function of the traditional set-membership normalized least mean square (SM-NLMS) algorithm, which is also denoted as lp-norm penalized SM-NLMS (LPSM-NLMS) algorithm. The derivation of the proposed LPSM-NLMS algorithm is given theoretically, resulting in a zero attractor in its iteration. By using this proposed zero attractor, the convergence speed is effectively accelerated and the channel estimation steady-state error is also observably reduced in comparison with the existing popular SM-NLMS algorithms for estimating exact sparse multipath channels. The estimation behaviors are investigated via a typical sparse wireless multipath channel, a typical network echo channel, and an acoustic channel. The computer simulation results show that the proposed LPSM-NLMS algorithm is better than those corresponding sparse SM-NLMS and traditional SM-NLMS algorithms when the channels are exactly sparse.

Sparse Multipath Channel Estimation Using Norm Combination Constrained Set-Membership NLMS Algorithms

A norm combination penalized set-membership NLMS algorithm with l0 and l1 independently constrained, which is denoted as l0 and l1 independently constrained set-membership (SM) NLMS (L0L1SM-NLMS) algorithm, is presented for sparse adaptive multipath channel estimations. The L0L1SM-NLMS algorithm with fast convergence and small estimation error is implemented by independently exerting penalties on the channel coefficients via controlling the large group and small group channel coefficients which are implemented by l0 and l1 norm constraints, respectively. Additionally, a further improved L0L1SM-NLMS algorithm denoted as reweighted L0L1SM-NLMS (RL0L1SM-NLMS) algorithm is presented via integrating a reweighting factor into our L0L1SM-NLMS algorithm to properly adjust the zero-attracting capabilities. Our developed RL0L1SM-NLMS algorithm provides a better estimation behavior than the presented L0L1SM-NLMS algorithm for implementing an estimation on sparse channels. The estimation performance of the L0L1SM-NLMS and RL0L1SM-NLMS algorithms is obtained for estimating sparse channels. The achieved simulation results show that our L0L1SM- and RL0L1SM-NLMS algorithms are superior to the traditional LMS, NLMS, SM-NLMS, ZA-LMS, RZA-LMS, and ZA-, RZA-, ZASM-, and RZASM-NLMS algorithms in terms of the convergence speed and steady-state performance.

Sparse-aware set-membership NLMS algorithms and their application for sparse channel estimation and echo cancelation

In this paper, we propose a type of sparsity-aware set-membership normalized least mean square (SM-NLMS) algorithm for sparse channel estimation and echo cancelation. The proposed algorithm incorporates an l1-norm penalty into the cost function of the conventional SM-NLMS algorithm to exploit the sparsity of the sparse systems, which is denoted as zero-attracting SM-NLMS (ZASM-NLMS) algorithm. Furthermore, an improved ZASM-NLMS algorithm is also derived by using a log-sum function instead of the l1-norm penalty in the ZASM-NLMS, which is denoted as reweighted ZASM-NLMS (RZASM-NLMS) algorithm. These zero-attracting SM-NLMS algorithms are equivalent to adding shrinkages in their update equations, which result in fast convergence speed and low estimation error when most of the unknown channel coefficients are zero or close to zero. These proposed algorithms are described and analyzed in detail, while the performances of these algorithms are investigated by using computer simulations. The simulation results obtained from sparse channel estimation and echo cancelation demonstrate that the proposed sparse SM-NLMS algorithms are superior to the previously proposed NLMS, SM-NLMS as well as zero-attracting NLMS (ZA-NLMS) algorithms.

Set-Membership NLMS Algorithm With Robust Error Bound

A new robust error bound for the set-membership normalized least mean square (SMNLMS-REB) is proposed in this brief. The new robust set-membership error bound leads to improved robustness against impulsive noise and steady-state misalignment relative to those achieved in the set-membership normalized least mean square (SMNLMS) algorithm. Stability analysis shows that the proposed algorithm is stable. Using the individual weight error variance (IWV) analysis method, new expressions for the steady-state mean square deviation (MSD) of the SMNLMS-REB are also obtained. Simulation results on system identification show that the robustness and probability of the update (PU) of the proposed SMNLMS-REB considerably outperform the traditional SMNLMS and other robust set-membership NLMS algorithms in the presence of impulsive noise.

Variable partial-update NLMS algorithms with data-selective updating

We note that some existing algorithms are based on the normalized least-mean square (NLMS) algorithm and aim to reduce the computational complexity of NLMS all inherited from the solution of the same optimization problem, but with different constraints. A new constraint is analyzed to substitute an extra searching technique in the set-membership partial-update NLMS algorithm (SM-PU-NLMS) which aims to get a variable number of updating coefficients for a further reduction of computational complexity. We get a closed form expression of the new constraint without extra searching technique to generate a novel set-membership variable-partial-update NLMS (SM-VPU-NLMS) algorithm. Note that the SM-VPU-NLMS algorithm obtains a faster convergence and a smaller mean-squared error (MSE) than the existing SM-PU-NLMS. It is pointed out that the closed form expression can also be applied to the conventional variable-step-size partial-update NLMS (VSS-PU-NLMS) algorithm. The novel variable-step-size variable-partial-update NLMS (VSS-VPU-NLMS) algorithm is also verified to get a further computational complexity reduction. Simulation results verify that our analysis is reasonable and effective.

A Family of Shrinkage Adaptive-Filtering Algorithms

A family of adaptive-filtering algorithms that uses a variable step size is proposed. A variable step size is obtained by minimizing the energy of the noise-free a posteriori error signal which is obtained by using a known $L_1{\hbox{-}}L_2$ minimization formulation. Based on this methodology, a shrinkage affine projection (SHAP) algorithm, a shrinkage least-mean-squares (SHLMS) algorithm, and a shrinkage normalized least-mean-squares (SHNLMS) algorithm are proposed. The SHAP algorithm yields a significantly reduced steady-state misalignment as compared to the conventional affine projection (AP), variable-step-size AP, and set-membership AP algorithms for the same convergence speed although the improvement is achieved at the cost of an increase in the average computational effort per iteration in the amount of 11% to 14%. The SHLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional LMS and variable-step-size LMS algorithms. Similarly, the SHNLMS algorithm yields a significantly reduced steady-state misalignment and faster convergence as compared to the conventional normalized least-mean-squares (NLMS) and set-membership NLMS algorithms.

Low-Complexity Set-Membership Channel Estimation for Cooperative Wireless Sensor Networks

In this paper, we consider a general cooperative wireless sensor network (WSN) with multiple hops and the problem of channel estimation. Two matrix-based set-membership (SM) algorithms are developed for the estimation of complex matrix channel parameters. The main goal is to significantly reduce the computational complexity, compared with existing channel estimators, and extend the lifetime of the WSN by reducing its power consumption. The first proposed algorithm is the SM normalized least mean squares (SM-NLMS) algorithm. The second is the SM recursive least squares (RLS) algorithm called BEACON. Then, we present and incorporate an error bound function into the two channel estimation methods, which can automatically adjust the error bound with the update of the channel estimates. Steady-state analysis in the output mean-square error (MSE) is presented, and closed-form formulas for the excess MSE and the probability of update in each recursion are provided. Computer simulations show good performance of our proposed algorithms in terms of convergence speed, steady-state mean square error, and bit error rate (BER) and demonstrate reduced complexity and robustness against time-varying environments and different signal-to-noise ratio (SNR) values.

Steady-State Mean-Square Performance Analysis of a Relaxed Set-Membership NLMS Algorithm by the Energy Conservation Argument

This paper presents an analysis of the steady-state mean-square error (MSE) of the set-membership normalized least-mean square (SM-NLMS) algorithm with relaxation and regularization parameters. These parameters are introduced for the purpose of deriving in a unified way the steady-state MSE performances of the epsiv-normalized least mean square (epsiv-NLMS) algorithm and a special case of the adaptive parallel subgradient projection (PSP) algorithm. The approach of the paper is to employ the energy conservation relation as a starting point of our analysis. This relation enables us to avoid the transient analysis of the SM-NLMS algorithm, which is in general hard due to the nonlinearity of the SM-NLMS algorithm. As a result, a few nonlinear equations whose solutions are theoretical steady-state MSEs are derived, where two types of reasonable assumptions are introduced to overcome the nonlinearity of the SM-NLMS algorithm. Our results are generalizations of well-known results of the steady-state MSE of the epsiv-NLMS. Extensive simulations show the close agreement between our theories and experiments.

Set-Membership Adaptive Algorithms Based on Time-Varying Error Bounds for CDMA Interference Suppression

This paper presents set-membership (SM) adaptive algorithms based on time-varying error bounds for code-division multiple-access (CDMA) interference suppression. We introduce a modified family of SM adaptive algorithms for parameter estimation with time-varying error bounds. The considered algorithms include modified versions of the SM normalized least mean square (SM-NLMS), the affine projection (SM-AP), and the bounding ellipsoidal adaptive constrained (BEACON) recursive least-square technique. The important issue of error-bound specification is addressed in a new framework that takes into account parameter estimation dependency, multiaccess, and intersymbol interference (ISI) for direct-sequence CDMA (DS-CDMA) communications. An algorithm for tracking and estimating the interference power is proposed and analyzed. This algorithm is then incorporated into the proposed time-varying error bound mechanisms. Computer simulations show that the proposed algorithms are capable of outperforming previously reported techniques with a significantly lower number of parameter updates and a reduced risk of overbounding or underbounding.

Set-membership binormalized data-reusing lms algorithms

This paper presents and analyzes novel data selective normalized adaptive filtering algorithms with two data reuses. The algorithms [the set-membership binormalized LMS (SM-BN-DRLMS) algorithms] are derived using the concept of set-membership filtering (SMF). These algorithms can be regarded as generalizations of the previously proposed set-membership NLMS (SM-NLMS) algorithm. They include two constraint sets in order to construct a space of feasible solutions for the coefficient updates. The algorithms include data-dependent step sizes that provide fast convergence and low-excess mean-squared error (MSE). Convergence analyzes in the mean squared sense are presented, and closed-form expressions are given for both white and colored input signals. Simulation results show good performance of the algorithms in terms of convergence speed, final misadjustment, and reduced computational complexity.

Set-membership binormalized data-reusing LMS algorithms

This paper presents and analyzes novel data selective normalized adaptive filtering algorithms with two data reuses. The algorithms [the set-membership binormalized LMS (SM-BN-DRLMS) algorithms] are derived using the concept of set-membership filtering (SMF). These algorithms can be regarded as generalizations of the previously proposed set-membership NLMS (SM-NLMS) algorithm. They include two constraint sets in order to construct a space of feasible solutions for the coefficient updates. The algorithms include data-dependent step sizes that provide fast convergence and low-excess mean-squared error (MSE). Convergence analyzes in the mean squared sense are presented, and closed-form expressions are given for both white and colored input signals. Simulation results show good performance of the algorithms in terms of convergence speed, final misadjustment, and reduced computational complexity.

Set-membership affine projection algorithm

This letter presents a new data selective adaptive filtering algorithm, the set-membership affine projection (SM-AP) algorithm. The algorithm generalizes the idea of the set-membership NLMS (SM-NLMS) algorithm to include constraint sets constructed from the past input and desired signal pairs. The resulting algorithm can be seen as a set-membership version of the affine-projection (AP) algorithm with an optimized step size. Also, the SM-AP algorithm does not trade convergence speed with misadjustment and computational complexity as most adaptive filtering algorithms. Simulations show the good performance of the algorithm, especially for colored input signals, in terms of convergence, final misadjustment, and reduced computational complexity.