Proportionate Normalized Least Mean Square Research Articles

Orthogonal time-frequency space (OTFS) modulation for underwater mobile acoustic communications

This paper investigates the Orthogonal Time-Frequency Space (OTFS) Modulation for Underwater Mobile Acoustic Communications where the communication channel suffers from severe multipath and Doppler effects simultaneously. Practical OTFS modulation schemes with different parameters are designed for acoustic transmission at a center frequency of 115 kHz and a bandwidth of 11.5 kHz. The schemes are tested in lake experiments where the transmitter was anchored and the receiver was towed by a boat at a speed of approximately 1 m/s or 3.6 km/h. The receiver utilizes low-complexity channel estimation and equalization algorithms, such as NLMS (Normalized Least Mean Squares) and IPNLMS (improved proportionate NLMS) algorithms. The results show some insights of the OTFS scheme for acoustic communications. First, the mobile acoustic channel characteristics are different in the 2D delay-Doppler domain than those in the 1D time and frequency domains for the Single-Carrier Coherent Modulation (SCCM) and the Orthogonal frequency division modulation (OFDM), respectively. Second, in mobile scenarios, the OTFS scheme receiver effectively and significantly reduces the accuracy requirements of the Doppler compensation algorithm and provides better frequency-selective fading suppression and Doppler effect robustness compared to SCCM and OFDM schemes. Third, the OTFS scheme has better anti-multipath performance and reduces multipath interference by effectively differentiating signals on different paths in the 2D delay-Doppler domain.

Hybrid metaheuristic method of ABC kernel filtering for nonlinear acoustic echo cancellation

This research work uses nonlinear kernel adaptive filtering to eliminate echo, a type of voice that is undesirable and communicated over the microphone. Adaptive filters enable the detection of time-varying potentials and the tracking of the signal’s dynamic changes. In this work, a hybrid metaheuristic technique that combines the Artificial Bee Colony (ABC) with the Kernel Adaptive Improved Proportionate and Normalized Least Mean Square (KIPNLMS) filter is developed to significantly boost echo cancellation efficiency. The unique adaptive filter based on sub-filter and proportionate adaptation is combined in the advanced technique, which presents an improved Non-linear Acoustic Echo Cancellation (NAEC) framework. An essential part of kernel techniques is that they translate the information on to a high-dimensional feature space, where linear filtering is performed. In the initial space, the arithmetic operations are carried out by evaluating inner products among pairs of input patterns, also known as kernels. Along with the ABC step size regulation technique, kernel-based adaptive filtering improves Signal to Noise Ratio (SNR) and accelerates convergence. The algorithm's effectiveness is assessed through simulation using signal Echo Return Loss Enhancement (ERLE). The performance of Kernel LMS, Kernal Normalized LMS (KNLMS), Kernal Proportionate NLMS, and KIPNLMS algorithms are compared. In contrast to typical kernel adaptive filters, the suggested ABC-KIPNLMS increases the ERLE more than 10 dB compared to other algorithms.

An Extended Version of the Proportional Adaptive Algorithm Based on Kernel Methods for Channel Identification with Binary Measurements

In recent years, kernel methods have provided an important alternative solution, as they offer a simple way of expanding linear algorithms to cover the non-linear mode as well. In this paper, we propose a novel recursive kernel approach allowing to identify the finite impulse response (FIR) in non-linear systems, with binary value output observations. This approach employs a kernel function to perform implicit data mapping. The transformation is performed by changing the basis of the data In a high-dimensional feature space in which the relations between the different variables become linearized. To assess the performance of the proposed approach, we have compared it with two other algorithms, such as proportionate normalized least-meansquare (PNLMS) and improved PNLMS (IPNLMS). For this purpose, we used three measurable frequency-selective fading radio channels, known as the broadband radio access Network (BRAN C, BRAN D, and BRAN E), which are standardized by the European Telecommunications Standards Institute (ETSI), and one theoretical frequency selective channel, known as the Macchi’s channel. Simulation results show that the proposed algorithm offers better results, even in high noise environments, and generates a lower mean square error (MSE) compared with PNLMS and IPNLMS.

A two-gain NLMS algorithm for sparse system identification

This paper introduces a modified normalized least-mean-square (NLMS) algorithm for sparse system identification. The proposed approach is in line with the proportionate NLMS (PNLMS)-type algorithms in the sense that different gains are considered in the coefficient update equation. However, in contrast to the PNLMS-type algorithms, the proposed approach considers only two different gains, one related to the active coefficients and other related to the inactive ones. Such an approach allows obtaining closed-form expressions for both gains without relying on proportionality functions and activation factors. As a result of the proposed strategy, the new algorithm, termed here two-gain NLMS (TG-NLMS), leads to both fast convergence and low computational complexity. Simulation results are shown aiming to confirm the effectiveness of the proposed algorithm.

Coefficient-Gradient-Based Individualized Stepsize Adaptation Mechanism for Robust System Identification

To efficiently reduce the impact of the trading-off between the convergence rate and the quality of identifying a system, and also to improve the robustness of the algorithm against unknown sparsity levels, a Modified Absolute Weighted Input using Log function (MAWILOG) for NLMS algorithm is proposed. The essence of the proposed algorithm is to assign, individually, each coefficient of the adaptive filter a variable stepsize that adapts according to a Log-term that takes advantage of the input power and the input signal underlying each filter coefficient, and adapts to the gradient value of each coefficient magnitude. Due to these attributes, the proposed approach outperforms the proportionate NLMS (PNLMS)-family regardless of sparsity level that is achieved by using the gradient of each coefficient individually to allocate large stepsize values for high gradient coefficients without directly inserting a sparse-aware constraint. Additionally, this technique is capable of overcoming the high computational complexity and high steady-state mean-square-deviation of the (PNLMS)-family. Simulation results of the proposed algorithm versus the comparable algorithms such as the NLMS, PNLMS, improved PNLMS, block-sparse PNLMS, and block-sparse IPNLMS are presented. Results have demonstrated that the proposed algorithm outperforms others in maintaining the lowest steady-state mean-square-deviation while attaining a fast convergence rate under various types of systems.

New sub-band proportionate forward adaptive algorithm for noise reduction in acoustical dispersive-and-sparse environments

In this study, we address the problem of acoustic noise reduction by two-channel forward adaptive filtering algorithm. In noise reduction applications, the normalized least mean square (NLMS) algorithm is recently implemented on the two-channel blind source separation (BSS) technique. Exactly in this paper, we propose a new implementation of two-channel forward BSS technique based on proportionate adaptive filtering algorithm in sub-band form. This new implementation is proposed exactly to resolve the problem of proportionate forward NLMS algorithm in term of convergence rate and speech quality when the acoustic environment is characterized by dispersive or sparse impulse responses. To prove the good performance of our proposed sub-band proportionate Forward NLMS algorithm (SP-FNLMS), we compare its performances with the full-band proportionate and non-proportionate versions exactly in four acoustical environments, more dispersive, dispersive, sparse and finally more sparse.

A novel cost-effective sparsity-aware algorithm with Kalman-based gain for the identification of long acoustic impulse responses

In this paper, a new robust sparsity (or sparseness)-aware adaptive filtering algorithm is proposed for the purpose of system identification and acoustic echo cancelation. It is named the improved proportionate fast normalized least mean square (IPFNLMS) algorithm. This latter has been derived by an effective integration of the update control matrix of the improved proportionate NLMS (IPNLMS) algorithm to the Kalman-based adaptation gain of the fast-NLMS (FNLMS) algorithm. Simulations were carried out both in synthetic and real long acoustic impulse responses at different sparseness levels with stationary and non-stationary inputs, followed by a verification with real experiment data. Results have shown interesting improvements for the proposed algorithm with respect to its ancestors in terms of convergence speed, steady-state performance, tracking capability and robustness against system sparsity variation.

A novel block-sparse proportionate NLMS algorithm based on the l2,0 norm

To ameliorate the performance of the normalized least mean square (NLMS) algorithm applied in identifying block-sparse system, a novel block-sparse proportionate NLMS (BS-PNLMS) algorithm based on the mixed l2,0 norm is presented in this paper. The cost function of proposed algorithm is obtained by introducing the approximated mixed l2,0 norm penalty in the cost function of BS-PNLMS algorithm, which is equivalent to attaching the mixed l2,0 norm zero attraction to the update equation. The proposed algorithm is named as the l2,0-BS-PNLMS algorithm. Futhermore, a variable step-size l2,0-BS-PNLMS is developed to further improve the performance of the l2,0-BS-PNLMS. Simulation results demonstrate the advantages of proposed algorithms.

The Bias-Compensated Proportionate NLMS Algorithm With Sparse Penalty Constraint

For compensating the bias caused by the noisy input which is always ignored by ordinary algorithms, two novel algorithms with zero-attraction (ZA) penalties are proposed in this paper. The first one constructs a bias-compensated term in the updating recursion of the zero-attraction proportionate normalized least mean square (PNLMS) algorithm which is named BC-ZA-PNLMS algorithm. The second one employs the bias-compensated term and the correntropy induced metric (CIM) constraint to renew the updating recursion of the PNLMS algorithm which is named BC-CIM-PNLMS algorithm. Both of these two algorithms are derived on the basis of unbiased criterion. Simulation examples are carried out, and the results indicate that the two newly developed unbiased algorithms outperform the related algorithms previously presented in other literatures for combating noisy input and measurement noises.

Filter proportionate normalized least mean square algorithm for a sparse system

SummaryIn this paper, the proportionate normalized least mean square (PNLMS) and its modifications, such as improved PNLMS (IPNLMS) and μ‐law PNLMS (MPNLMS) algorithms, developed for a sparse system, are analyzed for a compressed input signal. This analysis is based on a comparative study of the steady‐state error and convergence time for the original signal and the compressed signal. Further, in this paper, a filter PNLMS (FPNLMS) algorithm that is a modification of the IPNLMS algorithm is proposed. The FPNLMS algorithm uses a step size varying in time to adapt to the sparse system. Simulations are carried out to compare the proposed FPNLMS algorithm for different signal‐to‐noise ratio for a compressed input signal with existing algorithms, ie, PNLMS, MPNLMS, and IPNLMS algorithms. The FPNLMS algorithm achieves a better steady‐state and convergence time compared with other existing algorithms in both low and high SNRs. The FPNLMS algorithm is further simulated for a real transfer function to show its robustness compared with existing algorithms.

A bias‐compensated proportionate NLMS algorithm with noisy input signals

SummaryThis paper proposes a novel proportionate normalized least‐mean‐squares (PNLMS) algorithm that is robust to input noises. Through compensating for biases due to input noise added at the filter input, the proposed PNLMS algorithm avoids performance deterioration owing to the noisy input signals. Moreover, since the proposed PNLMS algorithm uses a new gain‐distribution matrix, it has a fast convergence rate compared with the existing PNLMS algorithms, even when there is no input noise. The experimental results verify that the proposed PNLMS algorithm enhances the filter performance for sparse system identification in the presence of input noises.

Robust Adaptive Filter Algorithms Against Impulsive Noise

This paper proposes a prefiltered observation-based adaptive filter algorithm that is robust against impulsive noise. Previous impulsive noise rejection algorithms were based on output error stochastic, so there was a trade-off relationship between impulsive noise detection and tracking performances. The proposed rejection algorithm is derived by using the statistics of the observed signal and the inequality such as the Schwarz and Young inequality in the absence of impulsive noise. From this, the proposed algorithm updates the weight vector only when the observed signal is not corrupted by impulsive noise. The proposed algorithm achieves the good tracking performance because it distinguishes between the system change and interruption of impulsive noise. In addition, the proposed algorithm has same performance without impulsive noise, compared with the normalized least-mean-square-type algorithm. Further, the proposed rejection algorithm could expand to various adaptive filtering structures, which suffer the performance degradation with impulsive noise, because it is easy to implement. Hence, the proposed algorithm is combined with the NLMS algorithm for dispersive systems and the proportionate NLMS algorithm for sparse systems. Simulation results show that the proposed algorithm achieves fast convergence rate, good tracking performance, and robustness under the impulsive noise environment.

A Proportionate Normalized Maximum Correntropy Criterion Algorithm with Correntropy Induced Metric Constraint for Identifying Sparse Systems

A proportionate-type normalized maximum correntropy criterion (PNMCC) with a correntropy induced metric (CIM) zero attraction terms is presented, whose performance is also discussed for identifying sparse systems. The proposed sparse algorithms utilize the advantage of proportionate schemed adaptive filter, maximum correntropy criterion (MCC) algorithm, and zero attraction theory. The CIM scheme is incorporated into the basic MCC to further utilize the sparsity of inherent sparse systems, resulting in the name of the CIM-PNMCC algorithm. The derivation of the CIM-PNMCC is given. The proposed algorithms are used for evaluating the sparse systems in a non-Gaussian environment and the simulation results show that the expanded normalized maximum correntropy criterion (NMCC) adaptive filter algorithms achieve better performance than those of the squared proportionate algorithms such as proportionate normalized least mean square (PNLMS) algorithm. The proposed algorithm can be used for estimating finite impulse response (FIR) systems with symmetric impulse response to prevent the phase distortion in communication system.

Proportionate NLMS With Unbiasedness Criterion for Sparse System Identification in the Presence of Input and Output Noises

This brief proposes a bias-compensated proportionate normalized least mean square (BCPNLMS) method for identifying sparse system when subjected to the noisy input. The proposed BCPNLMS algorithm, which combines the proportionate scheme and the unbiasedness criterion, is able to identify the system parameters with better steady-state accuracy and faster convergence speed than conventional NLMS, bias-compensated NLMS, and PNLMS algorithms. Robustness and high identification accuracy with noisy input can be achieved by introducing the bias-compensation term derived from the unbiasedness criterion. Simulation results on sparse system identification confirm the excellent performance of the proposed BCPNLMS in the presence of both input and output noises.

Efficient Adaptive Turbo Equalization for Multiple-Input–Multiple-Output Underwater Acoustic Communications

An efficient adaptive turbo equalization (ATEQ) scheme is proposed for multiple-input–multiple-output underwater acoustic (UWA) communications. The proposed ATEQ scheme utilizes two layers of iterative processing: The inner-layer iteration is the soft-decision-based equalizer parameters adaptation and filtering of received signals in the equalizer, and the outer-layer iteration is the Turbo exchange of extrinsic log-likelihood ratio between the equalizer and decoder. In contrast, the existing ATEQ schemes use hard-decision symbols for filter adaptation but soft symbols for filtering and Turbo iteration. When the adaptive filters are designed and updated via the normalized least mean squares (NLMS) or the improved proportionate NLMS algorithms for low computational complexity and good channel tracking, the soft symbols utilized in both the pilot-assisted and the decision-directed modes of the proposed ATEQ scheme achieve fast convergence with short training sequences, thus achieving high spectrum efficiency. The proposed scheme is evaluated by the field trail data collected in the 2008 Surface Processes and Acoustic Communications Experiment. The results demonstrate that the proposed ATEQ scheme is robust against the severe triply-selective UWA channels and mitigate slow-convergence problem commonly suffered by direct-adaptation equalizers.

Robust Proportionate Adaptive Filtering Algorithms Against Impulsive Interference

The Proportionate Normalized Least Mean Square (PNLMS) algorithm, as a popular tool of signal processing, achieves excellent performance for sparse system identification. However, in previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the Mean Square Error (MSE) criterion, which is optimal only when the measurement noise is Gaussian. However, when the noise is impulsive noise, the performances of the existing proportionate-type sparse adaptive algorithms deteriorate severely. In this paper, two novel proportionate adaptive algorithms, namely, Proportionate Maximum Correntropy Criterion (PMCC) algorithm based on maximum correntropy criterion algorithm and proportionate normalized least mean square algorithm based on arctangent cost function (P-Arc-NLMS) are proposed to address this problem. The corresponding computational complexity is analyzed. The simulations are done to confirm that the proposed algorithms have advantages, compared with the existing other algorithms proposed against impulsive interference in sparse system identification.

Cluster-Sparse Proportionate NLMS Algorithm With the Hybrid Norm Constraint

In this paper, an enhanced proportionate normalized least mean square (PNLMS) algorithm with the hybrid ${l_{2,0}}$ -norm constraint is proposed for block-sparse signal processing. The proposed algorithm penalizes a mixed ${l_{2,0}}$ -norm on the PNLMS to fully exploit the sparsity and handle block-sparse signals, which is called the ${l_{2,0}}$ norm constrained PNLMS (L20-PNLMS). The L20-PNLMS is well derived and carefully analyzed. Various experiments have been constructed to verify the effectiveness of the devised L20-PNLMS. The experimental results demonstrate that the devised L20-PNLMS performs better than the previous PNLMS algorithms do in block sparse signal processing.

A novel gain distribution policy based on individual-coefficient convergence for PNLMS-type algorithms

This paper introduces a new gain distribution policy for proportionate normalized least-mean-square (PNLMS)-type algorithms. In the proposed approach, gains assigned to the coefficients that have achieved the vicinity of their optimal values are transferred to other coefficients. To estimate such a vicinity, a metric based on the variation rate of the adaptive filter coefficient magnitude is devised, which is used as a way for assessing the individual-coefficient convergence. Then, the proposed approach is applied to the PNLMS, improved PNLMS (IPNLMS), and individual-activation-factor PNLMS (IAF-PNLMS), leading to enhanced versions of these algorithms. Simulation results show that the proposed approach (and the corresponding enhanced algorithms) performs well for different operating scenarios.

Formula omitted] optimality and a posteriori output estimate of the forgetting factor NLMS algorithm

The normalized least mean squares (NLMS) algorithm is widely used for adaptive filtering. The NLMS algorithm may be extended using a variety of weight parameters that improve its performance. One such extension involves appropriately introducing a forgetting factor into the NLMS algorithm using the H∞ framework. The resultant forgetting factor NLMS (FFNLMS) algorithm may be regarded as a special case of the improved proportionate NLMS (IPNLMS) algorithm. This work reveals that the FFNLMS algorithm is H∞-optimal, and the a posteriori output estimate is identical to the observation signal for sufficiently large times.

Efficient and Low Complexity Noise Cancellers for Cardiac Signal Enhancement using Proportionate Adaptive Algorithms

Objectives: To enhance the quality of Cardiac Signal for perfect diagnosis by the doctor. Methods/Statistical Analysis: We are introducing some adaptive filter structures for Cardiac Signal (CS) enhancement for the extraction of high resolution cardiac signals and these structures were based on the Proportionate Normalized Least Mean Square (PNLMS) algorithm. The main advantage of PNLMS over the conventional techniques is extraction of sparse coefficients, suitably weighing them and fast convergence. These ANCs are tested using MIT-BIH database to compare the performance. Findings: We consider Signal to Noise Ratio (SNR), Excess Mean Square Error (EMSE), Misadjustment (MSD), convergence curves and residual error plots as performance measures. Among the ANCs tested, PMNSRLMA based ANC is found to be better with reference to the considered performance measures and computational complexity. The average SNRI achieved by this ANC is 18.8856dBs for PLI elimination, 8.7580dBs for BW elimination, 8.5106dBs for MA elimination and 8.5012dBs for EM elimination. From the above results it is clear that in practical biotelemetry applications to minimize the computational complexity of the noise canceller we combine PNLMS with signature algorithms. Again, to reduce the complexity in the denominator of the normalized recursion, we use maximum normalized version of PNLMS. Finally, these variations result in seven algorithms in addition to PNLMS. Based on these algorithms, we develop various Adaptive Noise Cancellers (ANCs) to eliminate artifacts present in the CS and to present best quality signal to the doctor for diagnosis. Application/ Improvement: The standard of Cardiac Signal can be enhanced by improving data acquisition methods.