Comparison between Epsilon Normalized Least Means Square (ϵ-NLMS) and Recursive Least Squares (RLS) Adaptive Algorithms

Speech enhancement is a vital area of research, the performance of speech based human machine applications such as automatic speech recognition system, in car communication depends on the quality of speech communicated. Different methodologies have been used by various researchers to improve the quality of speech signal. In this paper an attempt is made to analyze the performance of Least Mean Square (LMS) and Recursive Least Squared (RLS) adaptive filter algorithm for speech enhancement application. The performance indices used for the evaluations is Mean Square Error (MSE), Signal to Noise Ration (SNR) and execution time. The detail analysis is done and experimentally the results are validated and certain modifications are suggested in the algorithm. The experimentation revels that LMS have fast convergence than RLS. The computational complexity of RLS is very high as compared to LMS.

Several new two-dimensional adaptive infinite-impulse response (IIR) filtering algorithms are derived and simulated. These new algorithms are based upon the one-dimensional version of the algorithm developed by Fan and Jenkins (1986). This algorithm was shown to experimentally possess the ability to converge to the global minimum of the mean square error (MSE) even in cases where the MSE surface is ill-conditioned. In addition, further enhancements to this new algorithm were made to improve convergence rate performance. An estimate of the Hessian is incorporated into the adaptive filter coefficient update expressions. Least Mean Square (LMS), Recursive Least Square (RLS), Gauss-Newton (GN), and Fast Quasi-Newton (FQN) forms of the two-dimensional Fan-Jenkins algorithm are formulated and compared via simulation for several examples.

A improved algorithm to perform channel estimation and equalization for multiple input multiple output(MIMO) systems in frequency and time-selective fading environments is put forward. lt contains two steps: training and tracking. In training phase, improved Kalman filtering, namely robust Kalman filtering(RKF), is exploited to estimate channel impulse response(CIR). After that, in tracking stage,the RKF and minimum mean-square error feedback decision equalizer (MMSE-DFE) cooperate to track the time-varying channel. The RKF recursions is presented and a closed-form solution for baud rate MIMO MMSE-DFE under perfect knowledge of CIR and correct past decisions conditions is derived. In addition, it regards unknown dc-offset due to zero intermediate frequency(IF) at the receiver as the mean of measurement noise, which is estimated as a byproduct through robust Kalman filters. Finally, it is compared with well-known ones,such as least mean-square (LMS), recursive least square (RLS), Kalman filtering (KF). All these show that the proposal exhibits better performance.

Electrocardiogram (ECG) signals are electrical signals generated corresponding to activity of heart. ECG signals are recorded and analysed to monitor heart condition. In initial raw form, ECG signals are contaminated with different types of noises. These noises may be electrode motion artefact noise, baseline wander noise and muscle noise also known as electromyogram (EMG) noise etc. In this paper, a descendent structure consists of adaptive filters is used to eliminate the three different types of noises (i.e., motion artefact noise, baseline wander noise and muscle noise). The two different adaptive filtering algorithms have been implemented; least mean square (LMS) and recursive least square (RLS) algorithm. The performance of these filters are compared on the basis of different fidelity parameters such as mean square error (MSE), normalised root mean squared error (NRMSE), signal-to-noise ratio (SNR), percentage root mean squared difference (PRD), and maximum error (ME) has been observed.

In this paper, a method of updating filter coefficients is proposed in which the RLS (Recursive Least Squares) algorithm is applied to a noise canceler with a filter for crosstalk removal. The RLS algorithm has an advantage over the Least Mean Square algorithm by virtue of better convergence. When the filter coefficients are updated including the filter for crosstalk removal, the error signal becomes nonlinear in terms of filter coefficients. Hence, a nonlinear RLS algorithm is derived in which such nonlinearity is taken into account. It is shown that the convergence is further improved in comparison with the conventional RLS algorithm. Finally, a method is proposed to reduce the noise contained in the transmitted voice signals of telephone by means of the present noise canceler and its effectiveness is evaluated. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(5): 36–44, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10039

WiMAX physical layer implemented Orthogonal Frequency Division Multiple Access (OFDMA) as one of the medium to conduct data transmission. OFDMA suffers from Intersymbol Interference (ISI) which can distort efficiency of the signal transmitted. ISI emerges in the system because of multipath. Basic Cascaded Least Square (CLS) with Decision Feedback Equalizer (DFE) had been proposed in previous research to minimize ISI in wireless communication system. This research will improve CLS performance in terms of convergence. CLS is a cascaded of two adaptive algorithms which are Least Mean Square (LMS) and Recursive Least Square (RLS). Although basic LMS has low complexity than RLS and has been used widely in wireless environment, LMS is suffering in terms of convergence. Updated Normalized Least Mean Square (NLMS) with training rate applied in this research to overcome disadvantage in LMS algorithm. This research justified that training rate is an alternative method to improve CLS-DFE in wireless communication system.

Piezo actuators are widely use in positioning and control applications. Piezo actuators are nonlinear and possess time varying hysteresis nature. For controlling piezo actuators mostly inverse hysteresis model or adaptive inverse control model are utilize. To implement adaptive inverse control, adaptive model of piezo actuator is to be determined. There are various adaptive methods viz. Recursive Least Square (RLS), Kalman Filter (KF), Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) by which the model can be determined. This paper discusses the system of piezo actuator and different methods of finding adaptive model for piezo actuator system. Further a comparative study of adaptive model identification is carried out and suitable model for this system is identified and discussed. A novel approach of identifying a suitable model is discussed in this paper. The experimentation is carried out using electro pneumatic positioner, which utilizes the piezo valve for positioning. LabVIEW 2014 is used along with data acquisition hardware for modeling of real time system. The results of experimentation shows that, RLS adaptive model is more suitable as compared to other adaptive algorithms.

Nonlinear system identification in noisy environments presents a significant challenge in adaptive filtering, particularly when dealing with impulsive noise, non-Gaussian distributions, and complex system dynamics. Traditional filtering approaches, including Least Mean Squares (LMS) and Recursive Least Squares (RLS), often exhibit performance degradation due to their reliance on second-order statistical assumptions. The Maximum Correntropy Criterion (MCC) has shown promise in improving robustness; however, it suffers from limitations in capturing highly nonlinear system behaviors. This study proposes a Generalized Maximum Correntropy Criterion (GMCC) with Spline Adaptive Filtering, leveraging B-spline basis functions to enhance function approximation and noise resilience. The GMCC framework was evaluated against LMS, RLS, and conventional MCC-based adaptive filtering methods across Gaussian, Laplacian, and impulsive noise environments. Experimental results demonstrate that GMCC consistently achieves lower Mean Squared Error (MSE) values across all noise scenarios, outperforming conventional approaches in both accuracy and convergence stability. Statistical analysis using ANOVA confirmed performance consistency, though differences were not statistically significant at the 95% confidence level. Practical applications include biomedical signal processing, financial modeling, radar tracking, and autonomous systems, where robust nonlinear filtering is essential. Future research should focus on optimizing computational efficiency, incorporating deep learning enhancements, and extending real-time implementations for IoT and edge computing applications.

On channel estimation for spatial modulated systems over time-varying channels

In the next-generation wireless communication systems, the broadband signal transmission over wireless channel often incurs the frequency-selective channel fading behavior and also results in the channel sparse structure which is dominant by very few large coefficients. To ensure the stable wireless propagation, various linear adaptive channel estimation algorithms, e.g., recursive least square (RLS) and least mean square (LMS), have been developed. However, the traditional algorithms are unable to exploit the channel sparsity. Supporting by the compressive sensing (CS) theory, channel estimation performance can be further improved by taking advantage of the sparsity. In this paper, RLS based fast adaptive sparse channel estimation algorithm is proposed by introducing two sparse constraint functions, L1-norm and L0-norm. To improve the flexibility of the proposed algorithms, this paper introduces a regularization parameter selection method to adaptively exploit the channel sparsity. Finally, Monte Carlo based computer simulations are conducted to validate the effectiveness of the proposed algorithms based robust channel estimation either for sparse or non-sparse channel.

Sparse adaptive filtering algorithms are utilized to exploit potential sparse structure information as well as to mitigate noises in many unknown sparse systems. Sparse recursive least square (RLS) algorithms have been attracted intensely attentions due to their low-complexity and easy- implementation. Basically, these algorithms are constructed by standard RLS algorithm and sparse penalty functions (e.g., l_1-norm). However, existing sparse RLS algorithms do not exploit the sparsity efficiently. In this paper, an improved adaptive filtering algorithm is proposed by incorporating a novel correntropy induced metric (CIM) constraint into RLS, which is termed as RLS- CIM algorithm. Specifically, we adopt a well-known Gaussian kernel in CIM and further devise a novel variable kernel width to control the sparse penalty in different transient-error scenarios. Numerical simulation results are given to corroborate the proposed algorithm via mean square deviation (MSD).

Smart antenna systems are of great importance in wireless communication and radar applications. They effectively enhance the system capacity and reduce the co-channel interference. Smart antenna is an array antenna that uses adaptive beamforming algorithms to steer the main beam toward the desired signal direction and reject the interfering signals of the same frequency from other directions without moving the antenna. This is achieved by continuously updating the weights of each radiating element (antenna). An algorithm with low complexity, low computation costs, high speed convergence rates and better performance is usually preferred. This paper introduces a new performance investigation and comparison between five different beamforming algorithms: Least Mean Square (LMS), Normalized Least Mean Square (NLMS), Sample Matrix Inversion (SMI), Recursive Least Square (RLS) and Hybrid Least Mean Square / Sample Matrix Inversion (LMS/SMI). In this investigation, the number of array elements and the displacement among them are changed in each algorithm. Simulation experiments are carried out, and the results are compared to verify the effectiveness of this investigation. The performance of each algorithm is optimized and demonstrated using MATLAB software package.

<p>Location Based Services (LBS) in the realms of Smart City realizations require accurate real time positioning information of objects and people indoors. Both VLC based and the RF based positioning techniques have been studied in the literature. In RF system, we use Recursive Least Square (RLS) multilateration algorithm to estimate the position of unknown target indoor. The RLS multilateration algorithm is based on the trilateration solution using algebraic method. Solution obtained from the trilateration is used in RLS algorithm and the solution is updated recursively. Since Machine Learning (ML) is one of the widely used approaches to improve the accuracy in indoor positioning, we have used Artificial Neural Network (ANN) to fine tune the simulated distances with Rician noise. Therefore, the proposed technique hybridizes RLS with Artificial Neural Network (ANN) to solve a multilateration problem of different sets of anchor nodes. </p> <p>We use MATLABTM for the simulation purpose. While simulating distances, Rician noise is considered for anchor-target distance and, noisy distances are fed into ANN filter. Instead of using directly simulated distances, estimated distances from ANN are used for RLS implementation. Results from the hybrid RLS-ANN are compared with pure RLS, pure least square (LS) and LS-ANN approaches. Hybrid RLS-ANN provides the least Root Mean Square Error (RMSE) among all the techniques and improves the accuracy up to 80% compared to the pure LS multilateration technique. Complexity of the proposed technique is relatively low with significantly increased accuracy. </p> <p>We also compare the results with different sets of anchor nodes for RLS implementation. Hybrid RLS-ANN algorithm is used for anchor nodes <em>N </em>= 4 to <em>N </em>= 10. Comparing the results, it has been shown that as the number of anchor nodes increases, the RMSE decreases steadily. RLS multilateration with large number of anchor nodes performs better than LS multilateration. On the other hand, distance error is largely reduced by using ANN training and RLS with ANN estimated distances further improves the accuracy. </p> <p>In VLC system, we analyze the impact of SNR on indoor positioning. VLC indoor positioning is analyzed based on SNR distribution on the room indoor. Distance measurement is analyzed with three parameters: angle of incidence, angle of irradiance and transmitter FOV. Since SNR has the direct impact on the VLC indoor distance measurement, a comparative study of the SNR variation with respect to transmitter FOV, receiver FOV, angles of incidence and irradiance is presented, and corresponding distance measurement error is analyzed. </p>

Recursive least squares (RLS) is widely used in identification and estimation. An unfortunate weakness of RLS is the divergence of its covariance matrix in cases where the data are not sufficiently persistent. To solve this problem, [1] introduced the exponential forgetting and resetting algorithm (EFRA), whose covariance update equation is modified so that the covariance matrix remains bounded. Unfortunately, EFRA does not include RLS as a special or limiting case, and cannot easily approximate RLS estimates. In this paper, we derive a modified RLS variant of EFRA that includes RLS without forgetting as a limiting case, and that can closely approximate RLS with forgetting. An additional advantage of MRLS relative to EFRA is greater ease in choosing parameters to set the covariance bounds.

A new adaptive algorithm is proposed by introducing some modifications to the recursive least squares (RLS) algorithm. Except for the noise variance, the proposed algorithm does not require any statistics or knowledge of the desired signal, thus, it is suitable for adaptive filtering for channel estimation in code division multiple access (CDMA) systems in cases where the standard RLS approach cannot be used. A theoretical analysis demonstrates the convergence of the proposed algorithm, and simulation results for CDMA channel estimation show that the proposed algorithm outperforms existing channel estimation schemes.