On the robustness of LMS algorithms with time-variant diagonal matrix step-size

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.

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.

The proportionate normalized least mean square (PNLMS) algorithm is used in sparse system identification for its simplicity and adaptively step-size adjusting scheme. However, the PNLMS has the noisy input and the non-Gaussian output noise problem. A bias Compensated PNLMF algorithm (called BCPNLMF) for identifying sparse system has been proposed to solve aforementioned issues. The BCPNLMF algorithm which takes advantage of the bias compensated and the proportionate scheme, can achieve better steady-state accuracy and faster convergence speed besides identify the system parameters in noisy input and output with non-Gaussian character environments. Simulation results carried out in sparse system identification confirm the remarkable performance of the BCPNLMF, compared with other well-known algorithms.

Several set-membership (SM) based proportionate normalized least-mean-square (PNLMS) using the modified filtered-x (MFx) structures are proposed for active noise control. It is shown by simulations that the proposed algorithms that have a reduced numerical complexity can obtain better performance than MFx-PNLMS for various ANC paths.

In this paper, a feedback interference cancellation scheme for digital on-channel repeaters (DOCRs) in terrestrial-digital multimedia broadcasting (TDMB) system is introduced. In order to mitigate the feedback signal in DOCR, an interference cancellation scheme using proportionate normalized least mean squares (PNLMS) algorithm is proposed. Simulation results confirm the RFP performance improvement at the DOCR and the BER performance improvement of T-DMB in time-varying typical urban channel.

Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.

The reorderable matrix method is a convenient way of representing static tabular data (i.e. matrices) visually. In this paper, we present an approach to use the reorderable matrix method for visualizing time-varying matrix data. Solutions to the problems encountered during the adaptation of this visualization method for time-varying matrices and proposals to solve the problems related to the automatic reordering of static tabular data are discussed. The approach is illustrated by visualizing sensitivity matrices generated during the simulation of metabolic network models.

Echo cancelers which cover longer impulse responses (/spl ges/64 ms) are desirable. Long responses create a need for more rapidly converging algorithms in order to meet the specifications for network echo cancelers devised by the ITU (International Telecommunication Union). In general, faster convergence implies a higher sensitivity to near-end disturbances, especially Previously, a fast converging algorithm called the proportionate NLMS (normalized least mean squares) algorithm (PNLMS) has been proposed. This algorithm exploits the sparseness of the echo path in order to increase the convergence rate. A robust version of PNLMS has also been presented which combines a double-talk detector with techniques from robust statistics to make the algorithm insensitive to double-talk. This paper presents a generalization of the robust PNLMS algorithm to a robust proportionate aAffine projection algorithm (APA) called PAPA that converges very fast.

A fixed-point implementation of a minimum mean square error (MMSE) based frequency domain (FD) equalizer with soft interference cancellation (SC) is studied. The equalizer additionally processes a priori information about the transmitted symbols and is used for turbo equalization. In this paper, we analyze the quantization and the clipping for different fixed-point representations and modulation schemes. The analysis allows to derive efficient representations for all symbols within the equalizer. This procedure is demonstrated for a generic system configuration featuring a 16-QAM. Finally, a fixed-point implementation in an integrated design environment for FPGAs verifies the theoretical studies and shows the device utilizations for different FPGAs that are embedded in current software defined radios. The results show, that on average 10 bits per symbol are required for a near-optimum equalization performance utilizing less than 8% area of state of the art FPGAs.

This paper presents high quality and robust Infinite Impulse Response (IIR) adaptive howling suppressor (AHS) developed based on adaptive notch filters (ANF) with regularisation. The proposed method uses Normalised Least Mean Square (NLMS) adaptation algorithm with leakage factor based on moving-average technique. The proposed system uses combination of front end de-correlation and modified NLMS adaptation. This is to ensure faster howling detection and very robust performance under different types of input signals and at different power levels. The proposed leakage factor introduced during adaptation, ensures stability of operation even when howling build-up frequency is oscillating in the neighbourhood bands. The performance test results obtained with the proposed system demonstrates quick detection and stable operation when compared to the recent techniques. The additional complexity involved with the proposed system compared to traditional methods is marginal or negligible.

This research aims to use the Adaptive Minimum Bit Error Rate (AMBER) for Wideband Code Division Multiple Access (WCDMA). AMBER and Normalized AMBER (NAMBER) algorithms for WCDMA systems are derived and implemented. Its Bit Error Rate (BER) performance is measured using a WCDMA Frequency Division Duplex (FDD) Downlink Physical Layer model. The new methods are compared to the original WCDMA system and the NLMS Adaptive Combiner. Results show around 5 dB performance gain over the single antenna system, and around 2 dB performance gain over the Dual Antenna Normalized Least Mean Squares (NLMS) Adaptive Combiner system in an Additive White Gaussian Noise channel at a BER of 10-2.5. However, complex computation requirements render the algorithms impractical for widespread use. Simplifications and alternative implementations have to be investigated.

A special class of recurrent neural network (RNN) termed Zhang neural network (ZNN) has recently been proposed for time-varying matrix square roots finding. Such a ZNN model can be constructed via monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different choices of activation functions lead to different performance of the ZNN model. In this paper, to pursue the superior convergence and robustness, a special type of activation functions (i.e., hyperbolic sine activation functions) is used in the ZNN model for online solution of time-varying matrix square roots. Theoretical analysis and simulation results further demonstrate the superior performance of the ZNN model using hyperbolic sine activation functions in the context of (very) large model-implementation errors, in comparison with that using linear activation functions.

In single-carrier aeronautical communication systems, the time-varying multipath propagation characteristics of the channel give rise to severe inter-code interference. Radio channel distortion compensation and inter-code interference cancellation are generally achieved by equalization techniques. In this paper, zero-forcing equalization, minimum mean square error equalization and minimum mean square error adaptive equalization algorithms for SC-FDE systems are investigated, but the traditional LMS algorithms cannot meet the performance requirements of convergence speed and steady-state error at the same time because the step size factor is fixed. This paper investigates the variable step size LMS algorithm and proposes an improved variable step size LMS algorithm, which uses the non-linear relationship between the error factor and the error function to construct a correlation correction function, to regulate the error factor in a small range, and to further correct the step size factor through the change of the error factor. The LMS algorithm is divided into a training mode and a tracking mode, and the two modes are combined to achieve a faster convergence rate. The computer simulation results are consistent with the theoretical analysis and confirm that the algorithm outperforms the original algorithm.

This paper proposes a new regularized transform domain normalized LMS (R-TDNLMS) algorithm and studies its mean and mean square convergence performances. The proposed algorithm extends the conventional TDNLMS algorithm by imposing a regularization term on the filter coefficients to reduce the variance of estimators due to the lacking of excitation in a certain frequency band or in the presence of modeling errors. Difference equations describing the mean and mean square convergence behaviors of this algorithm are derived so as to characterize its convergence condition and steady-state excess mean square error (MSE). It shows that regularization can help to reduce the MSE by trading slight bias for variance. Based on this analysis, a new formula to select the regularization parameter for white Gaussian inputs is proposed, which leads to a new variable regularized TDNLMS (VR-TDNLMS) algorithm. Computer simulations are conducted to examine the improved convergence performance, steady-state MSE and robustness to power-varying inputs of the proposed algorithm and verify the effectiveness of the theoretical analysis. Furthermore, the application of the proposed VR-TDNLMS algorithm to the design and implementation of acoustic system identification and active noise control (ANC) systems show that they considerably outperforms traditional TDNLMS algorithms at low excitation or in the presence of modeling errors. Moreover, the theoretical analysis provides simple design formulas for achieving a given excess MSE (EMSE) and step-size bound for stable operation.

Automated Essay Grading (AEG) systems that are currently available use different techniques to extract specific written dimensions features to assess the written prose. Several Neuro-Fuzzy approaches have been applied to try to solve the short essay AEG problem. The main idea behind this approach is to identify the number of main keywords (5 inputs) each of which has 4 synonyms based on specific constraints. These inputs have been processed by developing two general models including; Artificial Neural Network Back-propagation optimization technique and Subtractive Clustering technique. Furthermore a third general model have developed to incorporate more main keywords by processing double the number of previous models input, single output with specific constraints by combining Subtractive clustering and Neuro Fuzzy techniques. The Sub-Clustering Neuro Fuzzy model could be used for a variable number of inputs. More than 900 generated datasets have been used representing questions related to information technology field. The correlation coefficient have been used to measure the agreements between the actual and predicted marks of the models, and used two error measures including; Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) to indicate the performance of the developed models. The average results obtained from all three general models indicates the suitability and adequacy of the developed models to solve the short essay AEG problem and shows that the preliminary results are promising.