Promoting convergence in multi-channel blind signal separation using PNLMS

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.

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.

One of the most important applications of adaptive filter is Interference or noise cancellation. The objective of adaptive interference cancellation is to obtain an estimate of the interfering signal and to subtract it from the corrupted signal and hence obtain a noise free signal. The tracking performances of the LMS and NLMS algorithms are compared when the input of the adaptive filter is no stationary For this purpose, the filter uses an adaptive algorithm to change the value of the filter coefficients, so that it acquires a better approximation of the signal after each iteration. The LMS (Least Mean Square), and its variant the NLMS (Normalized LMS) are two of the adaptive algorithms widely in use. This paper presents a comparative analysis of the LMS and the NLMS in case of interference cancellation from speech signals. For each algorithm, the effects of two parameters-filter length and step size have been analyzed. Finally, the performances of the two algorithms in different cases have been compared.

Among all adaptive noise cancellers, Widrow and Hoff's least mean square (LMS) algorithm has probably become the most popular because of its robustness, good tacking properties and simplicity of implementation. An important limitation of LMS algorithm is that the selection of a certain value for the step size implies compromise between speed of convergence and steady-state misadjustment, The variable step size normalized least-mean-square (VSS- NLMS) algorithm is appropriate to solve the conflicting requirement of fast convergence and low misadjustment of the LMS algorithm. To reduce noise in the output signal of the ANC, a step size for coefficient update is controlled according to the signal-to-noise ratio (SNR). This paper investigates the performance of a noise canceller with DSP processor (TI TMS320C6713) using the LMS algorithm, normalized least-mean-square (NLMS) algorithm, and VSS-NLMS algorithm. Results show the proposed combination of hardware and VSS-NLMS algorithm has not only a faster convergence rate but also lower distortion when compared with the fixed step size LMS algorithm and NLMS algorithm in real-time environments.

A novel adaptive filter algorithm has been proposed that provides faster convergence than the least mean square (LMS) and normalized LMS (NLMS) algorithms. The NLMS algorithm is studied and modified so that the error sequence is used for designing the step size parameter at each iteration. A strategy to reduce the computational complexity the NLMS adaptation requires is used in the proposed algorithm. Computer simulations demonstrate that in the scenario of channel equalization, the proposed algorithm based on the structure of a transversal filter accomplishes faster start-up than the combined LMS/F algorithm recently addressed.

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models.

The adaptive feedback canceller (AFC) based on the least mean square (LMS) or normalized LMS (NLMS) algorithm shows poor convergence for sparse impulse response, since they do not consider the characteristics of the impulse response. The acoustic feedback path of the hearing aid exhibits sparse characteristics consisting of few active coefficients and many non active (near to zero) coefficient values. This paper proposes an improved gradient controlled improved proportionate NLMS (IGC-IPNLMS) algorithm for cancelling the feedback phenomenon in hearing aids. The IGC-IPNLMS algorithm employs a variable convergence factor, an estimate of the gradient vector for allocating step size, the controlling parameter of the IGC-IPNLMS algorithm is also updated in each iteration based on the sparseness measure. Further, the reduction in computational complexity is achieved by using sparse partial update method along with the IGC-IPNLMS algorithm (SIGC-IPNLMS) for feedback cancellation. The simulation results show the superior performance of the proposed method for white noise and speech segment as input.

This paper presents fixed-point dedicated architecture of NLMS (Normalized Least Mean Square) adaptive filtering algorithm for the harmonics power line interference cancelling. The NLMS is the normalized version of the LMS algorithm, whose main characteristics are related to the increase of speed of adaptation, and low sensitivity to the power reference signal. The developed architecture was described in VHDL and synthesized to FPGA. Synthesis results indicate that the interference canceller based on NLMS filter is able to efficiently cancel the interferences in the fundamental frequency, and its high order harmonics, with faster convergence speed than the previously proposed prominent solution that uses the LMS adaptive filter.

The role of the intelligent optimization algorithm in the blind separation algorithm is to make the independence decision function enter the global optimal position, but the performance of many optimization algorithms depends on the choice of control parameters. In this paper, we use the simplex neighborhood convex set approximation idea, combined with the full random search and multi-role state of the search operator, we use a single-parameter surface-simplex swarm evolution (SSSE), which has a single parameter and pure randomness. The characteristics of the search can overcome the shortcomings of the algorithm’s dependence on the control parameters and easily fall into the local optimum, and improve the application effectiveness of the blind separation algorithm. In the experiment, the fourth-order cumulant (kurtness) is used as the criterion function in ICA, and the improved blind separation algorithm is applied to the blind separation of speech and background music signals. Experimental results show that the improved algorithm effectively separates speech components from the background. The music component and the algorithm have better performance in terms of convergence speed, algorithm stability, and separation effect.

This paper proposes a new variable step-size adaptive filtering algorithm based on the LMS algorithm and compares its performance with Least Mean Squares(LMS), Normalized Least Mean Squares(NLMS), Modified Sigmoid- LMS(MLMS) and Regularized NLMS(RNLMS) algorithms. The results indicate that compared to the other comparative algorithms, this algorithm can more effectively improve the signal-to-noise ratio of the filter output. Furthermore, within a wide input signal-to-noise ratio range, this algorithm can consistently enhance the filter signal-to-noise ratio output, effectively addressing the problem of inconsistent filtering effects caused by the input signal-to-noise ratio sensitivity in algorithms such as NLMS algorithms.

This paper is focusing on the performance of the proposed exponentially weight recursive least square (EW-RLS) and normalized least mean square (NLMS) channel estimator using simulations, in the context of the communication system with MIMO antenna operating in outdoor environments. Different training rates and different Doppler frequencies are used to track time-variations of the channel. Three adaptive algorithms are considered; namely the least squares (LS), RLS algorithm and the least mean square (LMS) algorithm. In channel estimation, RLS is widely used especially for slow time-varying. Even though RLS is little bit complex compare to LMS, but it has faster convergence speed. The performance is evaluated in terms of the mean square error (MSE) of the channel estimate, and the system bit error rate (BER), for different Doppler frequencies (correspond to different mobility speeds). Simulation results have demonstrated that time-domain adaptive channel estimation and tracking in MIMO OFDM systems based on the decision directed (DD) EW-RLS and DD-NLMS is very effective in slowly to moderate time-varying fading channels. This paper provides analysis, evaluation and computer simulations in MATLAB.

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.

Adaptive filtering has been successfully used in canceling line echos in the telephone network since the 1960’s [179, 443, 387]. In these cases, the adaptive filter is used to model the unknown echo path in a communications channel and then cancel the echo signals from the conversation. An adaptive filter is required because the echo path is not only unknown, but also because it is different for each network path. However, the acoustic echo cancellation problem is not as easily solved with conventional adaptive filtering systems due to the requirements for a much longer adaptive impulse response and for faster convergence since the acoustic echo path is time-varying during the communication transmission. In this chapter, we summarize key results from adaptive filter theory, and discuss the least mean square (LMS) and normalized least mean square (NLMS) algorithms used to adjust an adaptive filter. We then examine adaptive filtering in subbands as one method for acoustic echo cancellation. Simulations (using a measured room response with speech signals) demonstrate that the oversampled subband adaptive system provides improved performance for acoustic echo cancellation applications.

This paper compares the convergence rate performance of the normalized least-mean-square (NLMS) algorithm to that of the standard least-mean-square (LMS) algorithm, which is based on a well-known interpretation of the NLMS algorithm as a form of the LMS via input normalization. With this interpretation, the analysis is considerably simplified and the difference in rate of parameter convergence can be compared directly by evaluating both the condition number of the normalized and unnormalized input correlation matrix. This paper derives the condition number expressions for the normalized input correlation matrix of which the arbitrary-length filter model is linear with respect to its adaptable parameters and contain only two distinct unnormalized eigenvalues. These expressions, which require that the input samples be statistically stationary and zero-mean Gaussian distributed, provide an important insight into the relative convergence performance of the NLMS algorithm to that of the LMS as a function of filter length. This paper also provides a conjecture which set bounds on the NLMS condition number for any arbitrary number of distinct unnormalized eigenvalues.