An improved NLMS algorithm for channel equalization

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.

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.

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.

In the radio observation based on the large single antenna, in order to reduce the interference of navigation signal L 2 from observation of the red-shifted H I spectral line at L-band, we used the an auxiliary channel and normalized LMS algorithm, and proposed new evaluating indicators deduced by theoretical method. Finally, we verified the suppression performance and the indicators' utility by multiple simulations and statistical method.

The transversal adaptive filter using the least mean square (LMS) algorithm of Widrow and Ropf (1976) has been widely used mainly due to its relative ease of implementation. The major drawback of this time-domain LMS (TDLMS) algorithm is that as the eigenvalue spread of the input autocorrelation matrix increases, the convergence speed of the algorithm decreases. This led to the transform domain adaptive filters where the input signals are orthogonalized. Normalized frequency domain LMS algorithms (NFDLMS) are known to be faster than the time domain implementations. However, in some implementations with low signal to return noise ratio, NFDLMS algorithms can have stability problems. The stability problem can be solved by weighting the normalization gain /spl mu/. We perform computer simulations for the telephone echo channel and show that the modified /spl mu/-weighted NFDLMS algorithm is 8 times faster than the time-domain LMS (TDLMS) algorithm and more stable than the NFDLMS algorithm over a wide range of signal to noise ratios.

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.

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.

Energy detection (ED) receiver is one of two popular receivers for non-coherent (NC-) ultra-wideband (UWB) Green Communications. In this paper, weighted ED (WED) receivers are further investigated for NC-UWB systems using different adaptive filtering algorithms. In the conventional normalized least mean square (NLMS) algorithm, a fixed step-size is used to update the weighting coefficients of WED receivers, and therefore there must be a trade-off between the steady state error and the convergence speed. Correspondingly, an improved NLMS (INLMS) algorithm was recently proposed to address this issue. In this paper, parameter optimization is discussed for the INLMS algorithm and accordingly the parameter optimized (PO-) INLMS algorithm is presented. Moreover, convergence behavior and bit error rate (BER) performance are evaluated for adaptive WED receivers. Simulation results show that compared to the traditional NLMS algorithm, PO-INLMS possesses significant benefits in convergence rate together with about 0.3-dB-gain in terms of the BER performance, and therefore the PO-INLMS based WED receiver can be considered as a promising candidate for energy-aware NC-UWB Green Communications.

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.

Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.

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.

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.

In this investigation, an adaptive filter algorithm using Fractional Fourier transform (FrFT) has been developed for enhancement of targets in microstructure noise. In particular, the FrFT is introduced as a transformation tool to prepare ultrasonic signals for a more compact support. It also reduces the non-stationarity of signals. Furthermore, a normalized least mean square (NLMS) filter is applied on the transformed signal to suppress the grain noise. In order to evaluate the performance of the algorithm, various experimental ultrasonic data sets are acquired from a large grained specimen with embedded defects. A 5-MHz broadband transducer is utilized for data acquisition. The proposed algorithm is applied to discriminate defects in presence of high grain scattering noise. The experimental study shows that the algorithm greatly reduces grain noise and improves the signal-to-grain-noise ratio by about 12 dB. With the help of FrFT and the NLMS filter, the algorithm successfully identifies defects embedded in grain noise. This type of study can broaden the scope of applying adaptive filter in material evaluation and target detection.

This paper aims to apply adaptive filtering algorithms in sensor array processing for underwater surveillance and detection systems with linear arrays. Adaptive filters are iterative in nature and continuously update the filter taps to minimize the error signal based upon certain criterion. Adaptive filters are used in beamforming to place the main beam in the direction of desired signal and place nulls in the direction of unwanted signals. Adaptive filters are also used in spectral analysis of acoustic signals for background noise cancellation. This paper evaluates the performance of three adaptive filtering algorithms with respect to sensor array design parameters i.e. number of sensors, sensor spacing, number of incident signals and their angular separation. The three adaptive filtering algorithms namely least mean square (LMS), normalized LMS (NLMS), and sample matrix inversion (SMI) have been compared in the context of linear array beamforming. The paper provides detailed discussions on the simulation results of these adaptive algorithms in terms of convergence speed, beamwidth, null depths and maximum side lobe levels. In addition the paper illustrates a practical example of applying adaptive filters in underwater sensor array processing systems for detection of target’s acoustic signatures.

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.