Noise Reduction in RTL-SDR using Least Mean Square and Recursive Least Square

Adaptive filter algorithm is a widely used method in communication systems, control systems, digital signal processing etc. This method helps to find out the unknown parameters iteratively by adjusting the filter parameters. There are many efficient adaptive filter algorithms. But among them, the basic algorithms are: Least Mean Square (LMS) and Recursive Least Square (RLS) Algorithms. The LMS algorithm is based on gradient optimization and the RLS algorithm is based on direct form FIR and lattice realization. The RLS algorithm is popular because of its fast convergence although the LMS algorithm is very simple to implement. There are modified LMS algorithms and they are: Leaky Least Mean Square (LLMS) Algorithm and Normalized Least Mean Square (NLMS) Algorithm. „Step size‟ is an important parameter which is used to implement any of these LMS algorithms. In case of RLS algorithm, one term „forgetting factor‟ plays an important role in times of implementing any system.

Channel estimation in wireless communication system using various supervised learning algorithms traditionally involves two very popular algorithms namely Least Mean Square (LMS) and Recursive Least Square (RLS). The concept of variable step size adaptive algorithms came into picture later on to achieve a trade-off between convergence speed and mathematical complexity of these two algorithms (LMS and RLS). The family of variable step size least mean square (VSSLMS) algorithms consists of various members depending on their separate step size adaptation rule. In this paper, a new modified variable step size algorithm is proposed employing a simple mathematical adaptation strategy- the “reward-punishment” rule. The performance of the newly developed algorithm is analyzed in estimating an unknown time varying Rayleigh faded channel and compared with the performance of existing algorithms. The computer simulation shows that the “reward-punishment based variable step size least mean square” algorithm exhibits faster convergence rate compared to LMS and other competitors from VSSLMS family of algorithms and consequently acts as better trade-off between LMS and RLS algorithm. The mathematical complexity measured in terms of CPU time usage also indicates betterment over existing VSSLMS algorithms.

An efficient channel estimation and interference cancelation method for a fixed point to point (p2p) microwave link is designed and investigated; it is based on Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. The LMS and RLS algorithms are compared. The objective is to minimize the computational complexity of channel estimation by using algorithms and to increase channel capacity by implementing 2×2 MIMO systems. Both the channel estimation algorithms and interference cancelation approaches are modeled on the same grounds. Cross-polar interference and fading effects on received signals are analyzed and countered. The performances are compared with one another through simulation results and with analytical results presented in different texts and publications.

Through the study of multiuser detection algorithm, Least Mean Square (LMS), Recursive Least Square (RLS) and Kalman algorithm, the following conclusions are drawn: the convergence of blind LMS algorithm is better than the non-blind, but not stable. RLS and Kalman algorithm are more complex than LMS algorithm, but have better convergence properties, higher SIR and better tracking ability. RLS algorithm and Kalman algorithm are the same complex, but the Kalman algorithm has better performance.

In this paper, we present computationally efficient iterative channel estimation algorithms for Turbo equalizer-based communication receiver. Least Mean Square (LMS) and Recursive least Square (RLS) algorithms have been widely used for updating of various filters used in communication systems. However, LMS algorithm, though very simple, suffers from a relatively slow and data dependent convergence behaviour; while RLS algorithm, with its fast convergence rate, finds little application in practical systems due to its computational complexity. Variants of LMS algorithm, Variable Step Size Normalized LMS (VSSNLMS) and Multiple Variable Step Size Normalized LMS algorithms, are employed through simulation for updating of channel estimates for turbo equalization in this paper. Results based on the combination of turbo equalizer with convolutional code as well as with turbo codes alongside with iterative channel estimation algorithms are presented. The simulation results for different normalized fade rates show how the proposed channel estimation based-algorithms outperformed the LMS algorithm and performed closely to the well known Recursive least square (RLS)-based channel estimation algorithm.

We consider linear prediction problems in a stochastic environment. The least mean square (LMS) algorithm is a well-known, easy to implement and computationally cheap solution to this problem. However, as it is well known, the LMS algorithm, being a stochastic gradient descent rule, may converge slowly. The recursive least squares (RLS) algorithm overcomes this problem, but its computational cost is quadratic in the problem dimension. In this paper we propose a two timescale stochastic approximation algorithm which, as far as its slower timescale is considered, behaves the same way as the RLS algorithm, while it is as cheap as the LMS algorithm. In addition, the algorithm is easy to implement. The algorithm is shown to give estimates that converge to the best possible estimate with probability one. The performance of the algorithm is tested in two examples and it is found that it may indeed offer some performance gain over the LMS algorithm.

The Karhunen-Loeve (KL) transform is a tool to analyse the repolarization period in the ECG. Adaptive algorithms improve the KL series estimation. The recursive least squares (RLS) and least mean squares (LMS) algorithms are studied when applied to estimate the KL coefficients of the ST-T complex in the ECG signal. The performance of RLS and LMS algorithms are compared both in improvement of signal-to-noise ratio (SNR) and in convergence rate. It is presented a specific initialization for the LMS algorithm that obtains the same performance than RLS with lower calculations and without the numerical instability problem, making it the most suitable for the KL estimation.

This paper deals with analytical modelling of microstrip patch antenna (MSA) by means of artificial neural network (ANN) using least mean square (LMS) and recursive least square (RLS) algorithms. Our contribution in this work is twofold. We initially provide a tutorial-like exposition for the design aspects of MSA and for the analytical framework of the two algorithms while our second aim is to take advantage of high nonlinearity of MSA to compare the effectiveness of LMS and that of RLS algorithms. We investigate the two algorithms by using gradient decent optimization in the context of radial basis function (RBF) of ANN. The proposed analysis is based on both static and adaptive spread factor. We model the forward side or synthesis of MSA by means of worked examples and simulations. Contour plots, 3D depictions, and Tableau presentations provide a comprehensive comparison of the two algorithms. Our findings point to higher accuracies in approximation for synthesis of MSA using RLS algorithm as compared with that of LMS approach; however the computational complexity increases in the former case.

The performance of adaptive FIR filters governed by the recursive least-squares (RLS) algorithm, the least mean square (LMS) algorithm, and the sign algorithm (SA), are compared when the optimal filtering vector is randomly time-varying. The comparison is done in terms of the steady-state excess mean-square estimation error /spl xi/ and the steady-state mean-square weight deviation, /spl eta/. It is shown that /spl xi/ does not depend on the spread of eigenvalues of the input covariance matrix, R, in the cases of the LMS algorithm and the SA, while it does in the case of the RLS algorithm. In the three algorithms, /spl eta/ is found to be increasing with the eigenvalue spread. The value of the adaptation parameter that minimizes /spl xi/ is different from the one that minimizes /spl eta/. It is shown that the minimum values of /spl xi/ and /spl eta/ attained by the RLS algorithm are equal to the ones attained by the LMS algorithm in any one of the three following cases: (1) if R has equal eigenvalues, (2) if the fluctuations of the individual elements of the optimal vector are mutually uncorrelated and have the same mean-square value, or (3) if R is diagonal and the fluctuations of the individual elements of the optimal vector have the same mean-square value. Conditions that make the values of /spl xi/ and /spl eta/ of the LMS algorithm smaller (or greater) than the ones of the RLS algorithm are derived. For Gaussian input data, the minimum values of /spl xi/ and /spl eta/ attained by the SA are found to exceed the ones attained by the LMS algorithm by 1 dB independently of R and the mutual correlation between the elements of the optimal vector.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, we will analyze the Least Mean Square(LMS) and Recursive Least Square(RLS) algorithms. Then, we apply these two algorithms to a Multiple-input Multiple-output(MIMO-OFDM) system based on Space-Time Block Coding(STBC), and do some simulations on these two algorithms. From the simulation, it is found that the convergence speed of the RLS algorithm is faster than LMS algorithm, i.e., the performance of RLS is better than LMS algorithm.

The electrical potential of the heart known as Electrocardiogram(ECG) are contaminated by noises like Power Line Interference, Baseline wander and Electrode Motion etc.,. To improve the reliability of the signal, it is necessary to eliminate these noises. Fixed Coefficient filters are very difficult for denoising the ECG signals. The dynamic changes in the ECG signals can be tracked by means of adaptive filters. Different adaptive filters available currently are Least Mean Square (LMS) and Recursive Least Square (RLS) algorithms. The LMS algorithm is considered for its less complexity and efficiency. The computational complexity of the LMS algorithm can be still be improved by using various other algorithms like Sign LMS Algorithm(SLMS), Error Nonlinear Sign LMS algorithm(ENSLMS). When there is a sparse impulse response, the system should dynamically inherit the sparseness level and this is achieved by exploiting the information about the system sparseness. In this paper, a new approach of combining the ENSLMS and ZA-ENLMS is proposed for noise cancellation in ECG. The designed structures are simulated using MATLAB 2014b, Xilinx System Generator and implemented in Virtex 5 FPGA. The performance analysis is done in terms of SNR and computational complexity. The implementation results show that the number of sliced LUT's and the number of slice registers has been reduced to 5.1% and 3.22% respectively compared with the proposed combination.

Orthogonal Frequency Division Multiplexing (OFDM) has recently been applied in wireless communication systems due to its high data rate transmission capability with high bandwidth efficiency and its robustness to multi-path delay. Fading is the one of the major aspect which is considered in the receiver. To cancel the effect of fading, channel estimation and equalization procedure must be done at the receiver before data demodulation. In this paper dealt the comparisons of various algorithms, complexity and advantages, on the capacity enhancement for OFDM systems channel estimation techniques. Mainly three prediction algorithms are used in the equalizer to estimate the channel responses namely, Least Mean Square (LMS), Normalized Least Mean Square (NLMS) and Recursive Least Square (RLS) algorithms. These three algorithms are considered in this work and performances are statically compared by using MATLAB Software.

In wireless sensor networks operating over short inter-node distances, both computation power and radio power influence the battery life. In such a scenario, to evaluate the utility of Smart Antennas (SA) from a power perspective, one has to consider the power consumed in the beamforming (BF) unit (computation power) and the power consumed in the radio unit (radio power). Both computation power and radio power in turn depend on the number of iterations of the BF algorithms. In this paper, two iterative adaptive BF algorithms, Least Mean Square (LMS) algorithm and Recursive Least Square (RLS) algorithm are considered. Computation power measurements have been carried out for a StrongARM SA-1100 processor platform. A closed form expression for optimal number of iterations has been derived for a given bit error rate (BER) that minimizes the total power consumption. It is found that optimal number of iterations increases linearly with path loss exponent and decreases logarithmic with BER. We have analyzed the effect of different BERs and path loss exponents on the optimal number of iterations. Simulation results suggest that RLS algorithm becomes more effective compared to the LMS algorithm in terms of number of iterations at higher path loss exponents. This study yields a new, power optimal stopping criterion, thereby providing a green design for SA systems.

In this paper, we have analyzed the simulation of various adaptive techniques used in wireless communication as a comprehensive view. For this analysis we have derived the algorithm for least mean square (LMS), recursive least square (RLS) and minimum mean square error (MMSE). These adaptive filtering techniques are the best way to mitigate the effect of interference in a communication system. As the power of digital signal processors has increased, adaptive filters have become much more common and are now routinely used in devices such as mobile phones and other communication devices, camcorders and digital cameras, and medical monitoring equipment. Moreover, we have performed the simulation of LMS and RLS algorithm with their error rejection. We, hope that this paper will help both academic as well as industry research by providing the various adaptive techniques at one place along with their simulation result.

Because of the fact that mobile communication channel changes by time, it is necessary to employ adaptive channel equalizers in order to combat the distorting effects of the channel. Least Mean Squares (LMS) algorithm is one of the most popular channel equalization algorithms and is preferred over other algorithms such as the Recursive Least Squares (RLS) and Maximum Likelihood Sequence Estimation (MLSE) when simplicity is a dominant decision factor. However, LMS algorithm suffers from poor performance and convergence speed within the training period specified by most of the standards. The aim of this study is to improve the convergence speed and performance of the LMS algorithm by adjusting the step size using fuzzy logic. The proposed method is compared with the Channel Matched Filter-Decision Feedback Equalizer (CMF-DFE) [1] which provides multi path propagation diversity by collecting the energy in the channel, Minimum Mean Square Error-Decision Feedback Equalizer (MMSE-DFE) [2] which is one of the most successful equalizers for the data packet transmission, normalized LMS-DFE (N-LMS-DFE) [3], variable step size (VSS) LMS-DFE [4], fuzzy LMS-DFE [5,6] and RLS-DFE [7]. The obtained simulation results using HIPERLAN/1 standards have demonstrated that the proposed LMS-DFE algorithm based on fuzzy logic has considerably better performance than others.