Research on geometric algebra-based robust adaptive filtering algorithms in wireless communication systems

The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.

The minimum error entropy (MEE) criterion closely relies on the quadratic information potential (QIP) estimates of Renyi’s entropy. Nevertheless, the conventional obtained QIP estimates are numerically unstable, especially when the error samples contain outliers, resulting in the optimal solution of the MEE criterion deviating from the target vector to a certain extent. To address this problem, we introduce the M-estimate method from robust statistics into the QIP estimation process; thus, a robust estimation method called instantaneous M-estimate QIP (IM-QIP) is proposed, and several important properties of IM-QIP are presented. The proposed IM-QIP estimates could be implemented simply while ensuring great robustness. Naturally, we further propose the corresponding instantaneous M-estimate MEE (IM-MEE) criterion and apply it to adaptive filtering. A robust recursive adaptive filtering algorithm, called the recursive IM-MEE (RIM-MEE) algorithm, is proposed and analyzed in this article, along with its stability and theoretical steady-state performance. Additionally, we demonstrate that the RIM-MEE algorithm achieves a smaller theoretical bound compared to the traditional MEE algorithm under heavy-tailed and skewed noise conditions. The simulation results revealed the robustness of the IM-QIP estimates and verified the theoretical expectations and superior performance of the RIM-MEE algorithm.

Adaptive filters are prevalent in many real‐time signal processing applications. Many adaptive algorithms already exist, but most of them assume white Gaussian noise as disturbance. However, for many applications such as electrocardiogram, foetus heart rate measurement, low frequency atmospheric noise, underwater acoustic noise and signal measurement in instrumentation, the impulsive noise is more common. This study presents a modified robust mixed norm (MRMN) adaptive filter algorithm robust to impulsive noise with higher convergence rate and lower steady state error (SSE). MRMN adaptive filter algorithm has been simulated using Matlab and Xilinx system generator high level synthesis tool and a significant improvement in SSE and convergence speed is obtained compared with the existing adaptive filter algorithms for similar specifications. The proposed algorithm is also described using VHDL and synthesised using Xilinx synthesiser tool in order to implement on field‐programmable gate array (FPGA). The FPGA post route and place implementation results show nearly 90% reduction in resource utilisation and nearly 2.6 times improvement in clock frequency as compared with the existing FPGA based implementation for similar specifications.

A novel least-mean kurtosis adaptive filtering algorithm based on geometric algebra (GA-LMK) is proposed for multidimensional signal processing. First, taking advantage of geometric algebra (GA) in terms of the representation of multidimensional signal, the GA-LMK algorithm represents a multidimensional signal as a GA multivector. Second, we extend the original least mean kurtosis (LMK) algorithm in GA space for multidimensional signal processing. The proposed GA-LMK algorithm minimizes the cost function of negated kurtosis of the error signal in GA space, and provides a way to make tradeoff problem between convergence rate and steady-state error. Third, we study the steady-state behavior of the GA-LMK algorithm under Gaussian noises to acquire conditions of misadjustment. The simulation results show that our proposed GA-LMK adaptive filtering algorithm can outperform significantly existing the state-of-the-art algorithms in terms of convergence rate and steady-state error.

The purpose of adaptive filter is to solve the dilemma of fast convergence rate and low mean square error. In the past two decades many adaptive filter algorithms have been presented and have claimed that they have good convergence speed and tracking properties. This paper describes the concept of adaptive noise cancellation, an alternative method of estimating signals corrupted by additive noise or interference. This paper summarizes three promising algorithms and gives a performance comparision via extensive simulation. Step size is the main parameter for the convergence rate and mean square error. The simulation analysis showed that RLS algorithm had faster convergence speed and smaller steady state error compared with basic LMS algorithm.The results shown, for convergence rate with less no of taps is the most difficult phase in signal processing applications for the perfect working of any system.

Entropy-based cost functions are enjoying a growing attractiveness in unsupervised and supervised classification tasks. Better performances in terms both of error rate and speed of convergence have been reported. In this letter, we study the principle of error entropy minimization (EEM) from a theoretical point of view. We use Shannon's entropy and study univariate data splitting in two-class problems. In this setting, the error variable is a discrete random variable, leading to a not too complicated mathematical analysis of the error entropy. We start by showing that for uniformly distributed data, there is equivalence between the EEM split and the optimal classifier. In a more general setting, we prove the necessary conditions for this equivalence and show the existence of class configurations where the optimal classifier corresponds to maximum error entropy. The presented theoretical results provide practical guidelines that are illustrated with a set of experiments with both real and simulated data sets, where the effectiveness of EEM is compared with the usual mean square error minimization.

The LMS adaptive filter algorithm can be viewed as the application of a simple iterative linear equation solver to an estimated time variantWiener-Hopf equation.With this interpretation we can utilize the “bag-of-tricks” available in numerical linear algebra in devising new adaptive filter algorithms. Making use of the preconditioning paradigm, we present in this paper a new family of NLMS-type adaptive filter whose performance can be tailored to possible a priori knowledge of the autocorrelation properties of the input signal. The design of circulant preconditioning matrices for such adaptive filter algorithms is the main contribution of the paper.

Given the complex traffic factors and strong mobility of a transit vehicles, it is difficult to predict its travel time with the conventional prediction models. The emphasis of this research effort is to improve the adaptability of the Kalman filter model with regard to transit bus travel time prediction. In order to resolve the filter divergence and calculated divergence in the prediction process, an adaptive fading Kalman filter algorithm is put forward in this paper. Compared with the conventional Kalman filter prediction model, a "forgotten factor" is added to the adaptive fading Kalman filter algorithm to restrain the influence of the old data on the filter. Furthermore, it can correct the predictive value and the model parameters with the latest measured value, hence higher adaptability and predictive accuracy. Finally, the GPS data of transit vehicles in the city of Yichun is used in the paper to verify the effectiveness of the new model. The results reveal that the adaptive fading Kalman filter algorithm is more effective than the conventional one. It performs better in terms of convergence and dynamic adaptability, implying a brighter application prospect.

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.

A generalized least squares fast transversal filter algorithm for the decision feedback equalization of dispersive channels

This paper addresses the problem radio mobile channel identification and equalization by blind algorithms. For this, we have proposed two algorithms, which are compared with: cumulants based algorithms, and adaptive filter algorithms (such us the constant modulus algorithm (CMA), Fractional Space CMA (FSCMA) and Sign Kurtosis Maximization Adaptive Algorithm (SKMAA)). However, The simulation results in noisy environment and for different SNR values with QPSK or 4QAM modulation shows that the proposed algorithms gives a good identification and equalization versus to the cumulants and the adaptive filter algorithms, for radio mobile channel.

This paper describes a method for noise removal from ultrasonic signals used in NDE (Non Destructive Evaluation) applications. The method used is FPGA based adaptive noise cancellation. Indeed adaptive filtering is one of the core technologies in digital signal processing. We can find numerous application areas in science as well as in industry. Adaptive filtering techniques are used in a wide range of applications, including system identification, adaptive equalization, adaptive noise cancellation and echo cancellation. Characteristics of signals that are generated by systems of the above application are not known a priori. Under this condition, a significant improvement in performance can be achieved by using adaptive rather than fixed filters. An adaptive filter is a self-designing filter that uses a recursive algorithm (known as adaptation algorithm or adaptive filtering algorithm) to design itself. Here the algorithm used is normalized least mean square algorithm, which has good convergence and stability. Keywords; Adaptive noise cancellation, NLMS algorithm, NDE applications, ultrasonic grain noise.

This paper deals with the problem of echo cancellation of speech signals in an acoustic environment. In this regard, generally, different adaptive filter algorithms are employed, which may lack the flexibility of controlling the convergence rate, number of iterations, range of variation of filter coefficients, and tolerance consistency. In order to overcome these problems, unlike conventional approaches, we formulate the task of echo cancellation as a coefficient optimization problem whereby we introduce the particle swarm optimization (PSO) algorithm. In this case, the PSO is designed to perform the error minimization in frequency domain. From extensive experimentations, it is shown that the proposed PSO based acoustic echo cancellation method provides high echo cancellation performance in terms of echo return loss enhancement with a faster convergence rate in comparison to that obtained by some of the state-of-the-art methods.

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.

The generalized maximum correntropy criterion (GMCC) has been widely applied for robust adaptive filtering (AF) algorithm. The gradient-based GMCC (GB-GMCC) algorithm realizes good filtering performance for system identification under impulsive noise environments. However, the highly colored input signal can damage the convergence rate of GB-GMCC. Therefore, based on the data-reusing method, we propose a robust AF algorithm, called as data-reusing GMCC (DR-GMCC) algorithm, which uses the information of the latest <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> input data to remedy the convergence limitation of GB-GMCC. In addition, to enhance the filtering performance of DR-GMCC, we use a random strategy to select the past <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K$</tex> input data leading to a new algorithm, named as random DR-GMCC (RDR-GMCC). Furthermore, for RDR-GMCC, we also analyze the mean-square convergence and computational complexity. Compared with existing algorithms, simulation results verify that RDR-GMCC achieves better filtering accuracy and faster convergence rate.