A Fast and Robust Adaptive Blind Equalization Algorithm in High Speed Satellite Channel

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

This paper presents two classes of adaptive blind algorithms based on second- and higher order statistics. The first class contains fast recursive algorithms whose cost functions involve second and third- or fourth-order cumulants. These algorithms are stochastic gradient-based but have structures similar to the fast transversal filters (FTF) algorithms. The second class is composed of two stages: the first stage uses a gradient adaptive lattice (GAL) while the second stage employs a higher order-cumulant (HOC) based least mean squares (LMS) filter. The computational loads for these algorithms are all linearly proportional to the number of taps used. Furthermore, the second class, as various numerical examples indicate, yields very fast convergence rates and low steady state mean square errors (MSE) and intersymbol interference (ISI). MSE convergence analyses for the proposed algorithms are also provided and compared with simulation results. >

A new CMA adaptive beamforming algorithm based on modified conjugate gradient method is proposed. This algorithm focuses on a new technique for data block modification method with conjugate gradient, and overcomes the shortcoming of traditional CMA algorithms, which has slow convergence speed or vast complexity. Computer simulations show that the algorithm has better convergence performance and better SINR capability than other kinds of CMA algorithms.

Attention has been focused on the moving target detection in heavy sea clutter. On the basis of detection model of moving target with fluctuant amplitudes, a novel adaptive algorithm in fractional Fourier transform (FRFT) domain is proposed, which combines statistic-based and FRFT-based detection method. FRFT has good energy concentration property on linear frequency modulation (LFM) signal with the optimal transform angle, which is determined by calculating spectral kurtosis (SK) in FRFT domain. Grading iterative search method is used for good accuracy of parameter estimation and fast calculation speed. A novel adaptive line enhancer (ALE) in FRFT domain is proposed to suppress sea clutter and improve signal-to-clutter ratio (SCR), which provides less error and faster convergence. Leakage factor is introduced into the update equation of weight vector to reduce ‘memory effect’ and step size is normalised by the power of input signal with better convergence characteristic. In the end, both X-band and S-band real sea clutter is used for verification and the results present that the proposed algorithm has good convergence property and small mean square error (MSE). Weak moving target in low SCR environment (SCR=−6 dB) can be well detected and estimated, which indicates the effectiveness of the algorithm.

As an important component of autonomous intelligent systems, the research on autonomous positioning algorithms used by UAVs is of great significance. In order to resolve the problem whereby the GNSS signal is interrupted, and the visual sensor lacks sufficient feature points in complex scenes, which leads to difficulties in autonomous positioning, this paper proposes a new robust adaptive positioning algorithm that ensures the robustness and accuracy of autonomous navigation and positioning in UAVs. On the basis of the combined navigation model of vision/inertial navigation and satellite/inertial navigation, based on ESKF, a multi-source fusion model based on a federated Kalman filter is here established. Furthermore, a robust adaptive localization algorithm is proposed, which uses robust equivalent weights to estimate the sub-filters, and then uses the sub-filter state covariance to adaptively assign information sharing coefficients. After simulation experiments and dataset verification, the results show that the robust adaptive algorithm can effectively limit the impact of gross errors in observations and mathematical model deviations and can automatically update the information sharing coefficient online according to the sub-filter equivalent state covariance. Compared with the classical federated Kalman algorithm and the adaptive federated Kalman algorithm, our algorithm can meet the real-time requirements of navigation, and the accuracy of position, velocity, and attitude measurement is improved by 2–3 times. The robust adaptive localization algorithm proposed in this paper can effectively improve the reliability and accuracy of autonomous navigation systems in complex scenes. Moreover, the algorithm is general—it is not intended for a specific scene or a specific sensor combination– and is applicable to individual scenes with varied sensor combinations.

In this paper, a fast blind equalization with a two-stage generalized multilevel modulus algorithm (GMMA) and soft decision-directed (SDD) scheme is proposed for high-order QAM (64/256/1024QAM) systems on the downstream wired cable channel. The proposed fast blind equalization algorithm applies the two-stage convergence scheme and the SDD part uses the scheme with an adaptively selected decision region. In the first convergence stage, the joint GMMA and modified SDD equalization is applied for the purpose of the fast convergence. When the convergence process reaches the enough steady state, the convergence detector changes the first stage equalization to the second stage. In the second stage, the modified SDD scheme is applied to reduce the mean square error (MSE) further. On the wired cable channel at the 64/256/1024QAM modes, the proposed blind algorithm performs faster convergence speed than the previous blind methods do; meanwhile, the proposed algorithm also achieves smaller MSE than the other methods at the same signal-to-noise ratio (SNR).

Objectives Global navigation satellite system(GNSS) tomography, characterized by reconstructing the three-dimensional distribution of the atmospheric water vapor, has proved its capacity for studying the extreme weather events. The ill-conditioned problem resulting from the GNSS acquisition geometry is the critical issue of the GNSS tomography system. Algebraic reconstruction techniques, with the advantages of simple iteration and fast convergence, has been widely applied to the tropospheric tomography. However, the error allocation principle based on the intersection length of GNSS rays with each ray-voxel affects the accuracy of tomographic results. An improved adaptive algebraic reconstruction techniques are proposed to address this problem. Methods In view of the unreasonable error allocation in the traditional algorithm, we suggest a new error allocation principle based on the variation of water vapor density(WVD) in voxels for the adaptive algorithms, in which the product of the intersection length and WVD is considered as a new principle to redistribute the difference between the GNSS slant water vapor(SWV)and the reconstructed SWV. Besides, the weight matrix model of elevation angles is introduced to the improved algorithm to optimize the tomographic results. Results The new algorithms are tested by measured data from Xuzhou continuously operating reference stations(CORS) network and radiosonde during July2016. Experimental results reveal that the WVD derived from the adaptive algorithms performs better than that of the general algorithms in root mean squared error(RMSE), standard deviation(STD) and mean absolute error(MAE), and the RMSE is decreased by 25.91%, 15.81%, and 24.64% for adaptive algebraic reconstruction technique(AART), adaptive multiplicative algebraic reconstruction technique(AMART)and adaptive simultaneous iterative reconstruction technique(ASIRT) respectively. Under the conditions of light rain, moderate rain and heavy rain, the adaptive algorithms retrieve better water vapor profile than the traditional ones. Conclusions Overall, the water vapor profile derived from the adaptive algorithms agrees with the radiosonde distribution better than the traditional algorithms, which reveals the advantage of the proposed method on optimizing the tomography solutions.

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 CRIMNO criterion is extended to the case of fractionally spaced blind equalization. Simulation results show that the fractionally spaced CRIMNO algorithm, especially its adaptive version, converges faster than the synchronous CRIMNO algorithm, and faster than the fractionally spaced Goddard (1980) CMA algorithm. Insights into why the fractionally spaced blind equalization algorithm has faster convergence are given. >

Fast square-root RLS adaptive filtering algorithms

In digital communication system that the Modified Constant Modulus Algorithm (MCMA) reduced the use of the adaptive equalization algorithm to combat the Inter-symbol Interference (ISI). MCMA is relatively brief operation. The major point of MCMA that it only achieves moderate convergence rate and steady state mean square error (MSE). In this paper suggest, MCMA equalization improve the performance with parallel structure. It combines Modified Constant Modulus Algorithm(MCMA) and Modified Decision Directed(MDD) algorithm. By exploiting the inherent structural relationship between the 4-QAM signal's coordinates and 16-QAM signal's coordinates, another style of cost function for Modified Constant Modulus Algorithm(MCMA) is defined and If it happen to offset of received signals and MCMA is poor performance in order to overcome this because the paper combines apply for MCMA and MDD(Modified Decision Direct) algorithm. By computer simulation, we confirmed that the proposed PMCMA-MDD algorithm has the fater convergence rate and steady mean square error than the conventional MCMA.

In this paper, a two-dimensional (2-D) fast adaptive filtering algorithm based on the exponentially weighted least squares errors is developed for the non linear canonical piecewise quadratic (CPWQ) model. This algorithm take advantages of the non linear CPWQ modeling and the fast convergence of the exponentially weighted least squares adaptive algorithm. The simulation results show that the proposed method gives good results in image restoration. Experimental comparison with the canonical piecewise linear (CPWL) model shows the superiority of the non linear filter in term of image enhancement.

The speech enhancement is one of the effective techniques to solve speech degraded by noise. In this paper a fast speech enhancement method for noisy speech signals is presented, which is based on improved Kalman filtering. The conventional Kalman filter algorithm for speech enhancement needs to calculate the parameters of AR (auto-regressive) model, and perform a lot of matrix operations, which usually is non-adaptive. The speech enhancement algorithm proposed in this paper eliminates the matrix operations and reduces the calculating time by only constantly updating the first value of state vector X(n). We design a coefficient factor for adaptive filtering, to automatically amend the estimation of environmental noise by the observation data. Simulation results show that the fast adaptive algorithm using Kalman filtering is effective for speech enhancement.

The most popular robust adaptive beamforming technique is diagonal loading. However, no clear guidelines can be applied to choose the optimal diagonal loading factor, and beamforming techniques based on the uncertainty set of array steering vector still need to specify the bound of the uncertainty set. In this paper, we develop a novel robust adaptive algorithm. Firstly, we modify covariance fitting criteria (CFC) via replacing the conventional sample covariance matrix used in CFC by the general linear combination (GLC) covariance matrix estimates. Then we use the modified CFC to estimate the covariance matrix of array observation data in the standard capon beamforming formulation. The merits of our method we term GLC-CFC include applicability to arbitrary number of snapshots, robustness to the correlated sources and without the requirement of specifying any user-parameters. The excellent performance of our method in small snapshots size is demonstrated via numerical examples and compared with other classical adaptive beamforming algorithms.

Context: In the literature, numerous adaptive equalization techniques have been developed to effictively reduce inter-symbol interference in digital communication systems. Objective: This study conducts a comparative analysis of four such adaptive algorithms: NLMS, APA, PAP, and MRNQ, implemented within a decision feed-forward equalizer (DFE) stucture. The purpose of this evaluation is to identify the strengths and limitations of each algorithm under the same transmission conditions. The insights gained from this comparaison can guide the choice of equalization strategy for practical implementations in modern communication systems. Method: The performance of each equalizer is assessed using multiple evaluation criterion, including computational complexity, constellation diagram analysis, the Nyquist criterion, and mean squared error (MSE) performance. Results: All four algorithms effectively reduce inter-symbol interference and ensure proper signal equalization. However, DFE-PAP and APA-DFE show superior speed and accuracy, MRNQ-DFE offers a good trade-off, and NLMS-DFE performs the weakest. Conclusions: In summary, the study highlights DFE-PAP as the most efficient and pratical solution, combining strong ISI mitigation with low computationnal cost. While all algorithms perform well, DFE-PAP and APA-DFE demonstrate clear advantages in convergence speed and accuracy.