Analysis of Partial Diffusion LMS for Adaptive Estimation Over Networks with Noisy Links

Performance analysis of the deficient length augmented CLMS algorithm for second order noncircular complex signals

Recently proposed distributed adaptive estimation algorithms for wireless sensor networks (WSNs) do not consider errors due to noisy links, which occur during the transmission of local estimates between sensors. In this paper, we study the effect of noisy links on the performance of distributed incremental least-mean-square (DILMS) algorithm for the case of Gaussian regressors. More specifically, we derive theoretical relations which explain how steady-state performance of DILMS algorithm (in terms of mean-square deviation (MSD), excess mean-square error (EMSE), and mean-square error (MSE)) is affected by noisy links. In our analysis, we use a spatial-temporal energy conservation argument to evaluate the steady-state performance of the individual nodes across the entire network. Our simulation results show that there is a good match between simulations and derived theoretical expressions. However, the important result is that unlike the ideal links case, the steady-state MSD, EMSE and MSE are not monotonically increasing functions of step size parameter when links are noisy. In addition, the optimal step size is found in a closed form for a special case which minimizes the steady-state values of MSD, EMSE, and MSE in each node.

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.

The paper is concerned with analyzing the roundoff error effect on the tracking performance of the block least mean square (BLMS) algorithm when used in the adaptive identification of a time-varying plant. Rounding quantization is assumed. Expressions are derived for the steady state mean square error, steady state mean square weight deviation, and the corresponding optimum step sizes. It is found that the mean square error and the mean square weight deviation are decreasing functions of both the filter coefficients wordlength and the algorithm block size. Expressions for minimum and maximum block lengths are derived. The performance of the BLMS is compared to that of the conventional LMS algorithm. It is found that the BLMS possesses a higher resistance to roundoff errors than the LMS algorithm. The theoretical results of the paper are validated by computer simulations.

Recently, a zero-attractor natural gradient non-parametric maximum likelihood (ZA-NG-NPML) algorithm has been proposed for sparse channel estimation in the presence of non-Gaussian noise. The ZA-NG-NPML outperforms existing sparse channel estimation algorithms in the presence of non-Gaussian noise in terms of mean square error (MSE) and convergence. In this brief, a rigorous second order convergence analysis of ZA-NG-NPML algorithm is presented and upper bound on the steady state mean square deviation of active and inactive taps is derived. Further, we also derive the upper bound on the steady state excess MSE for ZA-NG-NPML. Simulation results validate the derived upper bound.

A convex combination LMS (least mean square) algorithm based on Krylov subspace transform is proposed in this paper. In this approach, impulse response of the unknown system is firstly transformed into Krylov subspace, in which the system structure is changed into sparse. Then an improved proportionate normalized LMS (IPNLMS) algorithm and a variable tap-length normalized LMS (VTNLMS) algorithm are combined. Simulations are performed to show the convergence performance of the combined algorithm. The results show that both a fast convergence rate and small steady state mean square deviation (MSD) are obtained.

Decision Feedback Equalizer (DFE) offers a good compromise between complexity and performance for channels with strong Intersymbol Interference (ISI). However, their blind or Decision-Directed (DD) adaptation may endure the inherent limitation from blind equalization algorithm or DD algorithm, i.e., 1) the blind equalization such as Constant Modulus Algorithm (CMA) has the ¿eye-opened¿ ability, but moderate convergence rate and steady state Mean Square Error (MSE); 2) the DD algorithm has faster convergence rate and lower steady state MSE, but it always cannot work unless the MSE of received signals is very low. So for overcoming above disadvantages we study the geometrical relation between CMA1-2 and DD algorithm and obtain the method of soft switch between CMA1-2 and DD algorithm. Consequently a new DFE based on CMA1-2 and DD algorithm is proposed. Based on theoretical analysis and computer simulations, the proposed approach is shown to be much more effective than the conventional DFE.

A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size mu . The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N/sub c/ and steady state mean square excess estimation error epsilon . It is shown that N/sub c/ is proportional to 1/( mu lambda ), with lambda being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N/sub c/ epsilon is independent of mu . For a given epsilon , the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of mu that achieves tolerable values of N/sub c/ and epsilon is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on mu . An optimum value of mu is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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. >

Deep in-memory architecture (DIMA) provides considerable latency and throughput improvements over conventional digital architectures. DIMA reads multiple bits per bit-line (BL) in each cycle, and performs mixed-signal processing at the periphery of the bit cell array (BCA). Past work [1] used adaptive filtering as a means to analyse the impact of nonlinear read operation on gradient descent methods implemented on DIMA. Gradient descent techniques are typically implemented in block fashion in DIMA since write operations have high overhead. This work uses block least mean square (BLMS) adaptive filters as an example to study the impact of nonlinearity and variations encountered in DIMA. The insights gained from BLMS adaptive filters are used to realize recursive least square (RLS) adaptive filters. The steady state mean square error (MSE) of both filters remains unaffected while convergence rate and stability issues can arise when these filters are implemented on DIMA. The insights are useful in context of learning systems employing gradient descent techniques.

Distributed sparse diffusion estimation based on set membership and affine projection algorithm

In this paper, we investigate the impacts of network topology on the performance of a distributed estimation algorithm, namely combine- then-adaptive (CTA) diffusion LMS, based on the data with or without the assumptions of temporal and spatial independence with noisy links. The study covers different network models, including the regular, small-world, random and scale-free whose the performance is analyzed according to the mean stability, mean-square errors, communication cost (link density) and robustness. Simulation results show that the noisy links do not cause divergence in the networks. Also, among the networks, the scale free network (heterogeneous) has the best performance in the steady state of the mean square deviation (MSD) while the regular is the worst case. The robustness of the networks against the issues like node failure and noisier node conditions is discussed as well as providing some guidelines on the design of a network in real condition such that the qualities of estimations are optimized.

In this study, the effects of noisy links are investigated on the steady-state performance of mobile adaptive networks with diffusion least mean-squares strategies. The authors derive theoretical relations which explain how the steady-state performance metrics, including the steady-state network mean-square deviation and steady-state velocity mean-square-error is affected by noisy links. The provided analysis relies on the spatial–temporal energy conservation argument. The proposed simulation results reveal that although the noisy links degrade the performance of mobile adaptive networks; however, for suitably chosen combination coefficients the mobile adaptive network with noisy links provides a bounded estimation error. Finally, the proposed simulations verify that the derived theoretical analysis closely matches the actual steady-state performance observed in a network.

The steady state mean square prediction error is derived for the fixed-point RLS (recursive least squares) algorithm, both for the exponentially windowed RLS (forgetting factor, gamma >

A generalized performance evaluation method is presented for extended Kalman filter based state estimation of first order nonlinear dynamic systems. The first order nonlinear dynamic systems are placed in three categorizes in terms of the upper bound of the absolute values of the derivatives of the nonlinear functions. According to the proposed theoretical analysis, it is shown that different state estimation performances are achieved by applying the extended Kalman filter to the first order nonlinear systems in these three categorizes. The steady state mean square error performance of the filter is presented explicitly in terms of the bounds on the nonlinearity and noise variance. The advantage of this performance evaluation method is that the convergence property of estimation error variance can be easily concluded from the system nonlinearity before its implementation. This provides insight into what is going to happen in applications, e.g. for dynamic systems used in chaotic synchronization. The simulation of several different nonlinear dynamic systems shows the effectiveness of the proposed performance evaluation criteria.