2,397 research outputs found
A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost
We introduce a novel family of adaptive filtering algorithms based on a
relative logarithmic cost. The new family intrinsically combines the higher and
lower order measures of the error into a single continuous update based on the
error amount. We introduce important members of this family of algorithms such
as the least mean logarithmic square (LMLS) and least logarithmic absolute
difference (LLAD) algorithms that improve the convergence performance of the
conventional algorithms. However, our approach and analysis are generic such
that they cover other well-known cost functions as described in the paper. The
LMLS algorithm achieves comparable convergence performance with the least mean
fourth (LMF) algorithm and extends the stability bound on the step size. The
LLAD and least mean square (LMS) algorithms demonstrate similar convergence
performance in impulse-free noise environments while the LLAD algorithm is
robust against impulsive interferences and outperforms the sign algorithm (SA).
We analyze the transient, steady state and tracking performance of the
introduced algorithms and demonstrate the match of the theoretical analyzes and
simulation results. We show the extended stability bound of the LMLS algorithm
and analyze the robustness of the LLAD algorithm against impulsive
interferences. Finally, we demonstrate the performance of our algorithms in
different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin
Sparse Distributed Learning Based on Diffusion Adaptation
This article proposes diffusion LMS strategies for distributed estimation
over adaptive networks that are able to exploit sparsity in the underlying
system model. The approach relies on convex regularization, common in
compressive sensing, to enhance the detection of sparsity via a diffusive
process over the network. The resulting algorithms endow networks with learning
abilities and allow them to learn the sparse structure from the incoming data
in real-time, and also to track variations in the sparsity of the model. We
provide convergence and mean-square performance analysis of the proposed method
and show under what conditions it outperforms the unregularized diffusion
version. We also show how to adaptively select the regularization parameter.
Simulation results illustrate the advantage of the proposed filters for sparse
data recovery.Comment: to appear in IEEE Trans. on Signal Processing, 201
Compressive Diffusion Strategies Over Distributed Networks for Reduced Communication Load
We study the compressive diffusion strategies over distributed networks based
on the diffusion implementation and adaptive extraction of the information from
the compressed diffusion data. We demonstrate that one can achieve a comparable
performance with the full information exchange configurations, even if the
diffused information is compressed into a scalar or a single bit. To this end,
we provide a complete performance analysis for the compressive diffusion
strategies. We analyze the transient, steady-state and tracking performance of
the configurations in which the diffused data is compressed into a scalar or a
single-bit. We propose a new adaptive combination method improving the
convergence performance of the compressive diffusion strategies further. In the
new method, we introduce one more freedom-of-dimension in the combination
matrix and adapt it by using the conventional mixture approach in order to
enhance the convergence performance for any possible combination rule used for
the full diffusion configuration. We demonstrate that our theoretical analysis
closely follow the ensemble averaged results in our simulations. We provide
numerical examples showing the improved convergence performance with the new
adaptive combination method.Comment: Submitted to IEEE Transactions on Signal Processin
Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data
Adaptive networks rely on in-network and collaborative processing among
distributed agents to deliver enhanced performance in estimation and inference
tasks. Information is exchanged among the nodes, usually over noisy links. The
combination weights that are used by the nodes to fuse information from their
neighbors play a critical role in influencing the adaptation and tracking
abilities of the network. This paper first investigates the mean-square
performance of general adaptive diffusion algorithms in the presence of various
sources of imperfect information exchanges, quantization errors, and model
non-stationarities. Among other results, the analysis reveals that link noise
over the regression data modifies the dynamics of the network evolution in a
distinct way, and leads to biased estimates in steady-state. The analysis also
reveals how the network mean-square performance is dependent on the combination
weights. We use these observations to show how the combination weights can be
optimized and adapted. Simulation results illustrate the theoretical findings
and match well with theory.Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal
Processing, June 201
Linear MMSE-Optimal Turbo Equalization Using Context Trees
Formulations of the turbo equalization approach to iterative equalization and
decoding vary greatly when channel knowledge is either partially or completely
unknown. Maximum aposteriori probability (MAP) and minimum mean square error
(MMSE) approaches leverage channel knowledge to make explicit use of soft
information (priors over the transmitted data bits) in a manner that is
distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside
an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization
methods either estimate the channel or use a direct adaptation equalizer in
which estimates of the transmitted data are formed from an expressly linear
function of the received data and soft information, with this latter
formulation being most common. We study a class of direct adaptation turbo
equalizers that are both adaptive and nonlinear functions of the soft
information from the decoder. We introduce piecewise linear models based on
context trees that can adaptively approximate the nonlinear dependence of the
equalizer on the soft information such that it can choose both the partition
regions as well as the locally linear equalizer coefficients in each region
independently, with computational complexity that remains of the order of a
traditional direct adaptive linear equalizer. This approach is guaranteed to
asymptotically achieve the performance of the best piecewise linear equalizer
and we quantify the MSE performance of the resulting algorithm and the
convergence of its MSE to that of the linear minimum MSE estimator as the depth
of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin
Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields
The aim of this paper is to propose diffusion strategies for distributed
estimation over adaptive networks, assuming the presence of spatially
correlated measurements distributed according to a Gaussian Markov random field
(GMRF) model. The proposed methods incorporate prior information about the
statistical dependency among observations, while at the same time processing
data in real-time and in a fully decentralized manner. A detailed mean-square
analysis is carried out in order to prove stability and evaluate the
steady-state performance of the proposed strategies. Finally, we also
illustrate how the proposed techniques can be easily extended in order to
incorporate thresholding operators for sparsity recovery applications.
Numerical results show the potential advantages of using such techniques for
distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: text overlap with arXiv:1206.309
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