35 research outputs found
On the convergence of subgradient based blind equalization algorithm
In this article, we analyze the convergence behavior of the SGBA algorithm for the case where the relaxation rule is used for the step size. Our analysis shows that the monotonic convergence curve for the mean square distance to the optimal point is bounded between two geometric-series curves, and the convergence rate is dependent on the eigenvalues of the correlation matrix of channel outputs. We also provide some simulation examples for the verification of our analytical results related to the convergence behavior
Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques
In this paper, we propose a novel reduced-rank adaptive filtering algorithm
by blending the idea of the Krylov subspace methods with the set-theoretic
adaptive filtering framework. Unlike the existing Krylov-subspace-based
reduced-rank methods, the proposed algorithm tracks the optimal point in the
sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov
subspace, even when the estimated statistics become erroneous (e.g., due to
sudden changes of environments). Therefore, compared with those existing
methods, the proposed algorithm is more suited to adaptive filtering
applications. The algorithm is analyzed based on a modified version of the
adaptive projected subgradient method (APSM). Numerical examples demonstrate
that the proposed algorithm enjoys better tracking performance than the
existing methods for the interference suppression problem in code-division
multiple-access (CDMA) systems as well as for simple system identification
problems.Comment: 10 figures. In IEEE Transactions on Signal Processing, 201
Sparse Nonlinear MIMO Filtering and Identification
In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semiāblind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus aāpriori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation
Optimal Real-time Spectrum Sharing between Cooperative Relay and Ad-hoc Networks
Optimization based spectrum sharing strategies have been widely studied.
However, these strategies usually require a great amount of real-time
computation and significant signaling delay, and thus are hard to be fulfilled
in practical scenarios. This paper investigates optimal real-time spectrum
sharing between a cooperative relay network (CRN) and a nearby ad-hoc network.
Specifically, we optimize the spectrum access and resource allocation
strategies of the CRN so that the average traffic collision time between the
two networks can be minimized while maintaining a required throughput for the
CRN. The development is first for a frame-level setting, and then is extended
to an ergodic setting. For the latter setting, we propose an appealing optimal
real-time spectrum sharing strategy via Lagrangian dual optimization. The
proposed method only involves a small amount of real-time computation and
negligible control delay, and thus is suitable for practical implementations.
Simulation results are presented to demonstrate the efficiency of the proposed
strategies.Comment: One typo in the caption of Figure 5 is correcte
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Novel algorithms in wireless CDMA systems for estimation and kernel based equalization
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.A powerful technique is presented for joint blind channel estimation and carrier offset
method for code- division multiple access (CDMA) communication systems. The new
technique combines singular value decomposition (SVD) analysis with carrier offset parameter. Current blind methods sustain a high computational complexity as they require the computation of a large SVD twice, and they are sensitive to accurate knowledge of the noise subspace rank. The proposed method overcomes both problems by computing the SVD only once. Extensive simulations using MatLab demonstrate the robustness of the proposed scheme and its performance is comparable to other existing SVD techniques with significant lower computational as much as 70% cost because it does not require knowledge of the rank of the noise sub-space. Also a kernel based equalization for CDMA communication systems is proposed, designed and simulated using MatLab. The proposed method in CDMA systems
overcomes all other methods
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page