12,244 research outputs found
Asynchronous CDMA Systems with Random Spreading-Part II: Design Criteria
Totally asynchronous code-division multiple-access (CDMA) systems are
addressed. In Part I, the fundamental limits of asynchronous CDMA systems are
analyzed in terms of spectral efficiency and SINR at the output of the optimum
linear detector. The focus of Part II is the design of low-complexity
implementations of linear multiuser detectors in systems with many users that
admit a multistage representation, e.g. reduced rank multistage Wiener filters,
polynomial expansion detectors, weighted linear parallel interference
cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay
distribution on CDMA with suboptimum linear receiver structures are
investigated. Recursive expressions for universal weight design are given. The
performance in terms of SINR is derived in the large-system limit and the
performance improvement over synchronous systems is quantified. The
considerations distinguish between two ways of forming discrete-time
statistics: chip-matched filtering and oversampling
Sub-band common spatial pattern (SBCSP) for brain-computer interface
Brain-computer interface (BCI) is a system to translate humans thoughts into commands. For electroencephalography (EEG) based BCI, motor imagery is considered as one of the most effective ways. Different imagery activities can be classified based on the changes in mu and/or beta rhythms and their spatial distributions. However, the change in these rhythmic patterns varies from one subject to another. This causes an unavoidable time-consuming fine-tuning process in building a BCI for every subject. To address this issue, we propose a new method called sub-band common spatial pattern (SBCSP) to solve the problem. First, we decompose the EEG signals into sub-bands using a filter bank. Subsequently, we apply a discriminative analysis to extract SBCSP features. The SBCSP features are then fed into linear discriminant analyzers (LDA) to obtain scores which reflect the classification capability of each frequency band. Finally, the scores are fused to make decision. We evaluate two fusion methods: recursive band elimination (RBE) and meta-classifier (MC). We assess our approaches on a standard database from BCI Competition III. We also compare our method with two other approaches that address the same issue. The results show that our method outperforms the other two approaches and achieves similar result as compared to the best one in the literature which was obtained by a time-consuming fine-tuning process
The Degrees of Freedom of Partial Least Squares Regression
The derivation of statistical properties for Partial Least Squares regression
can be a challenging task. The reason is that the construction of latent
components from the predictor variables also depends on the response variable.
While this typically leads to good performance and interpretable models in
practice, it makes the statistical analysis more involved. In this work, we
study the intrinsic complexity of Partial Least Squares Regression. Our
contribution is an unbiased estimate of its Degrees of Freedom. It is defined
as the trace of the first derivative of the fitted values, seen as a function
of the response. We establish two equivalent representations that rely on the
close connection of Partial Least Squares to matrix decompositions and Krylov
subspace techniques. We show that the Degrees of Freedom depend on the
collinearity of the predictor variables: The lower the collinearity is, the
higher the Degrees of Freedom are. In particular, they are typically higher
than the naive approach that defines the Degrees of Freedom as the number of
components. Further, we illustrate how the Degrees of Freedom approach can be
used for the comparison of different regression methods. In the experimental
section, we show that our Degrees of Freedom estimate in combination with
information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio
Frame Permutation Quantization
Frame permutation quantization (FPQ) is a new vector quantization technique
using finite frames. In FPQ, a vector is encoded using a permutation source
code to quantize its frame expansion. This means that the encoding is a partial
ordering of the frame expansion coefficients. Compared to ordinary permutation
source coding, FPQ produces a greater number of possible quantization rates and
a higher maximum rate. Various representations for the partitions induced by
FPQ are presented, and reconstruction algorithms based on linear programming,
quadratic programming, and recursive orthogonal projection are derived.
Implementations of the linear and quadratic programming algorithms for uniform
and Gaussian sources show performance improvements over entropy-constrained
scalar quantization for certain combinations of vector dimension and coding
rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared
error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with
previous results on optimal decay of MSE. Reconstruction using the canonical
dual frame is also studied, and several results relate properties of the
analysis frame to whether linear reconstruction techniques provide consistent
reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few
minor correction
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