This paper examines the asymptotic (large sample) performance
of a family of non-data aided feedforward (NDA FF) nonlinear
least-squares (NLS) type carrier frequency estimators for burst-mode
phase shift keying (PSK) modulations transmitted through AWGN and
flat Ricean-fading channels. The asymptotic performance of these estimators
is established in closed-form expression and compared with the
modified Cram`er-Rao bound (MCRB). A best linear unbiased estimator
(BLUE), which exhibits the lowest asymptotic variance within the family
of NDA FF NLS-type estimators, is also proposed.
PCA and PLS aims:to get some
insight into the bilinear factor models Principal Component Analysis
(PCA) and Partial Least Squares (PLS) regression, focusing on the
mathematics and numerical aspects rather than how s and why s of
data analysis practice. For the latter part it is assumed (but not
absolutely necessary) that the reader is already familiar with these
methods. It also assumes you have had some preliminary experience
with linear/matrix algebra.
Numerical Computing with MATLAB （by Cleve Moler) is a textbook for an introductory course
in numerical methods, Matlab, and technical computing. The emphasis is on in-
formed use of mathematical software. We want you learn enough about the mathe-
matical functions in Matlab that you will be able to use them correctly, appreciate
their limitations, and modify them when necessary to suit your own needs. The
topics include
* introduction to Matlab,
* linear equations,
* interpolation,
* zero and roots,
* least squares,
* quadrature,
* ordinary di?erential equations,
* random numbers,
* Fourier analysis,
* eigenvalues and singular values,
* partial di?erential equations.
Toolbox for Numerical Computing with MATLAB （by Cleve Moler).
Numerical Computing with MATLAB （by Cleve Moler) is a textbook for an introductory course
in numerical methods, Matlab, and technical computing. The emphasis is on in-
formed use of mathematical software. We want you learn enough about the mathe-
matical functions in Matlab that you will be able to use them correctly, appreciate
their limitations, and modify them when necessary to suit your own needs. The
topics include
* introduction to Matlab,
* linear equations,
* interpolation,
* zero and roots,
* least squares,
* quadrature,
* ordinary di?erential equations,
* random numbers,
* Fourier analysis,
* eigenvalues and singular values,
* partial differential equations.
this directory
contains the following:
* The acdc algorithm for finding the
approximate general (non-orthogonal)
joint diagonalizer (in the direct Least Squares sense) of a set of Hermitian matrices.
[acdc.m]
* The acdc algorithm for finding the
same for a set of Symmetric matrices.
[acdc_sym.m](note that for real-valued matrices the Hermitian and Symmetric cases are similar however, in such cases the Hermitian version
[acdc.m], rather than the Symmetric version[acdc_sym] is preferable.
* A function that finds an initial guess
for acdc by applying hard-whitening
followed by Cardoso s orthogonal joint
diagonalizer. Note that acdc may also
be called without an initial guess,
in which case the initial guess is set by default to the identity matrix.
The m-file includes the joint_diag
function (by Cardoso) for performing
the orthogonal part.
[init4acdc.m]
The toolbox solves a variety of approximate modeling problems for linear static models. The model can be parameterized in kernel, image, or input/output form and the approximation criterion, called misfit, is a weighted norm between the given data and data that is consistent with the model. There are three main classes of functions in the toolbox: transformation functions, misfit computation functions, and approximation functions. The approximation functions derive an approximate model from data, the misfit computation functions are used for validation and comparison of models, and the transformation functions are used for deriving one model representation from another.
KEYWORDS: Total least squares, generalized total least squares, software implementation.
