deconvolution
density matrix
blind deconvolution problem
cases
problem
https://doi.org/10.1007/978-1-4615-6281-8_37
statistics
ML techniques
blind deconvolution
1997
banks
555-575
channels
noise-free case
signals
prediction
sinusoids
equalization
digital communication
covariance matrix
https://scigraph.springernature.com/explorer/license/
1997-01-01
FIR channels
parallel
data case
development
en
filter bank
2022-05-20T07:45
channel model
additive noise
subspace problem
finite covariance matrix
vector-valued signals
communication
spectral factor
music
matrix
model
results
false
second-order statistics
factorization
multichannel case
sum
equalizer
technique
assumption
triangular factorization
From Sinusoids in Noise to Blind Deconvolution in Communications
deconvolution problem
chapters
sum of sinusoids
noiseless
Equalization for digital communications constitutes a very particular blind deconvolution problem in that the received signal is cyclostationary. Oversampling (OS) (w.r.t. the symbol rate) of the cyclostationary received signal leads to a stationary vector-valued signal (polyphase representation (PR)). OS also leads to a fractionally-spaced channel model and equalizer. The multichannel formulation also arises in mobile communications, when multiple receiving antennas are used. In the multichannel case, channel and equalizer can be considered as an analysis and synthesis filter bank. Zero-forcing (ZF) equalization corresponds to a perfect-reconstruction filter bank. We show that in the multichannel case FIR ZF equalizers exist for a FIR channel. The noise-free multichannel power spectral density matrix has rank one and the channel can be found as the (minimum-phase) spectral factor. The multichannel linear prediction of the noiseless received signal becomes singular eventually, reminiscent of the single-channel prediction of a sum of sinusoids. As a result, a ZF equalizer can be determined from the received signal second-order statistics by linear prediction in the noise-free case, and by using a Pisarenko-style modification when there is additive noise. Due to the singularity and the FIR assumption, the spectral factorization reduces to the triangular factorization of a finite covariance matrix. In the given data case, Music (subspace) or ML techniques can be applied. We present these developments by drawing the parallel with existing techniques for the sinusoids in noise subspace problem.
ZF equalizer
perfect reconstruction filter banks
analysis
mobile communications
multichannel linear prediction
noise
antenna
spectral factorization
factors
multichannel formulation
signal second-order statistics
oversampling
synthesis filter bank
power spectral density matrix
singularity
spectral density matrix
formulation
modification
linear prediction
chapter
Slock
Dirk
978-1-4613-7883-9
Communications, Computation, Control, and Signal Processing
978-1-4615-6281-8
dimensions_id
pub.1010268352
Springer Nature - SN SciGraph project
Mobile Communications Dept., Eurecom Institute, B.P. 193, 06904, Sophia Antipolis Cedex, France
Mobile Communications Dept., Eurecom Institute, B.P. 193, 06904, Sophia Antipolis Cedex, France
Paulraj
Arogyaswami
Vwani
Roychowdhury
Electrical and Electronic Engineering
Charles D.
Schaper
Engineering
10.1007/978-1-4615-6281-8_37
doi
Springer Nature