Abstract: In this paper we propose an algorithm based on
higher order cumulants, for blind impulse response identification
of frequency radio channels and downlink (MC−CDMA) system
Equalization. In order to test its efficiency, we have compared with
another algorithm proposed in the literature, for that we considered
on theoretical channel as the Proakis’s ‘B’ channel and practical
frequency selective fading channel, called Broadband Radio Access
Network (BRAN C), normalized for (MC−CDMA) systems, excited
by non-Gaussian sequences. In the part of (MC−CDMA), we use the
Minimum Mean Square Error (MMSE) equalizer after the channel
identification to correct the channel’s distortion. The simulation
results, in noisy environment and for different signal to noise ratio
(SNR), are presented to illustrate the accuracy of the proposed
algorithm.
Abstract: In this paper a new cost function for blind equalization
is proposed. The proposed cost function, referred to as the modified
maximum normalized cumulant criterion (MMNC), is an extension
of the previously proposed maximum normalized cumulant criterion
(MNC). While the MNC requires a separate phase recovery system
after blind equalization, the MMNC performs joint blind equalization
and phase recovery. To achieve this, the proposed algorithm
maximizes a cost function that considers both amplitude and phase of
the equalizer output. The simulation results show that the proposed
algorithm has an improved channel equalization effect than the MNC
algorithm and simultaneously can correct the phase error that the
MNC algorithm is unable to do. The simulation results also show that
the MMNC algorithm has lower complexity than the MNC algorithm.
Moreover, the MMNC algorithm outperforms the MNC algorithm
particularly when the symbols block size is small.
Abstract: Higher-order Statistics (HOS), also known as
cumulants, cross moments and their frequency domain counterparts,
known as poly spectra have emerged as a powerful signal processing
tool for the synthesis and analysis of signals and systems. Algorithms
used for the computation of cross moments are computationally
intensive and require high computational speed for real-time
applications. For efficiency and high speed, it is often advantageous
to realize computation intensive algorithms in hardware. A promising
solution that combines high flexibility together with the speed of a
traditional hardware is Field Programmable Gate Array (FPGA). In
this paper, we present FPGA-based parallel architecture for the
computation of third-order cross moments. The proposed design is
coded in Very High Speed Integrated Circuit (VHSIC) Hardware
Description Language (VHDL) and functionally verified by
implementing it on Xilinx Spartan-3 XC3S2000FG900-4 FPGA.
Implementation results are presented and it shows that the proposed
design can operate at a maximum frequency of 86.618 MHz.
Abstract: In this paper we propose a family of algorithms based
on 3rd and 4th order cumulants for blind single-input single-output
(SISO) Non-Minimum Phase (NMP) Finite Impulse Response (FIR)
channel estimation driven by non-Gaussian signal. The input signal
represents the signal used in 10GBASE-T (or IEEE 802.3an-2006)
as a Tomlinson-Harashima Precoded (THP) version of random
Pulse-Amplitude Modulation with 16 discrete levels (PAM-16). The
proposed algorithms are tested using three non-minimum phase
channel for different Signal-to-Noise Ratios (SNR) and for different
data input length. Numerical simulation results are presented to
illustrate the performance of the proposed algorithms.
Abstract: In this paper, many techniques for blind identification of moving average (MA) process are presented. These methods utilize third- and fourth-order cumulants of the noisy observations of the system output. The system is driven by an independent and identically distributed (i.i.d) non-Gaussian sequence that is not observed. Two nonlinear optimization algorithms, namely the Gradient Descent and the Gauss-Newton algorithms are exposed. An algorithm based on the joint-diagonalization of the fourth-order cumulant matrices (FOSI) is also considered, as well as an improved version of the classical C(q, 0, k) algorithm based on the choice of the Best 1-D Slice of fourth-order cumulants. To illustrate the effectiveness of our methods, various simulation examples are presented.
Abstract: This paper addresses the problem of blind source separation
(BSS). To recover original signals, from linear instantaneous
mixtures, we propose a new contrast function based on the use of a
double referenced system. Our approach assumes statistical independence
sources. The reference vectors will be incrusted in the cumulant
to evaluate the independence. The estimation of the separating matrix
will be performed in two steps: whitening observations and joint
diagonalization of a set of referenced cumulant matrices. Computer
simulations are presented to demonstrate the effectiveness of the
suggested approach.
Abstract: This paper presents the cepstral and trispectral
analysis of a speech signal produced by normal men, men with
defective audition (deaf, deep deaf) and others affected by
tracheotomy, the trispectral analysis based on parametric methods
(Autoregressive AR) using the fourth order cumulant. These
analyses are used to detect and compare the pitches and the formants
of corresponding voiced sounds (vowel \a\, \i\ and \u\). The first
results appear promising, since- it seems after several experimentsthere
is no deformation of the spectrum as one could have supposed
it at the beginning, however these pathologies influenced the two
characteristics:
The defective audition influences to the formants contrary to the
tracheotomy, which influences the fundamental frequency (pitch).
Abstract: This paper deals with the localization of the wideband sources. We develop a new approach for estimating the wide band sources parameters. This method is based on the high order statistics of the recorded data in order to eliminate the Gaussian components from the signals received on the various hydrophones.In fact the noise of sea bottom is regarded as being Gaussian. Thanks to the coherent signal subspace algorithm based on the cumulant matrix of the received data instead of the cross-spectral matrix the wideband correlated sources are perfectly located in the very noisy environment. We demonstrate the performance of the proposed algorithm on the real data recorded during an underwater acoustics experiments.
Abstract: One of the primary uses of higher order statistics in
signal processing has been for detecting and estimation of non-
Gaussian signals in Gaussian noise of unknown covariance. This is
motivated by the ability of higher order statistics to suppress additive
Gaussian noise. In this paper, several methods to test for non-
Gaussianity of a given process are presented. These methods include
histogram plot, kurtosis test, and hypothesis testing using cumulants
and bispectrum of the available sequence. The hypothesis testing is
performed by constructing a statistic to test whether the bispectrum
of the given signal is non-zero. A zero bispectrum is not a proof of
Gaussianity. Hence, other tests such as the kurtosis test should be
employed. Examples are given to demonstrate the performance of the
presented methods.