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: 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: 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.