Cumulant based parametric multichannel FIR system identification methods

Cataloged from PDF version of article.In this paper, ''least squares'' and recursive methods for simultaneous identification of four nonminimum phase linear, time-invariant FIR systems are presented. The methods utilize the second- and fourth-order cumulants of outputs of the four FIR systems of which the common input is an independent, identically distributed (i.i.d.) non-Gaussian process. The new methods can be extended to the general problem of simultaneous identification of three or more FIR systems by choosing the order of the utilized cumulants to be equal to the number of systems. To illustrate the effectiveness of our methods, two simulation examples are included

System identification using a linear combination of cumulant slices

In this paper we develop a new linear approach to identify the parameters of a moving average (MA) model from the statistics of the output. First, we show that, under some constraints, the impulse response of the system can be expressed as a linear combination of cumulant slices. Then, this result is used to obtain a new well-conditioned linear method to estimate the MA parameters of a non-Gaussian process. The proposed method presents several important differences with existing linear approaches. The linear combination of slices used to compute the MA parameters can be constructed from dif- ferent sets of cumulants of different orders, providing a general framework where all the statistics can be combined. Further- more, it is not necessary to use second-order statistics (the autocorrelation slice), and therefore the proposed algorithm still provides consistent estimates in the presence of colored Gaussian noise. Another advantage of the method is that while most linear methods developed so far give totally erroneous estimates if the order is overestimated, the proposed approach does not require a previous estimation of the filter order. The simulation results confirm the good numerical conditioning of the algorithm and the improvement in performance with respect to existing methods.Peer Reviewe

Laboratory for Engineering Man/Machine Systems (LEMS): System identification, model reduction and deconvolution filtering using Fourier based modulating signals and high order statistics

Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm

Blind, MIMO system estimation based on PARAFAC decomposition of higher order output tensors

IEEE Transactions on Signal Processing, 54(11): pp. 4156-4168.We present a novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three- or four-way tensors constructed based on, respectively, third- or fourth-order cross spectra of the system outputs. The main difficulties in frequency-domain methods are frequency- dependent permutation and filtering ambiguities.We show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approach are that it does not require channel length information, needs no phase unwrapping, and unlike the majority of existing methods, needs no prewhitening of the system outputs

Blind equalization

An equalizer is an adaptive filter that compensates for the non-ideal characteristics of a communication channel by processing the received signal. The adaptive algorithm searches for the inverse impulse response of the channel, and it requires knowledge of a training sequence, in order to generate an error signal necessary for the adaptive process. There are practical situations where it would be highly desirable to achieve complete adaptation without the use of a training sequence, hence the the term blind . Examples of these situations are multipoint data networks, high-capacity line-of-sight digital radio, and reflection seismology. A blind adaptive algorithm has been developed, based on simplified equalization criteria. These criteria are that the second- and fourth-order moments of the input and output sequences are equalized. The algorithm is entirely driven by statistics, only requiring knowledge of the variance of the input signal. Because of the insensitivity of higher-order statistics to Gaussian processes, the algorithm performs well when additive white Gaussian noise is present in the channel. Simulations are presented in which the new blind equalizer developed is compared to other equalization algorithms

Blind identification of possibly under-determined convolutive MIMO systems

Blind identi¯cation of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identi¯cation for a MIMO system is to identify an unknown system, driven by Ni unobservable inputs, based on the No system outputs. We ¯rst present a novel blind approach for the identi¯cation of a over-determined (No ¸ Ni) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identi¯ed up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs.While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (No < Ni) case, all of which refer to systems that either have some special structure, or special No, Ni values. We propose a novel approach for blind identi¯cation of under-determined convolutive MIMO systems of general dimensions. As long as min(No;Ni) ¸ 2, we can always ¯nd the appropriate order of statistics that guarantees identi¯ability of the system response within trivial ambiguities. We provide the description of the class of identi¯able MIMO systems for a certain order of statistics K, and an algorithm to reach the solution.Finally we propose a novel approach for blind identi¯cation and symbol recovery of a distributed antenna system with multiple carrier-frequency o®sets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.Ph.D., Electrical Engineering -- Drexel University, 200

Blind estimation of FIR channels using spatial separation

Master'sMASTER OF ENGINEERIN

Efficient and Robust Signal Detection Algorithms for the Communication Applications

Signal detection and estimation has been prevalent in signal processing and communications for many years. The relevant studies deal with the processing of information-bearing signals for the purpose of information extraction. Nevertheless, new robust and efficient signal detection and estimation techniques are still in demand since there emerge more and more practical applications which rely on them. In this dissertation work, we proposed several novel signal detection schemes for wireless communications applications, such as source localization algorithm, spectrum sensing method, and normality test. The associated theories and practice in robustness, computational complexity, and overall system performance evaluation are also provided

A framework for non-Gaussian signal modeling and estimation

"June 1999."Includes bibliographical references (p. [225]-240).Sponsored by the U.S. Air Force. F49620-96-1-0072 Supported by the U.S. Army Research Laboratory under Cooperative Agreement, DAAL01-96-2-001Shawn M. Verbout