Tensor-Based Blind Channel Identification

A new blind channel identification and equalization method is proposed that exploits the cyclostationarity of oversampled communication signals to achieve identification and equalization of possibly nonminimum phase (multipath) channels without using training signals. Unlike most adaptive blind equalization methods for which the convergence properties are often problematic, the channel estimation algorithm proposed here is asymptotically ex-set. Moreover, since it is based on second-order statistics, the new approach may achieve equalization with fewer symbols than most techniques based only on higher-order statistics. Simulations have demonstrated promising performance of the proposed algorithm for the blind equalization of a three-ray multipath channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted algorithms, resulting in high pilot overhead. To address this issue, this article proposes a semi-blind joint channel and symbol estimation receiver without a pilot training stage for RIS-aided multiple-input multiple-output (MIMO) (including massive MIMO) communication systems. In a semi-blind system, a transmission symbol matrix and two channel matrices are coupled within the received signals at the base station (BS). We decouple them by building two parallel factor (PARAFAC) tensor models. Leveraging PARAFAC tensor decomposition, we transform the joint channel and symbol estimation problem into least square (LS) problems, which can be solved by Alternating Least Squares (ALSs). Our proposed scheme allows duplex communication. Compared to recently proposed pilot-based methods and semi-blind receivers, our results demonstrate the superior performance of our proposed algorithm in estimation accuracy and speed.

Alternating least squares (ALS) is a blind source separation method commonly used in chemometrics to simultaneously estimate the absorption spectrum and concentration of different components in a chemical sample. In this study, the transferability of ALS from chemometrics to agricultural remote sensing is evaluated. Due to the subpixel contribution of background components, spectral unmixing has become an indispensable processing step in the spectral analysis of agricultural areas. Yet, traditional unmixing techniques only allow estimating the subpixel cover distribution of different components, but fail to provide an estimate of pure spectral signature of the crop component. This info is, however, highly valuable, as this pure crop signature could be used to monitor the health status of trees. Here, we anticipate that ALS can provide a solution. ALS estimates both the concentration and the absorption spectra of different components in a chemical sample and this can easily be translated into estimating both the subpixel cover fraction and spectral signature of different components in a mixed image pixel. We tested the performance of ALS on binary synthetic mixtures of citrus canopy and soil spectra, as well as on a ray-tracing experiment of a virtual orchard. ALS indeed allowed to simultaneously estimate the subpixel cover distribution (RMSE=0.05), as well as the pure spectral signatures of different endmembers (RRMSE<;0.12), and considerably improved the extraction of biophysical parameters (Δ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> up to 0.43). Thus, ALS provides a promising new image analysis tool for agricultural remote sensing.

In order to solve the identification problem of oil pollutants containing micro content, the fluorescence characteristics of oil samples were studied using fluorescence excitation emission matrix spectra (EEMs) combined with parallel factor (PARAFAC) analysis. According to the conventional standard of oil content in water, simulated the component of oil pollution in I-V water was simulated by preparing samples of CCL4 with oil content. Firstly, measured the EEMs of 97# gasoline, 0# diesel, kerosene and CCL4 were measured individually, then the EEMs of 97# gasoline, 0# diesel, and kerosene in CCL4 were measured, and finally, the EEMs of the composite sample with all three oil contents in CCL4 were measured. The EEMs of the composite sample were superimposed by the EEMs of all its different components. It is therefore difficult to analyze the fluorescence component by chemical separation or simple fluorescence analysis. Since the EEMs of each oil component are already measured, we used the PARAFAC analysis to decompose the EEMs of the composite sample, and then extract the concentration ratio of each component. In this work, we solved the problem of identifying and quantifying the main micro-content petroleum pollutant in composite oil samples using EEMs and PARAFAC analysis.

Blind channel identification/estimation is very important for object detection, trace, localization in the ocean acoustics. Time domain blind identification algorithm requiring exact length of the channel being identification. Due to the characteristics of the shallow-water channel, the length of channel impulse response sequence is uncertain, Hence a frequency domain method for the blind MIMO (Multiple-Input Multiple-Output) underwater identification based on higher order statistics (HOS) is used to estimate the original acoustic channel from received signals on hydrophones only, with the low signal to noise ratio (SNR). The simulation results in the acoustic environment proved this work is effective and efficient for blind identification of the shallow-water acoustic channel.

A common assumption of blind channel identification methods is that the order of the true channel is known. This information is not available in practice, and we are obliged to estimate the channel order by applying a rank detection procedure to an overmodeled data covariance matrix. Information theoretic criteria have been widely suggested approaches for this task. We check the quality of their estimates in the context of order estimation of measured microwave radio channels and confirm that they are very sensitive to variations in the SNR and the number of data samples. This fact has prohibited their successful application for channel order estimation and hits created some confusion concerning the classification into under- and over-modeled cases. Recently, it has been shown that blind channel approximation methods should attempt to model only the significant part of the channel composed of the large impulse response terms because efforts toward modeling small leading and/or trailing terms lead to effective overmodeling, which is generically ill-conditioned and, thus, should be avoided. This can be achieved by applying blind identification methods with model order equal to the order of the significant part of the true channel called the effective channel order. Toward developing an efficient approach for the detection of the effective channel order, we use numerical analysis arguments. The derived criterion provides a maximally stable decomposition of the range space of an overmodeled data covariance matrix into signal and noise subspaces. It is shown to be robust to variations in the SNR and the number of data samples. Furthermore, it provides useful effective channel order estimates, leading to sufficiently good blind approximation/equalization of measured real-world microwave radio channels.

This paper describes a blind crosstalk channel identification method and its application to discrete multitone (DMT)-based digital subscriber line (DSL) systems. Cyclostationarity inherited in these systems is exploited to isolate effects of different sources, which allows separate selection and identification of crosstalk channels. Second-order statistics-based source separation is performed by controlling part of the cyclic-extension in the transmitted DMT block. The minimum changes required by this method facilitate its implementation in current DSL systems. All mentioned theoretical derivations are illustrated by numerical results obtained with measured DSL channels.

In this paper, we investigate channel parameter estimation for massive multiple-input multiple-output (MIMO) systems, where a large base station (BS) antenna array is used to provide multiplexing and diversity gains. We propose a Parallel Factor (PARAFAC)-based joint estimation scheme, which exploits the low-rank property of massive MIMO channels caused by the physical finite scattering environment. Specifically, we first parameterize the channel in terms of fading coefficients, directions of arrival (DOAs), and delays, thereby the channel is characterized via three equivalent PARAFAC models. Subsequently, we certify the identifiability of the three parameters of the PARAFAC models by exploiting the low-rank property. Then, we develop the proposed PARAFAC-based estimation scheme, which jointly estimates the three channel parameters using an alternating least squares (ALS) algorithm. Moreover, we analyze the computational complexity of the proposed scheme in terms of the required number of floating-point operations (FLOPs). Simulation results show that the proposed scheme achieves both a high performance and a low computational complexity.

The problem of blind user spatial signature estimation using the parallel factor (PARAFAC) analysis model is addressed in the context of applications to wireless communications. A time-varying user power loading in the uplink mode is proposed to enable identifiability and the application of PARAFAC analysis. Identifiability issues are carefully studied and two blind spatial signature estimation algorithms are developed. The first technique is based on the PARAFAC fitting trilinear alternating least squares (TALS) regression procedure, while the second one makes use of the joint approximate diagonalization algorithm. These techniques do not require any knowledge of the propagation channel and/or sensor array manifold and are applicable to a more general class of scenarios than earlier blind approaches to spatial signature estimation.

Parallel factor analysis (PARAFAC) is a branch of multi-way signal processing that has received increased attention recently. This is due to the large class of applications as well as the milestone identifiability results demonstrating the superiority to matrix (two-way) analysis approaches. A significant amount of research was dedicated to iterative methods to estimate the factors from noisy data. In many situations these require many iterations and are not guaranteed to converge to the global optimum. Therefore, suboptimal closed-form solutions were proposed as initializations. In this contribution we derive a closed-form solution to completely replace the iterative approach by transforming PARAFAC into several joint diagonalization problems. Thereby, we obtain several estimates for each of the factors and present a new matching scheme to select the best estimate for each factor. In contrast to the techniques known from the literature, our closed-form solution can efficiently exploit symmetric as well as Hermitian symmetric models and solve the underdetermined case, if there are at least two modes that are non-degenerate and full rank. This closed-form solution achieves approximately the same performance as previously proposed iterative solutions and even outperforms them in critical scenarios.

3.09 - Three-Way Calibration

A Khatri–Rao subspace approach to blind identification of mixtures of quasi-stationary sources

Blind identification of under-determined mixtures based on the characteristic function

One objective of seismic signal processing is to identify the layered subsurface structure by sending seismic wavelets into the ground. This is a blind deconvolution process since the seismic wavelets are usually not measurable and therefore, the subsurface face layers are identified only by the reflected seismic signals. Conventional methods often approach this problem by making assumptions about the subsurface structures and/or the seismic wavelets. In this paper an alternative technique is presented. It applies blind channel identification methods to prestack seismic deconvolution. A unique feature of this proposed method is that no such assumptions are needed. In addition, it fits into the structure of current seismic data acquisition techniques, thus no extra cost is involved. Simulations on both synthetic and field seismic data demonstrate that it is a promising new method for seismic signal processing.

International audience