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In this paper, a novel algorithm is proposed for the two-dimensional (2D) central direction-of-arrival (DOA) estimation of coherently distributed (CD) sources. Specifically, we focus on a centro-symmetric crossed array consisting of two uniform linear arrays (ULAs). Unlike the conventional low-complexity methods using the one-order Taylor series approximation to obtain the approximate rotational invariance relation, we first prove the symmetric property of angular signal distributed weight vectors of the CD source for an arbitrary centrosymmetric array, and then use this property to establish two generalized rotational invariance relations inside the array manifolds in the two ULAs. Making use of such relations, the central elevation and azimuth DOAs are obtained by employing a polynomial-root-based search-free approach, respectively. Finally, simple parameter matching is accomplished by searching for the minimums of the cost function of the estimated 2D angular parameters. When compared with the existing low-complexity methods, the proposed algorithm can greatly improve estimation accuracy without significant increment in computation complexity. Moreover, it performs independently of the deterministic angular distributed function. Simulation results are presented to illustrate the performance of the proposed algorithm.

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In practical applications such as mobile communication, radar and sonar, the effect of angular spread on the source energy can no longer be ignored due to multipath phenomena. Therefore, a spatially distributed source model is more realistic than the point source mode in these complex cases. A lot of direction-of-arrival (DOA) estimation methods for distributed sources have been published. Whereas researches concentrated on the complex circular signal case, the noncircular property of signal can be employed to further improve the estimation performance, which has received extensive attention recently. To date, several low-complexity DOA estimation algorithms for two-dimensional (2D) coherently distributed (CD) noncircular sources have been proposed. However, all these algorithms need obtain the approximate shift invariance relationship between the sub-arrays by applying the one-order Taylor series approximation to the generalized steering vectors, which may introduce additional errors and affect the estimation accuracy. In this paper, a novel 2D DOA estimation algorithm based on the symmetric shift invariance relationship is proposed using the centro-symmetric three-dimensional (3D) linear arrays. Firstly, the extended array model is established by exploiting the noncircularity of the signal. Then, it is proved that the deterministic angular distribution function vector of the CD source has a symmetrical property for arbitrary centro-symmetric array, based on which the symmetric shift invariance relationships of extended generalized steering vectors are established in the three sub-arrays of 3D linear arrays. On the premise of such relationships, the center azimuth and elevation DOAs are obtained by the polynomial rooting method without spectral peak searching. Finally, the cost function implementing the parameter matching is constructed by the symmetric shift invariance relationship of the generalized steering vector of the whole array. Theoretical analysis and simulation experiment show that compared with the existing low-complexity algorithms, the proposed algorithm avoids the additional errors introduced by the Taylor series approximation, which allows it to achieve higher estimation accuracy with the small complexity cost. Moreover, the proposed algorithm can achieve omnidirectional angle estimation in the three-dimensional space.

In this study, the iron-based carbon composite (hereafter FCN-x, x = 0, 400, 500, and 600 calcination) was synthesized by a simple high-temperature pyrolysis method using iron-containing sludge coagulant generated from wastewater treatment settling ponds in chemical plants. The FCN-x was used for the adsorptive reduction of aqueous phase Cr(VI) effectively. The FCN-x was characterized by scanning electron microscopy (SEM), X-ray diffraction (XRD), Fourier infrared spectrometer (FT-IR), X-ray photoelectron spectrometer (XPS), and Brunauer-Emmett-Teller theory (BET). FCN-x adsorption of Cr(VI) was examined in batch experiments using CrO42− as a function of physicochemical parameters. The chemical kinetics of Cr(VI) adsorption by FCN-500 were modeled by 1st and 2nd order empirical pseudo kinetics. Based on these experiments, FCN-500 has been selected for further studies on Cr(VI) adsorptive reduction. The maximum Cr(VI) adsorption by FCN-500 was 52.63 mg/g showing the highest removal efficiency. The Cr(VI) adsorption by the FCN-500 was quantified by the Langmuir isotherm. XPS result confirmed the reduction of Cr(VI) to Cr(III) by the FCN-500. The iron-based carbon composites have high reusability and application potential in water treatment. The electroplating wastewater with 117 mg/L Cr(VI) was treated with FCN-500, and 99.93% Cr(VI) was removed within 120 min, which is lower than the national chromium emission standard of the People’s Republic of China. This work illustrates the value-added role of sludge generated from dye chemical plants to ensure environmental sustainability.