The separation of signal-and-noise subspaces is a crucial step in many array signal processing applications, since the performance of most high-resolution methods mainly depends on the accuracy of separated signal-and-noise subspaces. If the resulting signal subspace is inaccurately estimated, high-resolution subspace-based algorithms would most likely fail. In this paper, we propose a high-accuracy method to complete the separation of signal-and-noise subspaces. In the developed scheme, eigenvalues of the covariance matrix of the data received by the uniform linear array are first employed to construct an ideal sample space using the Schur product of matrices. Then, the Gaussian kernel is introduced to map the sample space into a new high-dimensional feature space, where the resulting structure becomes linearly separable. In the sequel, we propose two fuzzy set-based methods to divide the feature space into two subspaces, which correspond to the signal-and-noise subspaces. In this way, the signal subspace becomes separated. Experimental results show that, compared with the results produced by five other commonly used algorithms, the proposed method yields much higher accuracy, especially for low signal-to-noise ratio thresholds and small snapshots.

The traditional 2D MUSIC algorithm fixes the azimuth or the elevation, and searches for the other without considering the directions of sources. A spectrum peak diffusion effect phenomenon is observed and may be utilized to detect the approximate directions of sources. Accordingly, a fast 2D MUSIC algorithm, which performs azimuth and elevation simultaneous searches (henceforth referred to as AESS) based on only three rounds of search is proposed. Firstly, AESS searches along a circle to detect the approximate source directions. Then, a subsequent search is launched along several straight lines based on these approximate directions. Finally, the 2D Direction of Arrival (DOA) of each source is derived by searching on several small concentric circles. Unlike the 2D MUSIC algorithm, AESS does not fix any azimuth and elevation parameters. Instead, the adjacent point of each search possesses different azimuth and elevation, i.e., azimuth and elevation are simultaneously searched to ensure that the search path is minimized, and hence the total spectral search over the angular field of view is avoided. Simulation results demonstrate the performance characters of the proposed AESS over some existing algorithms.

In this article, an augmented subspace-based algorithm for detecting the direction of arrival (DOA) of signals is presented. In the developed scheme, a uniform circular antenna array with a full range of lateral capacity is first transformed into a uniform linear antenna array in which the steering matrix has a Vandermonde form. This kind of structure can be exploited to formulate computationally efficient search-free estimation methods. In the process of virtual transformation, a novel DOA unit matrix of an assumed sector where the signals to be detected are located is built and optimized to find response matrices of the real and virtual antenna arrays to signals from the sector. By utilizing singular value decomposition (SVD) of the response matrix of the real antenna array to possible signals from the sector, a stable virtual transformation matrix between the real and virtual antenna arrays is obtained. Meanwhile, the aperture of the original array is also expanded during this process. Then, a virtual cyclic optimization algorithm is introduced to thoroughly mine information from the correlation matrices of the virtual antenna array receiving data and to optimize the signal subspace. Subsequently, the DOA can be efficiently determined through the reconstruction of the steering matrix. In the experimental part of the study, root-mean-square errors and probability of success are used to evaluate the performance of the algorithms. In particular, simulation results demonstrate that the proposed methods provide significant accuracy improvements, especially for low signal-to-noise ratio thresholds.

Many computing workloads in big data and machine learning applications are structured as directed acyclic graphs (DAG) and deployed on PC clusters for parallel execution using multiple physical or virtual machines. The scheduling of such workloads is critical to the application performance such as execution time and a plethora of techniques have been developed, taking into account various aspects such as data locality, network bandwidth, and server capability. We formulate DAG-structured workload scheduling as a nonlinear integer programming (NIP) problem and prove it to be NP-complete. Our empirical study reveals a positive correlation between scheduling plan distance (SPD) and finish time gap (FTG), and based on this finding, we propose a running time gap strategy (RTGS) to tackle this scheduling problem in multiprocessor environments. RTGS follows the main optimization strategy in the family of whale optimization algorithm (WOA). We derive a new function and use a greedy algorithm to generate an effective scheduling plan in RTGS. Extensive experiments with real production traces from Alibaba on simulation environments and realistic Hadoop environments show that our approach significantly improves the stability of WOA when applied to the scheduling problem of DAG-structured workloads, and also reduces the workload completion time by up to $$93\%$$ 93 % in comparison with seven state-of-the-art baseline algorithms.