Ahmet M. Elbir

SP
22papers
1,528citations
Novelty40%
AI Score40

22 Papers

SPJul 13, 2022
Federated Multi-Task Learning for THz Wideband Channel and DoA Estimation

Ahmet M. Elbir, Wei Shi, Kumar Vijay Mishra et al.

This paper addresses two major challenges in terahertz (THz) channel estimation: the beam-split phenomenon, i.e., beam misalignment because of frequency-independent analog beamformers, and computational complexity because of the usage of ultra-massive number of antennas to compensate propagation losses. Data-driven techniques are known to mitigate the complexity of this problem but usually require the transmission of the datasets from the users to a central server entailing huge communication overhead. In this work, we introduce a federated multi-task learning (FMTL), wherein the users transmit only the model parameters instead of the whole dataset, for THz channel and user direction-of-arrival (DoA) estimation to improve the communications-efficiency. We first propose a novel beamspace support alignment technique for channel estimation with beam-split correction. Then, the channel and DoA information are used as labels to train an FMTL model. By exploiting the sparsity of the THz channel, the proposed approach is implemented with fewer pilot signals than the traditional techniques. Compared to the previous works, our FMTL approach provides higher channel estimation accuracy as well as approximately 25 (32) times lower model (channel) training overhead, respectively.

SPJun 24, 2022
Implicit Channel Learning for Machine Learning Applications in 6G Wireless Networks

Ahmet M. Elbir, Wei Shi, Kumar Vijay Mishra et al.

With the deployment of the fifth generation (5G) wireless systems gathering momentum across the world, possible technologies for 6G are under active research discussions. In particular, the role of machine learning (ML) in 6G is expected to enhance and aid emerging applications such as virtual and augmented reality, vehicular autonomy, and computer vision. This will result in large segments of wireless data traffic comprising image, video and speech. The ML algorithms process these for classification/recognition/estimation through the learning models located on cloud servers. This requires wireless transmission of data from edge devices to the cloud server. Channel estimation, handled separately from recognition step, is critical for accurate learning performance. Toward combining the learning for both channel and the ML data, we introduce implicit channel learning to perform the ML tasks without estimating the wireless channel. Here, the ML models are trained with channel-corrupted datasets in place of nominal data. Without channel estimation, the proposed approach exhibits approximately 60% improvement in image and speech classification tasks for diverse scenarios such as millimeter wave and IEEE 802.11p vehicular channels.

SPMay 6, 2022
Federated Channel Learning for Intelligent Reflecting Surfaces With Fewer Pilot Signals

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Channel estimation is a critical task in intelligent reflecting surface (IRS)-assisted wireless systems due to the uncertainties imposed by environment dynamics and rapid changes in the IRS configuration. To deal with these uncertainties, deep learning (DL) approaches have been proposed. Previous works consider centralized learning (CL) approach for model training, which entails the collection of the whole training dataset from the users at the base station (BS), hence introducing huge transmission overhead for data collection. To address this challenge, this paper proposes a federated learning (FL) framework to jointly estimate both direct and cascaded channels in IRS-assisted wireless systems. We design a single convolutional neural network trained on the local datasets of the users without sending them to the BS. We show that the proposed FL-based channel estimation approach requires approximately 60% fewer pilot signals and it exhibits 12 times lower transmission overhead than CL, while maintaining satisfactory performance close to CL. In addition, it provides lower estimation error than the state-of-the-art DL-based schemes.

SPAug 8, 2023
Sparse Array Design for Direction Finding using Deep Learning

Kumar Vijay Mishra, Ahmet M. Elbir, Koichi Ichige

In the past few years, deep learning (DL) techniques have been introduced for designing sparse arrays. These methods offer the advantages of feature engineering and low prediction-stage complexity, which is helpful in tackling the combinatorial search inherent to finding a sparse array. In this chapter, we provide a synopsis of several direction finding applications of DL-based sparse arrays. We begin by examining supervised and transfer learning techniques that have applications in selecting sparse arrays for a cognitive radar application. Here, we also discuss the use of meta-heuristic learning algorithms such as simulated annealing for the case of designing two-dimensional sparse arrays. Next, we consider DL-based antenna selection for wireless communications, wherein sparse array problem may also be combined with channel estimation, beamforming, or localization. Finally, we provide an example of deep sparse array technique for integrated sensing and communications (ISAC) application, wherein a trade-off of radar and communications performance makes ISAC sparse array problem very challenging. For each setting, we illustrate the performance of model-based optimization and DL techniques through several numerical experiments. We discuss additional considerations required to ensure robustness of DL-based algorithms against various imperfections in array data.

61.3ITMar 13
Boosting Spectral Efficiency via Spatial Path Index Modulation in RIS-Aided mMIMO

Ahmet M. Elbir, Abdulkadir Celik, Asmaa Abdallah et al.

Next generation wireless networks focus on improving spectral efficiency (SE) while reducing power consumption and hardware cost. Reconfigurable intelligent surfaces (RISs) offer a viable solution to meet these requirements. In order to enhance the SE, index modulation (IM) has been regarded as one of the enabling technologies via the transmission of additional information bits over the transmission media such as subcarriers, antennas and spatial paths. In this work, we explore the usage of spatial paths and introduce spatial path IM (SPIM) for RIS-aided massive multiple-input multiple-output (mMIMO) systems. Thus, the proposed framework improves the network efficiency and the coverage with the use of RIS while SPIM provides SE improvement. In order to perform SPIM, we exploit the spatial diversity of the millimeter wave channel and assign the index bits to the spatial patterns of the channel between the base station and the users through RIS. We introduce a low complexity approach for the design of hybrid beamformers, which are constructed by the steering vectors corresponding to the selected spatial path indices for SPIM-mMIMO. Furthermore, we conduct a theoretical analysis on the SE of the proposed SPIM approach, and derive the SE relationship between the SPIM-based hybrid beamforming and fully digital (FD) beamforming. Via numerical simulations, we validate our theoretical results and show that the proposed SPIM approach presents an improved SE performance, even higher than that of the use of FD beamformers while using a few RF chains.

LGMay 7, 2021
A Hybrid Architecture for Federated and Centralized Learning

Ahmet M. Elbir, Sinem Coleri, Anastasios K. Papazafeiropoulos et al.

Many of the machine learning tasks rely on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) entailing huge communication overhead. To overcome this, federated learning (FL) has been suggested as a promising tool, wherein the clients send only the model updates to the PS instead of the whole dataset. However, FL demands powerful computational resources from the clients. In practice, not all the clients have sufficient computational resources to participate in training. To address this common scenario, we propose a more efficient approach called hybrid federated and centralized learning (HFCL), wherein only the clients with sufficient resources employ FL, while the remaining ones send their datasets to the PS, which computes the model on behalf of them. Then, the model parameters are aggregated at the PS. To improve the efficiency of dataset transmission, we propose two different techniques: i) increased computation-per-client and ii) sequential data transmission. Notably, the HFCL frameworks outperform FL with up to 20\% improvement in the learning accuracy when only half of the clients perform FL while having 50\% less communication overhead than CL since all the clients collaborate on the learning process with their datasets.

SPFeb 27, 2021
Terahertz-Band Joint Ultra-Massive MIMO Radar-Communications: Model-Based and Model-Free Hybrid Beamforming

Ahmet M. Elbir, Kumar Vijay Mishra, Symeon Chatzinotas

Wireless communications and sensing at terahertz (THz) band are increasingly investigated as promising short-range technologies because of the availability of high operational bandwidth at THz. In order to address the extremely high attenuation at THz, ultra-massive multiple-input multiple-output (MIMO) antenna systems have been proposed for THz communications to compensate propagation losses. However, the cost and power associated with fully digital beamformers of these huge antenna arrays are prohibitive. In this paper, we develop wideband hybrid beamformers based on both model-based and model-free techniques for a new group-of-subarrays (GoSA) ultra-massive MIMO structure in low-THz band. Further, driven by the recent developments to save the spectrum, we propose beamformers for a joint ultra-massive MIMO radar-communications system, wherein the base station serves multi-antenna user equipment (RX), and tracks radar targets by generating multiple beams toward both RX and the targets. We formulate the GoSA beamformer design as an optimization problem to provide a trade-off between the unconstrained communications beamformers and the desired radar beamformers. To mitigate the beam split effect at THz band arising from frequency-independent analog beamformers, we propose a phase correction technique to align the beams of multiple subcarriers toward a single physical direction. To further decrease the ultra-massive MIMO computational complexity and enhance robustness, we also implement deep learning solutions to the proposed model-based hybrid beamformers. Numerical experiments demonstrate that both techniques outperform the conventional approaches in terms of spectral efficiency and radar beampatterns, as well as exhibiting less hardware cost and computation time.

SPFeb 23, 2021
Federated Learning for Physical Layer Design

Ahmet M. Elbir, Anastasios K. Papazafeiropoulos, Symeon Chatzinotas

Model-free techniques, such as machine learning (ML), have recently attracted much interest towards the physical layer design, e.g., symbol detection, channel estimation, and beamforming. Most of these ML techniques employ centralized learning (CL) schemes and assume the availability of datasets at a parameter server (PS), demanding the transmission of data from edge devices, such as mobile phones, to the PS. Exploiting the data generated at the edge, federated learning (FL) has been proposed recently as a distributed learning scheme, in which each device computes the model parameters and sends them to the PS for model aggregation while the datasets are kept intact at the edge. Thus, FL is more communication-efficient and privacy-preserving than CL and applicable to the wireless communication scenarios, wherein the data are generated at the edge devices. This article presents the recent advances in FL-based training for physical layer design problems. Compared to CL, the effectiveness of FL is presented in terms of communication overhead with a slight performance loss in the learning accuracy. The design challenges, such as model, data, and hardware complexity, are also discussed in detail along with possible solutions.

SPFeb 15, 2021
Federated Dropout Learning for Hybrid Beamforming With Spatial Path Index Modulation In Multi-User mmWave-MIMO Systems

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Millimeter wave multiple-input multiple-output (mmWave-MIMO) systems with small number of radio-frequency (RF) chains have limited multiplexing gain. Spatial path index modulation (SPIM) is helpful in improving this gain by utilizing additional signal bits modulated by the indices of spatial paths. In this paper, we introduce model-based and model-free frameworks for beamformer design in multi-user SPIM-MIMO systems. We first design the beamformers via model-based manifold optimization algorithm. Then, we leverage federated learning (FL) with dropout learning (DL) to train a learning model on the local dataset of users, who estimate the beamformers by feeding the model with their channel data. The DL randomly selects different set of model parameters during training, thereby further reducing the transmission overhead compared to conventional FL. Numerical experiments show that the proposed framework exhibits higher spectral efficiency than the state-of-the-art SPIM-MIMO methods and mmWave-MIMO, which relies on the strongest propagation path. Furthermore, the proposed FL approach provides at least 10 times lower transmission overhead than the centralized learning techniques.

LGNov 13, 2020
Hybrid Federated and Centralized Learning

Ahmet M. Elbir, Sinem Coleri, Kumar Vijay Mishra

Many of the machine learning (ML) tasks are focused on centralized learning (CL), which requires the transmission of local datasets from the clients to a parameter server (PS) leading to a huge communication overhead. Federated learning (FL) overcomes this issue by allowing the clients to send only the model updates to the PS instead of the whole dataset. In this way, FL brings the learning to edge level, wherein powerful computational resources are required on the client side. This requirement may not always be satisfied because of diverse computational capabilities of edge devices. We address this through a novel hybrid federated and centralized learning (HFCL) framework to effectively train a learning model by exploiting the computational capability of the clients. In HFCL, only the clients who have sufficient resources employ FL; the remaining clients resort to CL by transmitting their local dataset to PS. This allows all the clients to collaborate on the learning process regardless of their computational resources. We also propose a sequential data transmission approach with HFCL (HFCL-SDT) to reduce the training duration. The proposed HFCL frameworks outperform previously proposed non-hybrid FL (CL) based schemes in terms of learning accuracy (communication overhead) since all the clients collaborate on the learning process with their datasets regardless of their computational resources.

SPOct 7, 2020
Cognitive Learning-Aided Multi-Antenna Communications

Ahmet M. Elbir, Kumar Vijay Mishra

Cognitive communications have emerged as a promising solution to enhance, adapt, and invent new tools and capabilities that transcend conventional wireless networks. Deep learning (DL) is critical in enabling essential features of cognitive systems because of its fast prediction performance, adaptive behavior, and model-free structure. These features are especially significant for multi-antenna wireless communications systems, which generate and handle massive data. Multiple antennas may provide multiplexing, diversity, or antenna gains that, respectively, improve the capacity, bit error rate, or the signal-to-interference-plus-noise ratio. In practice, multi-antenna cognitive communications encounter challenges in terms of data complexity and diversity, hardware complexity, and wireless channel dynamics. DL solutions such as federated learning, transfer learning and online learning, tackle these problems at various stages of communications processing, including multi-channel estimation, hybrid beamforming, user localization, and sparse array design. This article provides a synopsis of various DL-based methods to impart cognitive behavior to multi-antenna wireless communications for improved robustness and adaptation to the environmental changes while providing satisfactory spectral efficiency and computation times. We discuss DL design challenges from the perspective of data, learning, and transceiver architectures. In particular, we suggest quantized learning models, data/model parallelization, and distributed learning methods to address the aforementioned challenges.

SPSep 5, 2020
A Survey of Deep Learning Architectures for Intelligent Reflecting Surfaces

Ahmet M. Elbir, Kumar Vijay Mishra

Intelligent reflecting surfaces (IRSs) have recently received significant attention for 6G wireless communications as they enable the control of the wireless propagation environment. The use of IRS also provides reducing the hardware complexity, physical size, weight as well as cost of conventional large antenna arrays. However, deployment of the IRS entails dealing with multiple channel links between the base station (BS) and the users. Further, the BS and IRS beamformers require a joint design, wherein the IRS elements must be rapidly reconfigured. Data-driven techniques, such as deep learning (DL), are critical in addressing these challenges. The lower computation time and model-free nature of DL make it robust against data imperfections and environmental changes. At the physical layer, DL has been shown to be effective for IRS signal detection, channel estimation, and active/passive beamforming using architectures such as supervised, unsupervised, and reinforcement learning. This article provides a synopsis of these techniques for designing DL-based IRS-assisted wireless systems.

SPAug 25, 2020
Federated Learning for Channel Estimation in Conventional and RIS-Assisted Massive MIMO

Ahmet M. Elbir, Sinem Coleri

Machine learning (ML) has attracted a great research interest for physical layer design problems, such as channel estimation, thanks to its low complexity and robustness. Channel estimation via ML requires model training on a dataset, which usually includes the received pilot signals as input and channel data as output. In previous works, model training is mostly done via centralized learning (CL), where the whole training dataset is collected from the users at the base station (BS). This approach introduces huge communication overhead for data collection. In this paper, to address this challenge, we propose a federated learning (FL) framework for channel estimation. We design a convolutional neural network (CNN) trained on the local datasets of the users without sending them to the BS. We develop FL-based channel estimation schemes for both conventional and RIS (intelligent reflecting surface) assisted massive MIMO (multiple-input multiple-output) systems, where a single CNN is trained for two different datasets for both scenarios. We evaluate the performance for noisy and quantized model transmission and show that the proposed approach provides approximately 16 times lower overhead than CL, while maintaining satisfactory performance close to CL. Furthermore, the proposed architecture exhibits lower estimation error than the state-of-the-art ML-based schemes.

SPJun 19, 2020
A Deep Learning Framework for Hybrid Beamforming Without Instantaneous CSI Feedback

Ahmet M. Elbir

Hybrid beamformer design plays very crucial role in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. Previous works assume the perfect channel state information (CSI) which results heavy feedback overhead. To lower complexity, channel statistics can be utilized such that only infrequent update of the channel information is needed. To reduce the complexity and provide robustness, in this work, we propose a deep learning (DL) framework to deal with both hybrid beamforming and channel estimation. For this purpose, we introduce three deep convolutional neural network (CNN) architectures. We assume that the base station (BS) has the channel statistics only and feeds the channel covariance matrix into a CNN to obtain the hybrid precoders. At the receiver, two CNNs are employed. The first one is used for channel estimation purposes and the another is employed to design the hybrid combiners. The proposed DL framework does not require the instantaneous feedback of the CSI at the BS. We have shown that the proposed approach has higher spectral efficiency with comparison to the conventional techniques. The trained CNN structures do not need to be re-trained due to the changes in the propagation environment such as the deviations in the number of received paths and the fluctuations in the received path angles up to 4 degrees. Also, the proposed DL framework exhibits at least 10 times lower computational complexity as compared to the conventional optimization-based approaches.

SPJun 2, 2020
Federated Learning in Vehicular Networks

Ahmet M. Elbir, Burak Soner, Sinem Coleri et al.

Machine learning (ML) has recently been adopted in vehicular networks for applications such as autonomous driving, road safety prediction and vehicular object detection, due to its model-free characteristic, allowing adaptive fast response. However, most of these ML applications employ centralized learning (CL), which brings significant overhead for data transmission between the parameter server and vehicular edge devices. Federated learning (FL) framework has been recently introduced as an efficient tool with the goal of reducing transmission overhead while achieving privacy through the transmission of model updates instead of the whole dataset. In this paper, we investigate the usage of FL over CL in vehicular network applications to develop intelligent transportation systems. We provide a comprehensive analysis on the feasibility of FL for the ML based vehicular applications, as well as investigating object detection by utilizing image-based datasets as a case study. Then, we identify the major challenges from both learning perspective, i.e., data labeling and model training, and from the communications point of view, i.e., data rate, reliability, transmission overhead, privacy and resource management. Finally, we highlight related future research directions for FL in vehicular networks.

SPMay 20, 2020
Federated Learning for Hybrid Beamforming in mm-Wave Massive MIMO

Ahmet M. Elbir, Sinem Coleri

Machine learning for hybrid beamforming has been extensively studied by using centralized machine learning (CML) techniques, which require the training of a global model with a large dataset collected from the users. However, the transmission of the whole dataset between the users and the base station (BS) is computationally prohibitive due to limited communication bandwidth and privacy concerns. In this work, we introduce a federated learning (FL) based framework for hybrid beamforming, where the model training is performed at the BS by collecting only the gradients from the users. We design a convolutional neural network, in which the input is the channel data, yielding the analog beamformers at the output. Via numerical simulations, FL is demonstrated to be more tolerant to the imperfections and corruptions in the channel data as well as having less transmission overhead than CML.

SPApr 24, 2020
Sparse Array Selection Across Arbitrary Sensor Geometries with Deep Transfer Learning

Ahmet M. Elbir, Kumar Vijay Mishra

Sparse sensor array selection arises in many engineering applications, where it is imperative to obtain maximum spatial resolution from a limited number of array elements. Recent research shows that computational complexity of array selection is reduced by replacing the conventional optimization and greedy search methods with a deep learning network. However, in practice, sufficient and well-calibrated labeled training data are unavailable and, more so, for arbitrary array configurations. To address this, we adopt a deep transfer learning (TL) approach, wherein we train a deep convolutional neural network (CNN) with data of a source sensor array for which calibrated data are readily available and reuse this pre-trained CNN for a different, data-insufficient target array geometry to perform sparse array selection. Numerical experiments with uniform rectangular and circular arrays demonstrate enhanced performance of TL-CNN on the target model than the CNN trained with insufficient data from the same model. In particular, our TL framework provides approximately 20% higher sensor selection accuracy and 10% improvement in the direction-of-arrival estimation error.

SPJan 29, 2020
Deep Channel Learning For Large Intelligent Surfaces Aided mm-Wave Massive MIMO Systems

Ahmet M. Elbir, A Papazafeiropoulos, P. Kourtessis et al.

This letter presents the first work introducing a deep learning (DL) framework for channel estimation in large intelligent surface (LIS) assisted massive MIMO (multiple-input multiple-output) systems. A twin convolutional neural network (CNN) architecture is designed and it is fed with the received pilot signals to estimate both direct and cascaded channels. In a multi-user scenario, each user has access to the CNN to estimate its own channel. The performance of the proposed DL approach is evaluated and compared with state-of-the-art DL-based techniques and its superior performance is demonstrated.

SPDec 20, 2019
A Family of Deep Learning Architectures for Channel Estimation and Hybrid Beamforming in Multi-Carrier mm-Wave Massive MIMO

Ahmet M. Elbir, Kumar Vijay Mishra, M. R. Bhavani Shankar et al.

Hybrid analog and digital beamforming transceivers are instrumental in addressing the challenge of expensive hardware and high training overheads in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. However, lack of fully digital beamforming in hybrid architectures and short coherence times at mm-Wave impose additional constraints on the channel estimation. Prior works on addressing these challenges have focused largely on narrowband channels wherein optimization-based or greedy algorithms were employed to derive hybrid beamformers. In this paper, we introduce a deep learning (DL) approach for channel estimation and hybrid beamforming for frequency-selective, wideband mm-Wave systems. In particular, we consider a massive MIMO Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system and propose three different DL frameworks comprising convolutional neural networks (CNNs), which accept the raw data of received signal as input and yield channel estimates and the hybrid beamformers at the output. We also introduce both offline and online prediction schemes. Numerical experiments demonstrate that, compared to the current state-of-the-art optimization and DL methods, our approach provides higher spectral efficiency, lesser computational cost and fewer number of pilot signals, and higher tolerance against the deviations in the received pilot data, corrupted channel matrix, and propagation environment.

SPDec 9, 2019
DeepMUSIC: Multiple Signal Classification via Deep Learning

Ahmet M. Elbir

This letter introduces a deep learning (DL) framework for direction-of-arrival (DOA) estimation. Previous works in DL context mostly consider a single or two target scenario which is a strong limitation in practice. Hence, in this work, we propose a DL framework for multiple signal classification (DeepMUSIC). We design multiple deep convolutional neural networks (CNNs), each of which is dedicated to a subregion of the angular spectrum. In particular, each CNN is fed with the array covariance matrix and it learns the MUSIC spectra of the corresponding angular subregion. We have shown, through simulations, that the proposed DeepMUSIC framework has superior estimation accuracy and exhibits less computational complexity in comparison with both DL and non-DL based techniques.

SPNov 11, 2019
Hybrid Precoding for Multi-User Millimeter Wave Massive MIMO Systems: A Deep Learning Approach

Ahmet M. Elbir, Anastasios Papazafeiropoulos

In multi-user millimeter wave (mmWave) multiple-input-multiple-output (MIMO) systems, hybrid precoding is a crucial task to lower the complexity and cost while achieving a sufficient sum-rate. Previous works on hybrid precoding were usually based on optimization or greedy approaches. These methods either provide higher complexity or have sub-optimum performance. Moreover, the performance of these methods mostly relies on the quality of the channel data. In this work, we propose a deep learning (DL) framework to improve the performance and provide less computation time as compared to conventional techniques. In fact, we design a convolutional neural network for MIMO (CNN-MIMO) that accepts as input an imperfect channel matrix and gives the analog precoder and combiners at the output. The procedure includes two main stages. First, we develop an exhaustive search algorithm to select the analog precoder and combiners from a predefined codebook maximizing the achievable sum-rate. Then, the selected precoder and combiners are used as output labels in the training stage of CNN-MIMO where the input-output pairs are obtained. We evaluate the performance of the proposed method through numerous and extensive simulations and show that the proposed DL framework outperforms conventional techniques. Overall, CNN-MIMO provides a robust hybrid precoding scheme in the presence of imperfections regarding the channel matrix. On top of this, the proposed approach exhibits less computation time with comparison to the optimization and codebook based approaches.

SPFeb 27, 2018
Cognitive Radar Antenna Selection via Deep Learning

Ahmet M. Elbir, Kumar Vijay Mishra, Yonina C. Eldar

Direction of arrival (DoA) estimation of targets improves with the number of elements employed by a phased array radar antenna. Since larger arrays have high associated cost, area and computational load, there is recent interest in thinning the antenna arrays without loss of far-field DoA accuracy. In this context, a cognitive radar may deploy a full array and then select an optimal subarray to transmit and receive the signals in response to changes in the target environment. Prior works have used optimization and greedy search methods to pick the best subarrays cognitively. In this paper, we leverage deep learning to address the antenna selection problem. Specifically, we construct a convolutional neural network (CNN) as a multi-class classification framework where each class designates a different subarray. The proposed network determines a new array every time data is received by the radar, thereby making antenna selection a cognitive operation. Our numerical experiments show that {the proposed CNN structure provides 22% better classification performance than a Support Vector Machine and the resulting subarrays yield 72% more accurate DoA estimates than random array selections.