1 Machine Learning-Based Angle of Arrival Estimation for Ultra-Wide Band Radios Mostafa Naseri, Adnan Shahid, Gert-Jan Gordebeke, Sam Lemey, Michiel Boes, Samuel Van de Velde, and Eli De Poorter Abstract—This paper analyzes the feasibility of deep convo- lutional neural networks (DCNN) for accurate ultra-wideband (UWB) angle of arrival estimation that is robust against hard- ware imperfections. To this end, a uniform linear array with four antenna elements is leveraged and a DCNN approach is proposed and compared with traditional approaches, such as MUSIC and phase difference of arrival estimators, for different environments, number of available channel impulse responses, and polarization mismatches, in terms of absolute value of error and computational complexity. The proposed approach outperforms the traditional approaches up to 80 ◦ error reduction at a computational complexity increase of only 10% compared to MUSIC. Index Terms—Angle of arrival (AoA), ultra-wideband (UWB), channel impulse response (CIR), machine learning (ML), deep convolutional neural network (DCNN), PDoA, MUSIC. I. I NTRODUCTION U LTRA-wideband (UWB) has become a key technology for localization systems in GPS-denied environments [1], [2]. The UWB technology benefits from a high time-domain resolution leading to a precise time of flight (ToF) and high- resolution channel impulse response (CIR) measurements. The high resolution CIR provides useful information that could be used to tackle main localization challenges, e.g. multipath propagation, making UWB a key technology for challenging environments. The UWB technology enables several localization ap- proaches, among which angle of arrival (AoA) estimation is highly demanded. AoA estimation is a crucial task in narrow beam wireless data transmission and smart antenna systems to facilitate beamforming [3], vehicle to vehicle communication [4], and indoor positioning [5]. Unlike approaches that require two-way communication between anchor node and tag node, e.g. two-way ranging, in AoA estimation a feedback link is not required (in self localization) which results in better system scalability and complexity. In addition, current UWB position- ing systems typically use timing information to determine the distance between a mobile tag and several distributed anchor nodes. By adding an additional antenna and radio module on the anchor node (e.g. creating an antenna array), the phase and arrival time can be determined at each antenna element, enabling the extraction of angle-of-arrival information. Hence, Mostafa Naseri, Adnan Shahid, Gert-Jan Gordebeke, Sam Lemey, and Eli De Poorter are with IDLab, Department of Information Technology, Ghent University - imec, Ghent, Belgium (email: mostafa.naseri@ugent.be; adnan.shahid@ugent.be; gertjan.gordebeke@ugent.be; sam.lemey@ugent.be; eli.depoorter@ugent.be). Michiel Boes and Samuel Van de Velde are with Pozyx, Ghent, Belgium (email: michiel.boes@pozyx.io; samuel@pozyx.io). using AoA, the total required infrastructure cost can be re- duced significantly. Traditional AoA estimation methods are divided into several categories, namely spectral-based estimation, deterministic pa- rameter estimation, and subspace-based AoA estimation [6]. These methods are vulnerable to array imperfections caused by suboptimal antenna design, fabrication imperfections, inter- antenna interference, and installation platform effects. In ad- dition, challenging environmental effects, e.g. multipath and non-line of sight (NLoS), will degrade the performance of these traditional methods [7]. Modeling all of the afore- mentioned destructive effects is not necessarily an efficient approach, if not impractical. As opposed to the rule-based algorithms, a deep convo- lutional neural network (DCNN) is adopted in this work. DCNNs select features from the input without manual feature extraction and finds a mapping from the features in the ob- served data to the desired output, i.e. true AoA. DCNNs have demonstrated excellent performance in the image processing domain [8]. The DCNN can overcome modeling complications of the aforementioned antenna array imperfections and extract features from the antenna array output to make the algorithm robust against environmental changes. It should be noted that relying on simulation results for evaluating machine learning (ML) solutions could be misleading due to the fact that in the simulations, the interfering effects are artificially added to the system using known models [9]. However, such imperfections could be unknown, difficult to measure, or too complicated to be modeled. In this work, we use supervised ML to estimate the AoA from a set of labeled input-output pairs. Although almost all AoA estimation methods rely on the reception of the signal by an array of antennas (or one antenna that moves to different positions), [10] and [11] propose a single-antenna AoA estimation approach. Single antenna AoA estimation algorithms either require more complicated hardware [10] or exploit the angle-dependent property of the transmitter and receiver antenna pattern [11]. In the latter approach, the AoA estimator maps the CIR to AoA for one specific convolution of the impulse response of the transmit antenna, channel, and receive antenna. Since in this approach the estimator does not have access to differential information (between antenna elements), the mapping is environment- dependent for a fixed pair of transmit and receive antennas. In addition to the error performance of the adopted algo- rithm, its complexity plays an important role in an AoA esti- mation, especially for real-time applications [12]. For instance, iterative searches or singular value decomposition (SVD) increase the complexity of an algorithm and, hence, require a