In this paper, we investigate high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. Based on the triple-beam (TB) based channel model and the channel sparsity in the TB domain, we propose a beam structured channel estimation (BSCE) approach. Specifically, we show that the space-frequency-time (SFT) domain estimator design for each TB domain channel element can be transformed into that of a low-dimensional TB domain estimator and the resulting SFT domain estimator is beam structured. We also present a method to select the TBs used for BSCE. Then we generalize the proposed BSCE by introducing window functions and a turbo principle to achieve a superior trade-off between complexity and performance. Furthermore, we present a low-complexity design and implementation of BSCE by exploiting the characteristics of the TB matrix. Simulation results validate the proposed theory and methods.

Train localization during Global Navigation Satellite Systems (GNSS) outages presents challenges for ensuring failsafe and accurate positioning in railway networks. This paper proposes a minimalist approach exploiting track geometry and Inertial Measurement Unit (IMU) sensor data. By integrating a discrete track map as a Look-Up Table (LUT) into a Particle Filter (PF) based solution, accurate train positioning is achieved with only an IMU sensor and track map data. The approach is tested on an open railway positioning data set, showing that accurate positioning (absolute errors below 10 m) can be maintained during GNSS outages up to 30 s in the given data. We simulate outages on different track segments and show that accurate positioning is reached during track curves and curvy railway lines. The approach can be used as a redundant complement to established positioning solutions to increase the position estimate's reliability and robustness.

In this paper, we investigate signal detection for HF skywave massive multiple-input multiple-output (MIMO) communications with orthogonal frequency division multiplexing (OFDM) modulation. We first introduce beam based channel model (BBCM) in the space domain and reveal the sparsity of the channel in the space-beam domain. Based on the BBCM in the space domain, we propose a beam structured detector (BSD) for each subcarrier. Specifically, we prove that the space domain detector design can be transformed to that of a beam domain detector without sacrificing optimality, and the asymptotically optimal space domain detector is beam structured with a low-dimensional beam domain detector, thus significantly reducing the design and implementation complexities. Furthermore, we provide a beam selection criterion to choose the beams that are used for the BSD. Simulation results demonstrate the low complexity and satisfactory performance of the proposed detector.

Federated learning (FL) has emerged as an instance of distributed machine learning paradigm that avoids the transmission of data generated on the users' side. Although data are not transmitted, edge devices have to deal with limited communication bandwidths, data heterogeneity, and straggler effects due to the limited computational resources of users' devices. A prominent approach to overcome such difficulties is FedADMM, which is based on the classical two-operator consensus alternating direction method of multipliers (ADMM). The common assumption of FL algorithms, including FedADMM, is that they learn a global model using data only on the users' side and not on the edge server. However, in edge learning, the server is expected to be near the base station and have direct access to rich datasets. In this paper, we argue that leveraging the rich data on the edge server is much more beneficial than utilizing only user datasets. Specifically, we show that the mere application of FL with an additional virtual user node representing the data on the edge server is inefficient. We propose FedTOP-ADMM, which generalizes FedADMM and is based on a three-operator ADMM-type technique that exploits a smooth cost function on the edge server to learn a global model parallel to the edge devices. Our numerical experiments indicate that FedTOP-ADMM has substantial gain up to 33% in communication efficiency to reach a desired test accuracy with respect to FedADMM, including a virtual user on the edge server.

The development of future railway systems is contingent on the evolution of wireless communications technologies and their ability to serve more sophisticated use cases. Recent proposals to extend the 3rd Generation Partnership Project (3GPP) 4G or 5G standard for use in next-generation railway wireless communications presents a problem in that they are still based on Orthogonal Frequency Division Multiplexing (OFDM), which is vulnerable to Doppler-related effects when traveling at high speed. Orthogonal Time Frequency Space (OTFS) is a promising new modulation technique that can handle communication even in very high vehicle speed cases. In this paper, we investigate the performance of OTFS in terms of achievable rate under different High Speed Rail (HSR) environments, while taking into account the impact of practical but non-biorthogonal pulse shapes. Simulation results show that OTFS provides consistently high achievable rates regardless of the environment, and that the rates are relatively insensitive to the speed of travel.

Determination of train positions within a railway network must be fail-safe and of high accuracy. In train-bourne positioning, exploitation of geometrical map features is an important factor and uncertainties in the map information may affect the position estimate. In this paper, we present a method to estimate the position of a train in the track net and to identify the correct path behind a turnout, using absolute position estimates and geometrical map information of various accuracies. We evaluate the impact of uncertainties in the map representation on the correct identification of a path behind a turnout. We derive a formulation of a probabilistic track map and include the map information into a constrained multi-hypothesis Kalman filter. We show in numerical simulations on a crossover and a turnout that modelling existing map uncertainties significantly improves the track discrimination.

Although signal distortion-based peak-to-average power ratio (PAPR) reduction is a feasible candidate for orthogonal frequency division multiplexing (OFDM) to meet standard/regulatory requirements, the error vector magnitude (EVM) stemming from the PAPR reduction has a deleterious impact on the performance of high data-rate achieving multiple-input multiple-output (MIMO) systems. Moreover, these systems must constrain the adjacent channel leakage ratio (ACLR) to comply with regulatory requirements. Several recent works have investigated the mitigation of the EVM seen at the receivers by capitalizing on the excess spatial dimensions inherent in the large-scale MIMO that assume the availability of perfect channel state information (CSI) with spatially uncorrelated wireless channels. Unfortunately, practical systems operate with erroneous CSI and spatially correlated channels. Additionally, most standards support user-specific/CSI-aware beamformed and cell-specific/non-CSI-aware broadcasting channels. Hence, we formulate a robust EVM mitigation problem under channel uncertainty with nonconvex PAPR and ACLR constraints catering to beamforming/broadcasting. To solve this formidable problem, we develop an efficient scheme using our recently proposed three-operator alternating direction method of multipliers (TOP-ADMM) algorithm and benchmark it against two three-operator algorithms previously presented for machine learning purposes. Numerical results show the efficacy of the proposed algorithm under imperfect CSI and spatially correlated channels.

Downlink beamforming is a key technology for cellular networks. However, computing beamformers that maximize the weighted sum rate (WSR) subject to a power constraint is an NP-hard problem. The popular weighted minimum mean square error (WMMSE) algorithm converges to a local optimum but still exhibits considerable complexity. In order to address this trade-off between complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm for a MU-MISO downlink channel. The main idea consists of mapping a fixed number of iterations of the WMMSE into trainable neural network layers. However, the formulation of the WMMSE algorithm, as provided in Shi et al., involves matrix inversions, eigendecompositions, and bisection searches. These operations are hard to implement as standard network layers. Therefore, we present a variant of the WMMSE algorithm i) that circumvents these operations by applying a projected gradient descent and ii) that, as a result, involves only operations that can be efficiently computed in parallel on hardware platforms designed for deep learning. We demonstrate that our variant of the WMMSE algorithm convergences to a stationary point of the WSR maximization problem and we accelerate its convergence by incorporating Nesterov acceleration and a generalization thereof as learnable structures. By means of simulations, we show that the proposed network architecture i) performs on par with the WMMSE algorithm truncated to the same number of iterations, yet at a lower complexity, and ii) generalizes well to changes in the channel distribution.

Millimeter wave (mmWave) wireless technology is primarily considered for low latency communication in fifth-generation mobile technology (5G) and has the potential to revolutionize industrial automation and manufacturing processes. This article investigates multipath radio propagation in indoor industrial environments at the 24 GHz industrial, scientific and medical (ISM) mmWave frequency band. The wideband radio channel measurements were carried out in four different industrial environments in Sweden. The measurements were conducted using an affordable but highly competent in-house assembled mmWave testbed, reusing radio instruments available in our lab. The measurement environments were chosen based on their radio wave reflection characteristics. The multipath propagation characteristics are analyzed with respect to the power delay profile (PDP), coherence bandwidth, and root mean square (RMS) delay spread. Additionally, the Saleh-Valenzuela model parameters are estimated for these industrial environments.

Determination of train positions within a railway network must be fail-safe and of high accuracy. This is an essential task to solve to achieve a secure and efficient railway operation. In this paper, we present a method to estimate position and velocity of a train in the track net using given position estimates from an arbitrary information source, and improving the estimate by using geometrical track information. We focus on modelling and exploiting of the geometrical track information including possible uncertainties and examine the impact of uncertainties on the state estimate. We store the track information as a set of supporting points with Gaussian uncertainties and interpolate linearly. The track information is fed into a Kalman filter in form of soft constraints that is modified to account for state-dependent observation noise. A simulated test run shows that the average position and velocity error along track decreases significantly when modelling the uncertainty of the constraints, compared to using a Kalman filter with hard constraints. We evaluate the presented filter for different supporting point and measurement uncertainties and show that the performance within a typical parameter setting for train positioning is improved compared to the unconstrained Kalman filter and the Kalman filter with hard constraints.