The WMMSE beamforming algorithm is a popular approach to address the NP-hard weighted sum rate (WSR) maximization beamforming problem. Although it efficiently finds a local optimum, it requires matrix inverses, eigendecompositions, and bisection searches, operations that are problematic for real-time implementation. In our previous work, we considered the MU-MISO case with single-antenna receivers and effectively replaced such operations by resorting to a first-order method. Here, we consider the more general and challenging MU-MIMO case with multiple-antenna receivers. Our earlier approach does not generalize to this scenario and cannot be applied to replace all the hard-to-parallelize operations that appear in the MU-MIMO case. Thus, we propose to leverage a reformulation of the auxiliary WMMSE function given by Hu et al. By applying gradient descent and Schulz iterations, we formulate the first variant of the WMMSE algorithm applicable to the MU-MIMO case that is free from matrix inverses and other serial operations and hence amenable to both real-time implementation and deep unfolding. From a theoretical viewpoint, we establish its convergence to a stationary point of the WSR maximization problem. From a practical viewpoint, we show that in a deep-unfolding-based implementation, the matrix-inverse-free WMMSE algorithm attains, within a fixed number of iterations, a WSR comparable to the original WMMSE algorithm truncated to the same number of iterations, yet with significant implementation advantages in terms of parallelizability and real-time execution.

Machine learning has enabled extraordinary advancements in many fields and penetrates every aspect of our lives. Autonomous driving cars and automatic speech translators are just two examples of the numerous applications that have become a reality yet seemed so distant a few years ago. Motivated by this unprecedented success of machine learning, researchers have started investigating its potential within the field of wireless communications, and a plethora of outstanding data-driven solutions have appeared. 

In this thesis, we acknowledge the success of machine learning, and we corroborate its role in shaping the future generation of cellular systems. However, we argue that machine learning should be combined with solid theoretical foundations and expert knowledge as the basis of wireless systems. Machine learning allows a substantial performance gain when traditional approaches fall short, e.g., when modeling assumptions fail to capture reality accurately or when conventional algorithms are computationally costly. Likewise, the injection of domain knowledge into data-driven solutions can compensate for typical machine learning shortcomings, such as a lack of interpretability and performance guarantees, poor scalability, and questionable robustness. 

In this thesis, composed of five technical papers, we present novel hybrid model-based and data-driven approaches in three application areas: interference detection for satellite signals, channel prediction for link adaptation, and downlink beamforming in MU-MISO and MU-MIMO settings. We go beyond a mere application of machine learning and adopt a reasoned approach to integrate domain knowledge synergistically. As a result, the proposed approaches, on the one hand, achieve remarkable empirical performance and, on the other hand, are supported by theoretical analysis. Furthermore, we pay particular attention to the explainability of all our proposed approaches since the typical black-box nature of data-driven solutions constitutes one of the major obstacles to their actual deployment, especially in the wireless communications field.

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.

The weighted minimum mean square error (WMMSE) algorithm was proposed to provide a locally optimum solution to the otherwise NP-hard weighted sum rate maximization beamforming problem, but it can still be prohibitively complex for real-time implementation. With the success of deep unfolding in trading off complexity and performance, we propose to apply deep unfolding to the WMMSE algorithm. With respect to traditional end-to-end learning, deep unfolding incorporates expert knowledge, with the benefits of immediate and well-grounded architecture selection, fewer trainable parameters, and better explainability. However, the classical formulation of the WMMSE algorithm given by Shi et al. is not amenable for deep unfolding due to matrix inversions, eigendecompositions, and bisection searches. Therefore, we present an alternative formulation that circumvents these operations. By means of simulations, we show that the deep unfolded WMMSE algorithm performs on par with the original WMMSE algorithm, at a lower computational load.

In this paper, we analyze the two-node joint clock synchronization and ranging problem. We focus on the case of nodes that employ time-to-digital converters to determine the range between them precisely. This specific design choice leads to a sawtooth model for the captured signal, which has not been studied before from an estimation theoretic standpoint. In the study of this model, we recover the basic conclusion of a well-known article by Freris, Graham, and Kumar in clock synchronization. More importantly, we discover a surprising identifiability result on the sawtooth signal model: noise improves the theoretical condition of the estimation of the phase and offset parameters. To complete our study, we provide performance references for joint clock synchronization and ranging using the sawtooth signal model by presenting an exhaustive simulation study on basic estimation strategies under different realistic conditions. With our contributions in this paper, we enable further research in the estimation of sawtooth signal models and pave the path towards their industrial use for clock synchronization and ranging.

Clock synchronization and ranging over a wireless network with low communication overhead is a challenging goal with tremendous impact. In this paper, we study the use of time-to-digital converters in wireless sensors, which provides clock synchronization and ranging at negligible communication overhead through a sawtooth signal model for round trip times between two nodes. In particular, we derive Cramer-Rao lower bounds for a linearitzation of the sawtooth signal model, and we thoroughly evaluate simple estimation techniques by simulation, giving clear and concise performance references for this technology.

Highly accurate weather classifiers have recently received a great deal of attention due to their promising applications. An alternative to conventional Weather radars consists of using the measured attenuation data in commercial microwave links (CML) as input to a weather classifier. The design of an accurate weather classifier is challenging due to diverse weather conditions, the absence of predefined features, and specific domain requirements in terms of execution time and detection sensitivity. In addition to this, the quality of the data given as input to the classifier plays a crucial role as it directly impacts the classification output. However, the quality of the measured attenuation data in the CMLs poses a serious concern for different reasons, e.g. the nature of the data itself, the location of each link, and the geographical distance between the links. This mandates the adoption of a data preprocessing step before classification with the purpose to validate the quality of the input data. In this paper, we propose a data preprocessing framework which employs a deep learning model to (i) detect anomalies in the raw data and (ii) validate the measured CML attenuation data by adding quality flags. Moreover, the feasibility and possible generalizations of the proposed framework are studied by conducting an empirical case study performed on real data collected from CMLs at Ericsson AB in Sweden. The empirical evaluation indicates that the average area under the receiver operating characteristic curve exceeding 0.72 using the proposed data preprocessing framework.

Spectrum monitoring and interference detection are crucial for the satellite service performance and the revenue of SatCom operators. Interference is one of the major causes of service degradation and deficient operational efficiency. Moreover, the satellite spectrum is becoming more crowded, as more satellites are being launched for different applications. This increases the risk of interference, which causes anomalies in the received signal, and mandates the adoption of techniques that can enable the automatic and real-time detection of such anomalies as a first step toward interference mitigation and suppression. In this chapter, we present a machine learning (ML)-based approach which is able to guarantee a real-time and automatic detection of both short-term and long-term interference in the spectrum of the received signal at the base station. The proposed approach can localize the interference both in time and in frequency and is universally applicable across a discrete set of different signal spectra. We present experimental results obtained by applying our method to real spectrum data from the Swedish Space Corporation. We also compare our ML-based approach to a model-based approach applied to the same spectrum data and used as a realistic baseline. Experimental results show that our method is a more reliable interference detector.

Link adaptation provides high spectral efficiency in wireless communications by selecting appropriate transmission parameters, e.g., the modulation and coding scheme (MCS), based on the instantaneous wireless channel. However, link adaptation suffers from impairments due to channel state information (CSI) feedback delay. In this paper, we extend the data-driven MCS selection scheme in our previous work to the case ofoutdated CSI, by assuming that CSI history is available to the system. We present two approaches that leverage the CSI history to optimally select the MCS for the current channel, i.e., i) an end-to-end (E2E) machine learning approach and ii) a hybrid data-driven and model-based approach. The E2E method uses the CSI history as input to a neural network for MCS selection. Conversely, the hybrid method uses a lower-dimensionality sufficient statistic for the instantaneous CSI, computed from the CSI history, as input to a neural network for MCS selection. We demonstrate that replacing the CSI history with the sufficient statistic comes without loss of generality. Moreover, by means of numerical experiments, we show that both approaches effectively compensate for the feedback delay. However, we advocate the hybrid approach as it comes with the additional benefits of i) a smaller neural network, which in turn requires a lower amount of data and training time, ii) improved explainability, and iii) better insights into optimization choices.

Data-driven fault diagnosis is a promising approach for the early detection and isolation of malfunctions in power generation plants deploying solid oxide fuel cells (SOFCs). Despite the supervised classifier used in a data-driven system is trained by samples gathered under one specific design-point operating condition, during real operation the plant can move to a new, unexpected off-design operating condition, reducing the performance of the diagnosis system. This Short Communication demonstrates that this reduction is heavily mitigated if the supervised classifier is adapted to the new condition through the domain adaptation statistical technique. The present study shows that a probability of correct classification between 85% and 94% can be achieved in off-design, when a probability of 95% is obtained at the design-point.