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Joint communications and sensing (JCAS) is envisioned as a key feature in future wireless communications networks. In massive MIMO-JCAS systems, hybrid beamforming (HBF) is typically employed to achieve satisfactory beamforming gains with reasonable hardware cost and power consumption. Due to the coupling of the analog and digital precoders in HBF and the dual objective in JCAS, JCAS-HBF design problems are very challenging and usually require highly complex algorithms. In this paper, we propose a fast HBF design for JCAS based on deep unfolding to optimize a tradeoff between the communications rate and sensing accuracy. We first derive closed-form expressions for the gradients of the communications and sensing objectives with respect to the precoders and demonstrate that the magnitudes of the gradients pertaining to the analog precoder are typically smaller than those associated with the digital precoder. Based on this observation, we propose a modified projected gradient ascent (PGA) method with significantly improved convergence. We then develop a deep unfolded PGA scheme that efficiently optimizes the communications-sensing performance tradeoff with fast convergence thanks to the well-trained hyperparameters. In doing so, we preserve the interpretability and flexibility of the optimizer while leveraging data to improve performance. Finally, our simulations demonstrate the potential of the proposed deep unfolded method, which achieves up to 33.5% higher communications sum rate and 2.5dB lower beampattern error compared with the conventional design based on successive convex approximation and Riemannian manifold optimization. Furthermore, it attains up to a 65% reduction in run time and computational complexity with respect to the PGA procedure without unfolding.

Electrocardiography (ECG) signals play a pivotal role in many healthcare applications, especially in at-home monitoring of vital signs. Wearable technologies, which these applications often depend upon, frequently produce low-quality ECG signals. While several methods exist for ECG denoising to enhance signal quality and aid clinical interpretation, they often underperform with ECG data from wearable technology due to limited noise tolerance or inadequate flexibility in capturing ECG dynamics. This paper introduces HKF, a hierarchical and adaptive Kalman filter, which uses a proprietary state space model to effectively capture both intra- and inter-heartbeat dynamics for ECG signal denoising. HKF learns a patient-specific structured prior for the ECG signal's intra-heartbeat dynamics in an online manner, resulting in a filter that adapts to the specific ECG signal characteristics of each patient. In an empirical study, HKF demonstrated superior denoising performance (reduced Mean-Squared Error) while preserving the unique properties of the waveform. In a comparative analysis, HKF outperformed previously proposed methods for ECG denoising, such as the model-based Kalman filter and data-driven autoencoders. This makes it a suitable candidate for applications in extramural healthcare settings.

Pairs trading is a family of trading techniques that determine their policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on describing the pairwise relationship as a linear Space State (SS) model with Gaussian noise. This representation facilitates extracting financial indicators with low complexity and latency using a Kalman Filter (KF), which are then processed using classic policies such as Bollinger Bands (BB). However, such SS models are inherently approximated and mismatched, often degrading the revenue. In this work, we propose KalmanNet-aided Bollinger bands Pairs Trading (KBPT), a deep learning aided policy that augments the operation of KF-aided BB trading. KBPT is designed by formulating an extended SS model for pairs trading that approximates their relationship as holding partial co-integration. This SS model is utilized by a trading policy that augments KF-BB trading with a dedicated neural network based on the KalmanNet architecture. The resulting KBPT is trained in a two-stage manner, which first tunes the tracking algorithm in an unsupervised manner independently of the trading task, followed by its adaptation to track the financial indicators to maximize revenue while approximating BB with a differentiable mapping. KBPT thus leverages data to overcome the approximated nature of the SS model, converting the KF-BB policy into a trainable model. We empirically demonstrate that our proposed KBPT systematically yields improved revenue compared with model-based and data-driven benchmarks over various assets.

Dynamic systems of graph signals are encountered in various applications, including social networks, power grids, and transportation. While such systems can often be described as state space (SS) models, tracking graph signals via conventional tools based on the Kalman filter (KF) and its variants is typically challenging. This is due to the nonlinearity, high dimensionality, irregularity of the domain, and complex modeling associated with real-world dynamic systems of graph signals. In this work, we study the tracking of graph signals using a hybrid model-based/data-driven approach. We develop the GSP-KalmanNet, which tracks the hidden graphical states from the graphical measurements by jointly leveraging graph signal processing (GSP) tools and deep learning (DL) techniques. The derivations of the GSP-KalmanNet are based on extending the KF to exploit the inherent graph structure via designing a graph frequency domain filtering and replacing the Kalman gain (KG) with a graph filter that minimizes the prediction error. Thus, it considerably simplifies the computational complexity entailed in processing high-dimensional signals and increases the robustness to small topology changes. Then, we use data to learn the KG, namely, the graph filter, following the recently proposed KalmanNet framework, which copes with partial and approximated modeling, without forcing a specific model over the noise statistics. Restricting the KG to a graph filter in the proposed GSP-KalmanNet reduces learned parameters, thereby enhancing stability. Our empirical results demonstrate that the GSP-KalmanNet achieves enhanced accuracy and run time performance, and improved robustness to model misspecifications compared with both model-based and data-driven benchmarks.