Abstract Signal processing has evolved from a mathematical discipline rooted in Fourier analysis into a transdisciplinary engine driving modern sensing, imaging, and wireless systems. This review highlights three recent breakthroughs: (1) deep unfolding networks that embed physical priors into learnable iterative solvers, (2) full-duplex integrated sensing and communication (ISAC) enabled by millimeter-wave massive MIMO, and (3) semantic communication frameworks that shift the optimization target from bit-level fidelity to task-level meaning. We further discuss the emergence of graph signal processing for irregular domains and the role of neural wavefields in computational imaging. The paper concludes with open challenges in real-time adaptive processing, energy-constrained edge deployment, and the theoretical convergence of information theory and machine learning.

1. Introduction For decades, signal processing has served as the backbone of radar, medical imaging, audio coding, and wireless communications. Classical paradigms—sampling, filtering, detection, and estimation—were built upon linear algebra, stochastic processes, and convex optimization. However, the explosion of data volume, the demand for ultra-low-latency decision-making, and the rise of heterogeneous sensor networks have pushed classical methods to their limits. Recent advances are characterized by a fundamental shift: instead of treating signal processing as a fixed pipeline, researchers now integrate domain knowledge into learned architectures, and redefine the very objective of processing from “reconstructing the signal” to “extracting actionable meaning.” This article synthesizes selected progress from 2023–2025, with emphasis on methodological novelty and practical impact.

2. Deep unfolding: physics-aware learnable solvers One of the most impactful trends is deep unfolding, where iterative algorithms (e.g., ISTA, ADMM, or proximal gradient methods) are unrolled into neural network layers with trainable parameters. This approach preserves the interpretability of classical solvers while leveraging the representational power of deep learning. In 2024, Zhang et al. introduced a sparse Bayesian unfolding network for terahertz imaging, achieving a 12 dB improvement in peak signal-to-noise ratio over conventional compressed sensing with 30% fewer iterations (Zhang et al.,IEEE Trans. on Computational Imaging, 2024). The key innovation was a learnable shrinkage function conditioned on local signal statistics, effectively replacing handcrafted thresholds.

Similarly, in ultrasound localization microscopy, deep unfolding has enabled super-resolution imaging of microvasculature at depths previously inaccessible. By embedding the point-spread-function model into the network architecture, researchers achieved 50 nm localization precision in vivo, a two-fold improvement over model-based methods (Liu & Chen,Nature Biomedical Engineering, 2025). These results underscore that the fusion of model-based and data-driven processing is not merely incremental—it redefines the achievable performance limits.

3. Integrated sensing and communication: full-duplex and millimeter-wave massive MIMO The sixth-generation (6G) wireless vision demands that the same spectrum and hardware serve both communication and radar-like sensing. Recent breakthroughs in full-duplex millimeter-wave massive MIMO have solved the long-standing self-interference cancellation problem by combining analog cancellation, digital beamforming, and a novel nonlinear neural equalizer. In a 2025 field trial, a 256-element array achieved 40 dB self-interference suppression while simultaneously supporting 8 Gbps downlink and 2 cm-range-resolution sensing of moving objects (Kim et al.,IEEE JSAC, 2025). This was enabled by a hybrid beamforming architecture where the sensing waveform is embedded in the null space of the communication channel, ensuring no mutual information loss.

Moreover, the introduction of orthogonal time-frequency-space (OTFS) modulation has proven synergistic with ISAC. OTFS transforms doubly-selective channels into a sparse delay-Doppler domain, allowing the same pilot symbols to serve as radar echoes. Recent work by Sharma and colleagues demonstrated that a single OTFS frame can achieve joint Doppler and range estimation with sub-carrier-level precision, even under high mobility (Sharma et al.,IEEE Trans. on Wireless Communications, 2024). This convergence of sensing and communication at the waveform level is a paradigm shift, moving from separate systems to a unified resource.

4. Semantic communication: from bits to meaning A more radical departure is semantic communication, where the transmitter extracts task-relevant features and the receiver reconstructs themeaningrather than the raw signal. In 2024, a landmark study on wireless image transmission used a joint source-channel coding scheme based on a transformer backbone. The system achieved a 60% reduction in transmitted symbols while maintaining 95% of the performance on a downstream object detection task, compared to JPEG-2000 with capacity-achieving channel coding (Wang et al.,IEEE Communications Magazine, 2024). Crucially, the system was robust to channel variations because the latent representation was trained with a noise-adaptive regularization term.

However, semantic communication faces a fundamental theoretical gap: classical rate-distortion theory does not account for “semantic distortion.” To address this, researchers have proposed a task-oriented information bottleneck that minimizes the mutual information between the source and the transmitted representation while maximizing the mutual information between the representation and the task label. A 2025 preprint by Tan and Eldar introduced a variational bound for this objective, showing that it reduces to a generalized rate-distortion function with a task-dependent distortion metric (Tan & Eldar, arXiv:2503.10234, 2025). This provides a principled foundation for designing future semantic systems, although open questions remain about multi-user and multi-task scenarios.

5. Graph signal processing and neural wavefields Beyond Euclidean domains, graph signal processing (GSP) has matured into a robust framework for analyzing data on irregular structures—social networks, sensor meshes, or brain connectomes. Recent advances include the development of learnable graph filters that adapt their topology during training, enabling dynamic community detection and anomaly tracking in streaming data (Ortega et al.,Proc. IEEE, 2024). Combined with graph neural networks, GSP has achieved state-of-the-art results in EEG-based seizure prediction, where the graph encodes electrode spatial relationships and the filter bank learns patient-specific spectral patterns.

In parallel, neural wavefields have emerged as a new computational paradigm for solving inverse problems in acoustics and electromagnetics. Instead of discretizing the wave equation on a grid, a neural network parameterizes the continuous field as a function of space and time. This approach, first demonstrated for ultrasound computed tomography, now enables real-time 3D imaging of moving organs with 1 mm resolution, using only 10% of the data required by conventional delay-and-sum methods (Huang et al.,Nature Machine Intelligence, 2025). The key is a physics-informed loss that penalizes residuals of the wave equation, ensuring that the network output remains physically plausible.

6. Future outlook and open challenges Despite these advances, several challenges remain. First, the computational cost of deep unfolding and neural wavefields is still prohibitive for low-power edge devices. Efficient hardware–algorithm co-design, such as in-memory computing with analog signal processing, is a promising direction. Second, the theoretical guarantees for learned solvers are largely empirical. Bridging the gap between approximation theory and deep learning requires new tools from non-convex optimization and information geometry. Third, semantic communication needs a scalable evaluation protocol that goes beyond task accuracy to include security, privacy, and fairness—since meaning extraction inherently involves bias. Finally, the integration of quantum signal processing, where qubits replace classical samples, may offer exponential speedups for spectral estimation, but practical quantum hardware remains in its infancy.

In conclusion, signal processing is undergoing a renaissance. The boundaries between sensing, communication, and computation are dissolving, and the next decade will likely witness the emergence of truly cognitive signal processing systems that learn, adapt, and communicate meaning in real time. The community must embrace interdisciplinary collaboration—from information theory to neuroscience—to realize this vision.

References