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Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recently developed optimization techniques in areas ranging from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing or developing suitable algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions.

Integrated sensing and communication (ISAC) system stands out as a pivotal usage scenario of 6G. To explore the coordination gains offered by the ISAC technique, this paper introduces a novel communication-assisted sensing (CAS) system. The CAS system can endow users with beyond-line-of-sight sensing capability, wherein the base station with favorable visibility senses device-free targets, simultaneously transmitting the acquired sensory information to users. Within the CAS framework, we characterize the fundamental limits to reveal the achievable distortion between the state of the targets of interest and their reconstruction at the users' end. Finally, within the confines of this theoretical framework, we employ a typical application as an illustrative example to demonstrate the minimization of distortion through dual-functional waveform design, showcasing the potential of CAS in enhancing sensing capabilities.

A near-field wideband communication system is investigated in which a base station (BS) employs an extra-large scale antenna array (ELAA) to serve multiple users in its near-field region. To facilitate near-field multi-user beamforming and mitigate the spatial wideband effect, the BS employs a hybrid beamforming architecture based on true-time delayers (TTDs). In addition to the conventional fully-connected TTD-based hybrid beamforming architecture, a new sub-connected architecture is proposed to improve energy efficiency and reduce hardware requirements. Two wideband beamforming optimization approaches are proposed to maximize spectral efficiency for both architectures. 1) Fully-digital approximation (FDA) approach based on full channel state information (CSI): In this method, the TTD-based hybrid beamformer is optimized by the block-coordinate descent and penalty method to approximate the optimal digital beamformer. This approach ensures convergence to the stationary point of the spectral efficiency maximization problem. 2) Heuristic two-stage (HTS) approach based on partial CSI: In this approach, a piecewise-near-field approximation of near-field channels is first proposed to facilitate the design of TTD-based analog beamformers based on the outcomes of near-field beam training. Subsequently, the low-dimensional digital beamformer is optimized using knowledge of the low-dimensional equivalent channels, resulting in reduced computational complexity and channel estimation complexity. Our numerical results show that 1) the proposed approach effectively eliminates the spatial wideband effect, and 2) the proposed sub-connected architecture is more energy efficient and has fewer hardware constraints on the TTD and system bandwidth compared to the fully-connected architecture.

Sparse code multiple access (SCMA) is a promising technique for enabling massive connectivity and high spectrum efficiency in future machine-type communication networks. However, its performance crucially depends on well-designed multi-dimensional codebooks. In this paper, we propose a novel progressive codebook optimization scheme that can achieve near-optimal performance over downlink fading channels. By examining the pair-wise error probability (PEP), we first derive the symbol error rate (SER) performance of the sparse codebook in downlink channels, which is considered as the design criterion for codebook optimization. Then, the benchmark constellation group at a single resource element is optimized with a sequential quadratic programming approach. Next, we propose a constellation group reconstruction process to assign the sub-constellations in each resource element (RE) progressively. For the current RE, the assignment of the sub-constellations is designed by minimizing the error performance of the product distance of the superimposed codewords in previous REs. The design process involves both permutation and labeling of the sub-constellations in the benchmark constellation group. Simulation results show that the proposed codebooks exhibit significant performance gains over state-of-the-art codebooks in the low signal-to-noise ratio (SNR) region over various downlink fading channels.

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures has revolutionized the approaches to solving complex problems in physics and engineering. However, a persistent challenge faced by mainstream PINNs lies in their handling of discontinuous input data, leading to inaccuracies in predictions. This study addresses these challenges by incorporating the discretized forms of the governing equations into the PINN framework. We propose to combine the power of neural networks with the dynamics imposed by the discretized differential equations. By discretizing the governing equations, the PINN learns to account for the discontinuities and accurately capture the underlying relationships between inputs and outputs, improving the accuracy compared to traditional interpolation techniques. Moreover, by leveraging the power of neural networks, the computational cost associated with numerical simulations is substantially reduced. We evaluate our model on a large-scale dataset for the prediction of pressure and saturation fields demonstrating high accuracies compared to non-physically aware models.

Conventional Reconfigurable intelligent surfaces (RIS) for wireless communications have a local position-dependent (phase-gradient) scattering response on the surface. We consider more general RIS structures, called nonlocal (or redirective) RIS, that are capable of selectively manipulate the impinging waves depending on the incident angle. Redirective RIS have nonlocal wavefront-selective scattering behavior and can be implemented using multilayer arrays such as metalenses. We demonstrate that this more sophisticated type of surfaces has several advantages such as: lower overhead through coodebook-based reconfigurability, decoupled wave manipulations, and higher efficiency in multiuser scenarios via multifunctional operation. Additionally, redirective RIS architectures greatly benefit form the directional nature of wave propagation at high frequencies and can support integrated fronthaul and access (IFA) networks most efficiently. We also discuss the scalability and compactness issues and propose efficient nonlocal RIS architectures such as fractionated lens-based RIS and mirror-backed phase-masks structures that do not require additional control complexity and overhead while still offering better performance than conventional local RIS.

Cooperative molecular communication (MC) is a promising technology for facilitating communication between nanomachines in the Internet of Bio-Nano Things (IoBNT) field. However, the performance of IoBNT is limited by the availability of energy for cooperative MC. This paper presents a novel transmitter design scheme that utilizes molecule movement between reservoirs, creating concentration differences through the consumption of free energy, and encoding information on molecule types. The performance of the transmitter is primarily influenced by energy costs, which directly impact the overall IoBNT system performance. To address this, the paper focuses on optimizing energy allocation in cooperative MC for enhanced transmitter performance. Theoretical analysis is conducted for two transmitters. For scenarios with more than two users, a genetic algorithm is employed in the energy allocation to minimize the total bit error rate (BER). Finally, numerical results show the effectiveness of the proposed energy allocation strategies in the considered cooperative MC system.

An important use case of next-generation wireless systems is device-edge co-inference, where a semantic task is partitioned between a device and an edge server. The device carries out data collection and partial processing of the data, while the remote server completes the given task based on information received from the device. It is often required that processing and communication be run as efficiently as possible at the device, while more computing resources are available at the edge. To address such scenarios, we introduce a new system solution, termed neuromorphic wireless device-edge co-inference. According to it, the device runs sensing, processing, and communication units using neuromorphic hardware, while the server employs conventional radio and computing technologies. The proposed system is designed using a transmitter-centric information-theoretic criterion that targets a reduction of the communication overhead, while retaining the most relevant information for the end-to-end semantic task of interest. Numerical results on standard data sets validate the proposed architecture, and a preliminary testbed realization is reported.

Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. Our study finds that the Bayesian Optimization-Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

Reconfigurable intelligent surface (RIS) is a promising technique to improve the performance of future wireless communication systems at low energy consumption. To reap the potential benefits of RIS-aided beamforming, it is vital to enhance the accuracy of channel estimation. In this paper, we consider an RIS-aided multiuser system with non-ideal reflecting elements, each of which has a phase-dependent reflecting amplitude, and we aim to minimize the mean-squared error (MSE) of the channel estimation by jointly optimizing the training signals at the user equipments (UEs) and the reflection pattern at the RIS. As examples the least squares (LS) and linear minimum MSE (LMMSE) estimators are considered. The considered problems do not admit simple solution mainly due to the complicated constraints pertaining to the non-ideal RIS reflecting elements. As far as the LS criterion is concerned, we tackle this difficulty by first proving the optimality of orthogonal training symbols and then propose a majorization-minimization (MM)-based iterative method to design the reflection pattern, where a semi-closed form solution is obtained in each iteration. As for the LMMSE criterion, we address the joint training and reflection pattern optimization problem with an MM-based alternating algorithm, where a closed-form solution to the training symbols and a semi-closed form solution to the RIS reflecting coefficients are derived, respectively. Furthermore, an acceleration scheme is proposed to improve the convergence rate of the proposed MM algorithms. Finally, simulation results demonstrate the performance advantages of our proposed joint training and reflection pattern designs.