Orthogonal delay-Doppler division multiplexing (ODDM) modulation has recently been regarded as a promising technology to provide reliable communications in high-mobility situations. Accurate and low-complexity channel estimation is one of the most critical challenges for massive multiple input multiple output (MIMO) ODDM systems, mainly due to the extremely large antenna arrays and high-mobility environments. To overcome these challenges, this paper addresses the issue of channel estimation in downlink massive MIMO-ODDM systems and proposes a low-complexity algorithm based on memory approximate message passing (MAMP) to estimate the channel state information (CSI). Specifically, we first establish the effective channel model of the massive MIMO-ODDM systems, where the magnitudes of the elements in the equivalent channel vector follow a Bernoulli-Gaussian distribution. Further, as the number of antennas grows, the elements in the equivalent coefficient matrix tend to become completely random. Leveraging these characteristics, we utilize the MAMP method to determine the gains, delays, and Doppler effects of the multi-path channel, while the channel angles are estimated through the discrete Fourier transform method. Finally, numerical results show that the proposed channel estimation algorithm approaches the Bayesian optimal results when the number of antennas tends to infinity and improves the channel estimation accuracy by about 30% compared with the existing algorithms in terms of the normalized mean square error.

With the development of communication technology, the Internet of Vehicles (IoV) is becoming increasingly important, enabling vehicle-to-everything communication for real-time information exchange and processing, thereby significantly enhancing traffic efficiency and safety. In this article, we consider a joint beamforming design problem in IoV, where the objective is to minimize transmission power, computation rate, and communication rate within the integrated sensing, communication, and computation (ISCC) framework. Moreover, reconfigurable intelligent surfaces (RISs) can provide additional spatial degrees of freedom to enhance the performance of ISCC systems in IoV within limited spectrum, energy resources, and complex interference management. To address the joint beamforming design problem, we present a cooperative beamforming algorithm called weight performance optimization (WPO), which explores three single-objective optimization problems in sensing, computation, and communication within the IoV context, using alternating optimization (AO) to simplify and solve these foundational elements of the WPO framework within limited resources and vehicle mobility, enhancing resource distribution while maintaining a balance between power efficiency and system performance. Numerical results demonstrate the efficiency and potential advantages of our proposed algorithms. Specifically, the results show that the sensing error of the WPO algorithm is reduced by up to 92.2% compared to existing popular algorithms, while the computation rate and communication rate are increased by more than 29.5% and 23.9%, respectively.

Orthogonal delay-Doppler division multiplexing (ODDM) modulation has recently been considered a promising technology for enhancing communication system performance in high-mobility scenarios. Accurate and low-complexity channel estimation is one of the most significant challenges for massive multiple-input multiple-output (MIMO) ODDM systems, mainly due to the massive antenna arrays and high-mobility environments. In this paper, we focus on the downlink massive MIMO-ODDM communication systems, and propose a two-stage low-complexity channel estimation algorithm. Specifically, we first derive the effective channel model of the massive MIMO-ODDM systems, where the elements of the channel matrix do not follow a Bernoulli-Gaussian distribution, but their magnitudes do. Utilizing this characteristic, we employ the memory approximate message passing method to estimate the gains, delay, and Doppler of the multi-path channel, while the angles of the channel are estimated using the discrete Fourier transform method, achieving low-complexity Bayes-optimal results. Finally, numerical results demonstrate that the proposed algorithm can achieve improved estimation results, surpassing existing algorithms by approximately 2 dB.

Data collection and processing timely is crucial for mobile crowd integrated sensing, communication, and computation (ISCC) systems with various applications such as smart home and connected cars, which requires numerous integrated sensing and communication (ISAC) devices to sense the targets and offload the data to the base station (BS) for further processing. However, as the number of ISAC devices grows, there exists intensive interactions among ISAC devices in the processes of data collection and processing since they share the common network resources. In this paper, we consider the environment sensing problem in the large-scale mobile crowd ISCC systems and propose an efficient waveform precoding design algorithm based on the mean field game (MFG). Specifically, to handle the complex interactions among large-scale ISAC devices, we first utilize the MFG method to transform the influence from other ISAC devices into the mean field term and derive the Fokker-Planck-Kolmogorov equation, which models the evolution of the system state. Then, we derive the cost function based on the mean field term and reformulate the waveform precoding design problem. Next, we utilize the G-prox primal-dual hybrid gradient algorithm to solve the reformulated problem and analyze the computational complexity of the proposed algorithm. Finally, simulation results demonstrate that the proposed algorithm can solve the interactions among large-scale ISAC devices effectively in the ISCC process. In addition, compared with other baselines, the proposed waveform precoding design algorithm has advantages in improving communication performance and reducing cost function.

In large-scale multi-access edge computing (MEC) networks, each device should make the computation offloading decision distributively. In this paper, we target on a delay-optimal computation offloading problem in large-scale MEC systems, where each task has two properties: data size and computation amount. Because the detailed state information of massive devices are huge in large-scale systems, we propose a distributed computation offloading algorithm using the mean field game (MFG). To design the distributed computation offloading algorithm, we first formulate the delay-optimal computation offloading problem as a Markov decision process (MDP) and derive the Hamilton-Jaccobi-Bellman (HJB) equation with the unknown task allocation proportion, where the combined influence from other devices and MEC servers should be estimated. Based on MFG, we obtain the Fokker-Planck-Kolmogorov (FPK) equation to describe the evolution of the system’s collective behavior, with the influence from other devices and MEC servers formulated as the mean field. To solve the large-scale problem with the unknown allocation proportion, we propose a optimal computation offloading algorithm based on the generative adversarial networks (GAN) structure. For the generator, we generate the unknown task allocation proportion due to its non-calculability and insufficient dataset. For the discriminator, we train the value function, and propose a water-filling algorithm to prioritize the task offloading. Finally, the simulation results evaluate the performance of the proposed algorithm and show the performance gain compared to conventional algorithms.

In distributed random access (RA), each device should consider its own information as well as the influence from others, which is difficult to obtain with diverse capabilities of devices. In this paper, we study the RA problem for massive devices with heterogeneous device capabilities in large-scale energy harvesting IoT networks. To deal with the overload issue for massive devices with different capabilities, we propose an optimal RA policy by improving the conventional mean field games (MFG) via exchanging the mean field terms (MFT) among devices. Specifically, we formulate the delay optimal problem as a two-dimensional Markov Decision Process (MDP) problem involving both energy and data states. For distributed deployment of massive RA, we divide the MDP into multiple per-device subproblems, and propose the distributed RA scheme by solving the Hamilton-Jacobi-Bellman (HJB) equation using stochastic learning. Considering the deviation of MFT estimation induced by heterogeneous device capabilities, we design an MFT consensus scheme based on stochastic approximation by information exchange among neighbor devices. For reducing the state space and exchanging the MFT efficiently, we adopt the number of simultaneous access devices instead of the conventional MFT. Furthermore, we prove the convergence of the proposed scheme with coupling MFT and Q-factor. Finally, simulation results demonstrate that the proposed RA scheme outperforms baseline schemes on delay performance, especially in the heavy traffic load regime.

The random access (RA) decision of a device should depend on both its own state and the influence of others for avoiding the overload. However, the heterogeneous characteristics of massive devices lead to the difficult for estimating the influence. In this paper, we consider the RA problem for the large-scale energy harvesting IoT networks. To deal with the overload issue for massive heterogeneous devices, we propose a delay-optimal RA strategy by improving the conventional mean field games (MFG) via exchanging the mean field terms (MFT) among devices. Specifically, we formulate the delay-optimal problem as a two-dimensional Markov decision process (MDP) problem. For distributed deployment of massive random access, we divide the MDP into multiple per-device subproblems. With the given influence of other devices, i.e., MFT, we solve the per-device MDP and propose the optimal RA scheme via Hamilton-Jacobi-Bellman (HJB) equation. To obtain optimal access strategy, we adopt an online learning scheme to estimate the influence from others, where we transform MFT into the number of simultaneous access devices in order to reduce the state space significantly. Considering that the heterogeneous devices will cause the deviation of MFT estimation, we design a consensus scheme for the MFT based on stochastic approximation by information exchange among neighbor devices. Finally, simulation results show that the proposed RA scheme achieves a good delay performance comparing with other baselines.

Energy harvesting technology enables the devices to collect the energy from the surrounding environment. In energy harvesting networks, besides the coupling among different devices, the data transmission depends on the available energy of the devices as well, which leads to a complicated coupling and brings new technical challenges for delay optimization. In this paper, we study delay-optimal random access for large-scale energy harvesting networks. To overcome the challenges, we model a two-dimensional Markov decision process (MDP) with reflections to address the coupling between data and energy, and adopt the mean field game (MFG) theory to address the mutual coupling between devices by utilizing the large-scale property. Specifically, we decompose the optimization problem into two parts. First, to obtain the optimal access policy of each device, we derive the Hamilton-Jacobi-Bellman (HJB) equation which needs the statistical information of other devices. Second, to model the evolution of the state distribution in the system, we derive the Fokker-Planck-Kolmogorov (FPK) equation which needs the access policy of the devices. By solving these two coupled equations iteratively, we obtain the delay-optimal access solution by adopting the Lax-Friedrichs scheme and Lagrange relaxation method. Finally, the numerical results show that the proposed algorithm achieves significant performance gain compared to conventional algorithms.