Accurate radio environment map (REM) construction proves critical for efficient wireless spectrum management. Although conventional 2D REMs have demonstrated effectiveness in wireless network optimization, they inherently overlook vertical signal strength variations, which are vital for UAV operations, particularly in urban landscapes with skyscrapers or diverse terrain features. Current estimation approaches, including ground-based crowdsourcing, random sampling, and predetermined trajectory measurements, show limited capability in generating high-fidelity 3D REMs. This study proposes a joint optimization framework for UAV-enabled adaptive 3D radio mapping, integrating 3D REM construction with adaptive aerial sampling. At the heart of the construction module, a dual-branch encoder-decoder architecture fuses multi-scale features from sparse aerial measurements with building structural data, explicitly modeling obstruction effects through offline pre-training and online refinement to enhance generalization. For adaptive sampling, a diffusion-based trajectory planner dynamically optimizes UAV measurement paths by integrating environmental priors (e.g., building layouts), effectively overcoming the sparse-reward limitations inherent in reinforcement learning methods. Experimental validation demonstrates significant performance improvements across all evaluation metrics. Compared to 2D per-layer estimation methods, our 3D estimator achieves 49% superior structural similarity (SSIM) in construction accuracy, while the feature fusion module yields a 37% reduction in mean squared error (MSE). The diffusion-based planner outperforms reinforcement learning approaches by achieving 45% lower MSE and 18% higher SSIM in resultant map quality after 5,000 step iterations.

Over-the-air computation (AirComp) enables swift wireless data aggregation by leveraging the superposition property of multiple-access channels (MAC), making it essential for the seamless integration of communication and computing in future networks. Meanwhile, fluid antenna systems (FAS) offer dynamic spatial degrees of freedom (DoF) by reconfiguring antenna positions, thus enhancing adaptability under varying channel conditions. This paper investigates the integration of FAS into a communication and AirComp coexistence framework. We aim to jointly optimize the transceiver beamforming vectors and the antenna positioning vector (APV) to minimize the computation distortion while ensuring reliable cellular communication performance. To tackle this highly non-convex problem, we develop an efficient joint learning-optimization framework. Specifically, we propose a neural network (NN) framework with a dedicated surrogate loss function design to infer optimal APV based on multi-path channel conditions, while an alternating optimization (AO) method is developed to find a locally optimal solution of transceivers by iteratively optimizing each variables with the others being fixed. Besides, to provide analytical tractability and benchmark insight, the APV design problem is relaxed and transformed into a tractable quadratically constrained quadratic program (QCQP) by successive convex approximation (SCA) as a special case under line-of-sight (LoS) channels, which reveals the performance bounds and convergence properties of the system. Numerical results show that proposed method significantly improves the system performance compared with traditional fixed-position antenna (FPA) as well as various benchmark schemes with remarkable generalization capabilities across diverse channel conditions.

This paper introduces a comprehensive health monitoring and pedestrian localization solution that combines a foot-mounted inertial measurement unit (IMU) with a wrist-worn health monitoring device. The system uses pedestrian dead reckoning (PDR) along with an advanced gait recognition algorithm to deliver continuous 3D localization, achieving an accuracy of less than 1 meter in both indoor and outdoor settings. The wrist-worn sensor integrates electrocardiography (ECG), photoplethysmography (PPG), and an accelerometer to monitor vital signs in real time and detect falls. This integrated approach provides a reliable solution for healthcare monitoring, location tracking, and emergency response applications.

Wearable sensor–based human activity recognition (HAR) is essential for navigation and industrial automation, where real-time data processing is critical. However, the inherent nonlinearity and noise in sensor data make accurate and fast activity detection a challenging task, and traditional feature extraction techniques often struggle to capture the underlying dynamic changes. In this paper, we introduce WavI2I, a novel framework that enhances HAR by first applying the Continuous Wavelet Transform (CWT) to convert inertial sensor signals into time-frequency planes, which are then processed by Convolutional Neural Networks (CNNs). To further optimize feature extraction, we incorporate a nonlinear scale generator, ensuring a balanced focus on both high- and low-frequency components. These innovations strengthen the CNN’s ability to identify critical features, thereby improving recognition accuracy. Experiments on the UCI-HAR dataset confirm that WavI2I surpasses existing methods in terms of accuracy, computational efficiency, and model simplicity.

Pedestrian Dead Reckoning (PDR) technology demonstrates significant application value in smart city location services and IoT terminal positioning due to its signal-independent operation, autonomous navigation capability, and anti-interference advantages. However, existing shoulder-mounted inertial measurement units (IMUs) encounter gait characteristic modeling errors during practical deployment, particularly manifesting as nonlinear error accumulation caused by limited step-length prediction accuracy. To address this technical challenge, this study proposes a step-length estimation model based on residual neural networks (ResNet) with limited-sample training. The architecture achieves precise step-length prediction across various motion states through temporal feature extraction and multi-rate motion pattern analysis. Experimental results validated by five independent test sets demonstrate that the system achieves a relative displacement estimation error below 0.6%, with the mean absolute error (MAE) of single-step length prediction consistently remaining under 0.045 meters. Analytical verification confirms that the proposed step-length estimation method significantly enhances the step-length measurement accuracy of shoulder-mounted IMUs, providing an effective technical solution for high-precision indoor positioning of IoT devices.

This paper presents a practical TDOA-based method for UWB anchor localization, aiming to simplify the process of determining anchor positions, reduce costs, and improve efficiency. By utilizing a small number of tag position coordinates and the TDOA information between anchors and tags, and by introducing a weighted least squares approach, this method can quickly and effectively solve for UWB anchor coordinates even without any prior knowledge of their initial positions. Experimental results demonstrate that the proposed method can achieve positioning accuracy within 1 meter, with the rectangular trajectory demonstrating the highest stability and accuracy, as indicated by the lowest RMSE (Root Mean Square Error) and HDOP (Horizontal Dilution of Precision) values. Future research will focus on optimizing the algorithm under complex environmental conditions, integrating data from multiple sensors such as LiDAR or cameras, enhancing real-time performance, and developing user-friendly interfaces. These efforts aim to further enhance the method's robustness and practical applicability. Additionally, comparative experiments in diverse scenarios will be conducted to validate the effectiveness and applicability of the proposed approach.

While smartphone-based fingerprinting techniques have emerged as promising solutions for indoor localization, their efficacy remains constrained by suboptimal fingerprint database quality and algorithmic limitations in 2D coordinate estimation. Conventional approaches suffer from laborious data collection processes, constrained accuracy, and diminished reliability over extended periods. To address these challenges, this study proposes a novel attention-enhanced LSTM architecture synergistically integrating heterogeneous sensor data (WiFi, barometric pressure, and magnetometer) to achieve simultaneous planar localization and multi-floor identification. A dedicated foot-mounted inertial measurement system is introduced to streamline fingerprint database construction by enabling efficient sparse data acquisition through collaborative smartphone-device interactions. The developed LSTM-Attention framework demonstrates superior performance in initial position matching precision, accelerated model convergence, and enhanced trajectory consistency through adaptive feature weighting. Comprehensive evaluations across multi-story academic and office environments reveal pedestrian localization accuracy within 1.5 meters (horizontal) and floor discrimination success rates exceeding 95%, thereby advancing the state-of-the-art in smartphone-based 3D indoor positioning systems.

Over-the-air computation (AirComp) leverages the inherent superposition property of wireless multiple-access channels to enable direct signal aggregation from massive users. However, unfavorable channel conditions can severely degrade the computed mean square error (CMSE). To address this limitation, we introduce a reconfigurable intelligent surface (RIS) into the AirComp system. Unlike prior works that assume full signal reflection by each RIS element (RE) regardless of its phase shift, we adopt a practical model accounting for the coupling between the amplitude and phase of each RE. Based on this model, we formulate an optimization problem to minimize the CMSE by jointly optimizing transceiver design and the RIS reflection matrix. To tackle this highly nonconvex problem, we propose a dual-loop optimization framework, where the outer loop employs the genetic algorithm to obtain a near-optimal RIS reflection matrix and the inner loop uses an alternating optimization approach for transceiver design. Simulation results demonstrate that the proposed dual-loop algorithm outperforms baseline methods in reducing the CMSE.

Substations are critical infrastructures in modern power systems, requiring accurate and reliable personnel positioning to ensure operational safety and inspection efficiency. Pedestrian dead reckoning (PDR) technology has emerged as a preferred solution for real-time seamless positioning due to its autonomous, anti-jamming and passive characteristics. However, in practical applications, the PDR algorithm faces challenges such as the inability to provide absolute positioning due to unknown starting points and cumulative errors over time. To address these challenges, this paper proposes a head-mounted pedestrian positioning system (HPPS) integrating fisheye camera/real-time kinematic (RTK)/PDR based on factor graph optimization (FGO). First, a skyward-facing fisheye camera identifies non-line-of-sight (NLOS) signals caused by architectural obstructions, improving the absolute positioning accuracy of RTK. Next, an adaptive pedestrian gait detection and step length estimation algorithm based on head-mounted inertial measurement units (IMU) is developed to enhance PDR robustness. Finally, the FGO framework integrates the inputs of the fisheye camera, RTK, and PDR to achieve seamless indoor-outdoor positioning. Experimental results demonstrate that the proposed system achieves horizontal root mean square error (RMSE) values of less than 0.42 m and 0.35 m in two distinct outdoor substation environments and less than 1.36 m in indoor-outdoor scenarios. This work highlights the integration of precise positioning technologies within the Internet of Things (IoT) framework, advancing smart grid applications and enabling effective location tracking in complex environments.

Over-the-air computation (AirComp) is emerging as a promising technology for wireless data aggregation. However, its performance is hampered by users with poor channel conditions. To mitigate such a performance bottleneck, this paper introduces an active reconfigurable intelligence surface (RIS) into the AirComp system. We begin by exploring the ideal active RIS model and propose a joint optimization of the transceiver and RIS configuration to minimize the mean squared error (MSE) between the target and estimated function values. To manage the resulting tri-convex optimization problem, we employ the alternating optimization (AO) framework to decompose it into three convex subproblems, each of which can be solved optimally. We then investigate two specific cases and analyze their respective asymptotic performance to reveal the superiority of the active RIS in mitigating the MSE relative to its passive counterpart. Lastly, we adapt our transceiver and RIS configuration optimization approach to account for the self-interference of the active RIS. To handle the resulting highly non-convex problem, we further develop a two-layer AO framework. Simulation results confirm the superiority of the active RIS in enhancing AirComp performance compared to its passive counterpart.

In this paper, we study beamforming design for multi-user MIMO cognitive radio systems, where a secondary base station transmits multiple data streams to multiple secondary users while imposing interference on primary users. We focus on the weighted sum rate (WSR) maximization problem with the sum power constraint (SPC) and the interference constraints (ICs) by optimizing the beamforming matrices. Firstly, through an analysis of the generalized utility optimization problem, we prove that the WSR maximization problem with a single quadratic constraint can be simplified to an unconstrained WSR maximization problem with adaptive covariance matrices, which can be further solved by the weighted minimal mean square error (WMMSE) method with much lower complexity. Then, we propose the modified subgradient method (MSM)-reduced (R)-WMMSE algorithm for the general scenario and the null-space projection (NSP)-R-WMMSE algorithm for the special scenario with zero ICs. Finally, theoretical and numerical results show superior performances of the proposed algorithms compared to benchmark schemes in terms of computational complexity.

To protect user privacy and improve the transmitting environment of wireless communication, federated learning (FL) and reconfigurable intelligent surface (RIS) are proposed as promising technologies for future communication. Meanwhile, studies have proved that the combination of FL and RIS guarantees better performance for system models. However, the combined model still has problems such as high communication overhead and slow convergence speed. Therefore, in this paper, we proposed a channel quality based device selection and weighted averaging algorithm in a RIS-assisted federated learning model. Simulation results proved that the proposed algorithm outperforms the classic federated averaging (FedAvg) algorithm in convergence speed, test accuracy, and training loss.

With the continuous growth in demand for intelligent services, future 6G networks need to support higher communication efficiency and efficient intelligent connections. Semantic communication technology integrates the meaning of information into data processing and transmission, making it a potential paradigm for 6G. Considering that current research on semantic communication systems mainly focuses on the extraction and encoding of semantic features, with less attention to the impact of channel coding during the communication transmission process on system performance. Therefore, based on the CNN-Transformer (CT) semantic feature extraction and encoding scheme, this paper introduces a polar encoder, designing the end-to-end semantic CT-Polar communication system model frame-work. Through simulation verification, the CT-Polar designed in this paper demonstrated excellent performance in signal recovery on different datasets.

We consider a broadband over-the-air computation empowered model aggregation approach for wireless federated learning (FL) systems and propose to leverage an intelligent reflecting surface (IRS) to combat wireless fading and noise. We first investigate the conventional node-selection based framework, where a few edge nodes are dropped in model aggregation to control the aggregation error. We analyze the performance of this node-selection based framework and derive an upper bound on its performance loss, which is shown to be related to the selected edge nodes. Then, we seek to minimize the mean-squared error (MSE) between the desired global gradient parameters and the actually received ones by optimizing the selected edge nodes, their transmit equalization coefficients, the IRS phase shifts, and the receive factors of the cloud server. By resorting to the matrix lifting technique and difference-of-convex programming, we successfully transform the formulated optimization problem into a convex one and solve it using off-the-shelf solvers. To improve learning performance, we further propose a weight-selection based FL framework. In such a framework, we assign each edge node a proper weight coefficient in model aggregation instead of discarding any of them to reduce the aggregation error, i.e., amplitude alignment of the received local gradient parameters from different edge nodes is not required.We also analyze the performance of this weight-selection based framework and derive an upper bound on its performance loss, followed by minimizing the MSE via optimizing the weight coefficients of the edge nodes, their transmit equalization coefficients, the IRS phase shifts, and the receive factors of the cloud server. Furthermore, we use the MNIST dataset for simulations to evaluate the performance of both node-selection and weight-selection based FL frameworks.

Unmanned aerial vehicles (UAVs) are regarded as powerful assistance for emergency communications due to their disregard for the limitations of the geographic environment. In this paper, we consider a multi-UAV-assisted wireless emergency communication system, where UAVs are applied as aerial base stations to serve terrestrial device-to-device users (DUs). Our goal is to maximize the UAVs' energy efficiency (EE) through the user grouping strategy with a joint optimization scheme regarding UAVs' trajectories and transmit power. To deal with the resultant mix-integer non-linear programming problem, we divide the optimization process into two stages. In the first stage, we discretize the trajectory into a set of stop points (SPs). Then, the grouping of DUs is achieved by pre-planning the location and optimization range of SPs. In the second stage, with the determined DU grouping strategy, we apply Dinkelbach method and successive convex approximation to convert the original problem into a solvable convex optimization problem. Finally, simulation results verify the effectiveness of our proposed algorithm, which has better performance compared with benchmark schemes in the low user-density region.

In this paper, we investigate the communication designs of over-the-air computation (AirComp) empowered federated learning (FL) systems considering uplink model aggregation and downlink model dissemination jointly. We first derive an upper bound on the expected difference between the training loss and the optimal loss, which reveals that optimizing the FL performance is equivalent to minimizing the distortion in the received global gradient vector at each edge node. As such, we jointly optimize each edge node transmit and receive equalization coefficients along with the edge server forwarding matrix to minimize the maximum gradient distortion across all edge nodes. We further utilize the MNIST dataset to evaluate the performance of the considered FL system in the context of the handwritten digit recognition task. Experiment results show that deploying multiple antennas at the edge server significantly reduces the distortion in the received global gradient vector, leading to a notable improvement in recognition accuracy compared to the single antenna case.

This paper investigates the resource allocation and computation offloading problem for multi-access edge computing (MEC) systems, where multiple mobile users (MUs) equipped with multiple antennas access the base station in a non-orthogonal multiple access manner. We jointly optimize the offloading ratio, computational frequency and transmit precoding matrix of each MU to minimize the total energy consumption of all MUs while satisfying the latency constraints. The problem is formulated as a non-convex optimization problem and a two-layer iterative method is proposed to solve the problem efficiently with low complexity. Specifically, we first decompose the original problem into several subproblems, and then sequentially solve these subproblems in an alternative fashion. Furthermore, we also discuss the optimal decoding order of MUs under two different scenarios. Firstly, when the MUs’ channel conditions are similar, by deriving closed-form expressions for energy consumptions of all MUs, we prove that the optimal decoding order is only determined by the latency requirements. On the other hand, when the MUs’ channel conditions are different, we show that the optimal decoding order is determined by both the channel conditions and the latency requirements. As such, we propose a metric aiming to balance the effects of channel conditions and latency requirements on the MUs’ decoding order. Simulation results validate the convergence of the proposed method and demonstrate its superiority over benchmark algorithms.

The combination of cell-free massive multiple-input multiple-output (CF-mMIMO) and reconfigurable intelligent surface (RIS) is envisioned as a promising paradigm to improve network capacity and enhance coverage capability. However, to reap full benefits of RIS-aided CF-mMIMO, the main challenge is to efficiently design cooperative beamforming (CBF) at base stations (BSs), RISs, and users. Firstly, we investigate the fractional programing to convert the weighted sum-rate (WSR) maximization problem into a tractable optimization problem. Then, the alternating optimization framework is employed to decompose the transformed problem into a sequence of subproblems, i.e., hybrid BF (HBF) at BSs, passive BF at RISs, and combining at users. In particular, the alternating direction method of multipliers algorithm is utilized to solve the HBF subproblem at BSs. Concretely, the analog BF design with unit-modulus constraints is solved by the manifold optimization (MO) while we obtain a closed-form solution to the digital BF design that is essentially a convex least-square problem. Additionally, the passive BF at RISs and the analog combining at users are designed by primal-dual subgradient and MO methods. Moreover, considering heavy communication costs in conventional CF-mMIMO systems, we propose a partially-connected CF-mMIMO (P-CF-mMIMO) framework to decrease the number of connections among BSs and users. To better compromise WSR performance and network costs, we formulate the BS selection problem in the P-CF-mMIMO system as a binary integer quadratic programming (BIQP) problem, and develop a relaxed linear approximation algorithm to handle this BIQP problem. Finally, numerical results demonstrate superiorities of our proposed algorithms over baseline counterparts.

We consider a broadband over-the-air computation empowered model aggregation scheme for federated learning (FL) in Industrial Internet of Things systems. Due to fading and communication noise, the received global gradient parameters inevitably become inaccurate, leading to a notable decrease of the learning performance. Instead of discarding any edge nodes to reduce the aggregation error, we propose to assign each of them a proper weight coefficient in the model aggregation procedures, i.e., amplitude alignment of the received local gradient parameters from different edge nodes is not required in this paper. We derive an upper bound on the performance loss of the proposed FL scheme, which is shown to be related to the weight coefficients of edge nodes and the mean-squared error (MSE) between the desired global gradient parameters and the actually received ones. Then, we derive a closed-form expression for MSE and use it as the objective function to formulate an optimization problem with respect to the edge nodes’ transmit equalization coefficients, their weight coefficients, and the receive scalars of the cloud server. We transform the formulated optimization problem into a convex one and solve it optimally using CVX. Last, we leverage the popular MNIST dataset and conduct experiments to evaluate the prediction accuracy of the proposed FL scheme. Simulation results demonstrate its superior performances.

In this paper, we develop an efficient training beam sequence design approach for millimeter wave MISO tracking systems. We impose a discrete state Markov process assumption on the evolution of the angle of departure and introduce the maximum a posteriori criterion to track it in each beam training period. Since it is infeasible to derive an explicit expression for the resultant tracking error probability, we turn to its upper bound, which possesses a closed-form expression and is therefore leveraged as the objective function to optimize the training beam sequence. Considering the complicated objective function and the unit modulus constraints imposed by analog phase shifters, we resort to the particle swarm algorithm to solve the formulated optimization problem. Numerical results validate the superiority of the proposed training beam sequence design approach.

To leverage massive distributed data and computation resources, machine learning in the network edge is considered to be a promising technique, especially for large-scale model training. Federated learning (FL), as a paradigm of collaborative learning techniques, has obtained increasing research attention with the benefits of communication efficiency and improved data privacy. Due to the lossy communication channels and limited communication resources (e.g., bandwidth and power), it is of interest to investigate fast responding and accurate FL schemes over wireless systems. Hence, we investigate the problem of jointly optimized communication efficiency and resources for FL over wireless Internet of Things (IoT) networks. To reduce complexity, we divide the overall optimization problem into two subproblems, i.e., the client scheduling problem and the resource allocation problem. To reduce the communication costs for FL in wireless IoT networks, a new client scheduling policy is proposed by reusing stale local model parameters. To maximize successful information exchange over networks, a Lagrange multiplier method is first leveraged by decoupling variables, including power variables, bandwidth variables, and transmission indicators. Then, a linear-search-based power and bandwidth allocation method is developed. Given appropriate hyperparameters, we show that the proposed communication-efficient FL (CEFL) framework converges at a strong linear rate. Through extensive experiments, it is revealed that the proposed CEFL framework substantially boosts both the communication efficiency and learning performance of both training loss and test accuracy for FL over wireless IoT networks compared to a basic FL approach with uniform resource allocation.

In this paper, we consider a millimeter wave multiple-input single-output tracking system, where the time-varying angle of departure (AoD) is assumed to change following a discrete state Markov process. Depending on whether the associated AoD transition function is available or not, we propose two different training beam sequence design approaches. Specifically, in the case when the AoD transition function is available, we leverage the maximum a posteriori criterion to estimate the updated AoD in each beam tracking period. Since it is infeasible to derive an explicit expression for the resultant estimation error rate, we turn to its upper bound, which possesses a closed-form expression and is therefore used as the objective function to optimize the training beam sequence. Considering the complicated objective function and the unit modulus constraints imposed by the analog phase shifters, we resort to a particle swarm algorithm to solve the formulated optimization problem. In the case when the AoD transition function is unavailable, we turn to the maximum likelihood criterion for AoD estimation. To cope with the unknown AoD transition function, we reformulate the beam tracking problem as a partially observable Markov decision process problem and develop an actor-critic reinforcement learning framework to obtain an efficient training beam sequence design. Numerical results demonstrate superiorities of the proposed training beam sequence design approaches for both two cases.

In this paper, a novel training beam sequence design for multiuser millimeter wave tracking systems is proposed. For each receiver, a single-path channel model is firstly investigated, where we introduce a maximum a posteriori (MAP) criterion to estimate the time-varying angle of departure (AoD), followed by an extended Kalman filter to update the stale complex path gain. We then employ training beam sequence design to minimize the estimated AoD’s average mean squared error (AMSE), which however has no explicit expression. We firstly derive a closed-form upper bound for the AMSE and then simplify this upper bound into a tractable form, based on which a nonlinear optimization problem (NLP) is formulated. By solving this NLP optimally using its corresponding Karush-Kuhn-Tucker conditions, we obtain an efficient training beam sequence. The proposed MAP criterion and its associated training beam sequence design are further extended to multi-path scenarios, where a joint estimation of the multiple paths is firstly discussed, followed by a sequential estimation as a low-complexity alternative. Numerical results demonstrate the superiority of our proposed scheme over the existing benchmark methods, especially in the case when the receivers’ channels change rapidly.

In this paper, we propose a fast beam tracking strategy for mobile millimeter-wave systems, where the temporal variations of the angle of departure (AoD) are considered and modeled as a discrete Markov process. In contrast to most existing works that rely on the slow-fading assumption, we consider a more practical scenario in which the AoD can vary rapidly due to blockage and other environmental obstructions. In this case, the use of narrow training beams becomes inefficient, and therefore we propose to employ multiple radio-frequency chains generating wide beams to reduce the training time. By optimizing the selected training beams, we aim to minimize the average tracking error probability (ATEP). However, since the exact expression for ATEP is difficult to obtain, we derive its upper bound in a closed form, and aim to minimize this upper bound instead. The associated training beam sequence design problem is transformed into the construction of a bipartite graph that does not contain cycles of length 4, which is implemented with the progressive edge-growth algorithm. Numerical results demonstrate significant gains of the proposed beam tracking strategy over the existing benchmark methods.

In this paper, we propose a codebook-based beam tracking strategy for mobile millimeter-wave (mmWave) systems, where the temporal variation of the angle of departure (AoD) is considered. A closed-form upper bound of the average tracking error probability (ATEP) is derived and further optimized. We first consider a slow-varying scenario where narrow training beams implemented by single radio-frequency (RF) chain are employed. We show that the ATEP can be reduced by optimizing the power allocation strategy over these training beams, which is formulated and transformed into a second-order cone programming. The fast-varying scenario is further considered where the use of narrow training beams becomes inefficient due to the rapid variations of AoD. In order to reduce the training time, multiple RF chains generating wide beams are employed to track the AoD's variations, and the associated beam pattern design problem is shown to be a 0 - 1 nonlinear optimization problem (NLP). A sequential quadratic programming method is used to solve this binary NLP. To reduce the complexity, a progressive edge-growth algorithm is further introduced by associating the binary NLP with a bipartite graph. Numerical results demonstrate significant gains of the proposed beam tracking strategy over existing benchmarks for both scenarios.

In this paper, we consider the design of training beam sequence for sparse millimeter wave (mmWave) multiple-input multiple-output (MIMO) tracking systems. We use Markov random walks to model the temporal variations of the beam steering angle of arrival (AoA) and angle of departure (AoD), respectively. By exploiting the MIMO virtual channel representation, the AoA/AoD tracking problem is equivalent to choosing a set of directional training beams to find the nonzero elements in a two-dimensional virtual channel matrix. Furthermore, in contrast to existing work that used each transmitting-receiving beam pair once only, we consider a more general case such that each beam pair might be adopted more than once in the tracking procedure. As the number of repetitions of each transmitting-receiving beam pair can only be integer, the training beam sequence design problem is then formulated as an integer nonlinear programming (INLP) problem. To resolve the formulated INLP problem, we derive a tractable lower bound of the successful tracking probability and then decompose it into a set of convex INLP subproblems, which are solved by implementing an iterative branch-and-bound (BB) method. Numerical results show that our proposed iterative BB algorithm significantly outperforms the benchmark schemes and achieves near-optimal tracking performance.