• Proposes a novel hybrid framework combining RGBD-based CNN feature extraction, LSTM temporal modeling, and reinforcement learning for real-time wrinkle detection and correction. • Integrates physics-based mass–spring simulation with adaptive stiffness and damping control to enhance fabric realism under dynamic conditions. • Achieves high classification accuracy of 96.4 % across shallow, medium, and deep wrinkles, with significant gains over 2D models. • Demonstrates robust wrinkle reconstruction under occlusion using Mask R-CNN–based segmentation and synthetic occlusion training. • Validates real-time performance at 30 FPS with low temporal drift (0.0187) and MSE (0.0246), enabling applications in virtual fashion, robotics, and AR/VR environments. This study presents a novel framework for real-time cloth wrinkle detection and optimisation, combining physics-based modelling with LSTM-Reinforcement Learning (LSTM-RL) and advanced computer vision techniques. A curated dataset of 45,876 annotated static garment images was used, featuring wrinkle attributes such as location, depth, width, and geometry. CNNs were employed for feature extraction, enhanced by Mask R-CNN to handle occlusions and RGBD data for depth-aware wrinkle modelling. A mass-spring system simulated fabric dynamics under environmental forces, while LSTM networks predicted the temporal evolution of wrinkles. Reinforcement learning dynamically adjusted fabric parameters, improving adaptability. The proposed RGBD model achieved a wrinkle detection accuracy of 96.4 %, outperforming the 2D model by over 9 %. Key metrics include an MSE of 0.0246, drift of 0.0187, and a reward value of -0.13543, with low policy and value loss confirming the RL agent’s learning stability. These results demonstrate high accuracy, real-time performance, and robustness, with strong implications for virtual fashion, robotics, and AR/VR applications.

This work investigates the time-dependent statistical characteristics (SCs) of age of information (AoI) in V2I periodic-updating. The D/G/1/1 (non-)preemptive discrete-time (slotted) queue model is employed. The entire AoI process is split into a set of slot-specific AoI processes w.r.t. updating period (UP). A Markov multi-dimensional age process w.r.t. UP is used to track the evolution of slot-specific AoI. Accordingly, the time-dependent AoI distribution and expected AoI (EAoI) are derived, forming a framework to study the time-dependent AoI SCs under periodic updating. Based on the AoI SCs, we optimize the decision-making (DM) process at roadside unit to minimize age upon decisions, improving information freshness when conducting DMs. A quasiperiodic DM mechanism is regarded, where one DM slot is probabilistically determined in each UP. The optimal DM probabilities are obtained in closed-form. In the D/Geo/1/1 case, we find that the preemption-induced EAoI gains are identical among slots; for extremely reliable/error-prone channels, conducting DM at the second/middle slot in UP is optimal. Numerical results verify the effectiveness of theoretical analyses and DM process optimization.

The reconfigurable intelligent surface (RIS)-aided cognitive radio (CR) system holds significant promise for enhancing spectrum utilization. However, its practical implementation hinges critically on accurate channel state information (CSI). Obtaining full cascaded CSI in RIS-aided CR systems with the cross interference between multiple cascaded channels is challenging. To fill this gap, we propose the deep learning-based channel acquisition schemes for the users in static scenario and mobile scenario, respectively. In static scenario, we propose a novel deep neural network (DNN)-based channel estimation scheme named dual output parameter estimation (DOPE). This scheme achieves remarkable normalized mean square error (NMSE) performance in CSI estimation while significantly reducing the required pilot overhead. In mobile scenario, we propose a channel prediction scheme with hybrid recurrent neural network (RNN) and Transformer (HRT-CP). This scheme utilizes RNN to extract dynamic and static features of cascaded channels, and introduces Transformer’s powerful parallel processing capability to efficiently predict dynamic features. By combining static and dynamic features appropriately, the HRT-CP scheme has predicted the future cascaded CSI accurately, and mitigated the error accumulation phenomenon effectively. The simulation results under both near-field and far-field channel models demonstrate that our proposed schemes provide significant gains on NMSE performance compared to other benchmarks.

While spatial, temporal, and frequency domains are explored to enhance spectral efficiency (SE) in wireless communications, utilizing the polarization of electromagnetic (EM) waves also contributes to achieving this goal. Unlike conventional reconfigurable intelligent surface (RIS)-aided communications, polarization-transforming RIS (PTRIS) is first applied in this work to assist the line-of-sight (LoS) communication system. We introduce a novel framework for accurately modeling the direct and cascaded channels in the PTRIS-aided LoS communication system. This framework considers the spatial positions of the transmitter and receiver, the radiation patterns, antenna rotations, and the physical propagation mechanisms of EM waves based on antenna theory. The aperture field method is used to model the physical reflection of EM waves by PTRIS. Additionally, we aim to maximize SE by investigating four cases regarding the polarization-transforming capability of the PTRIS. Optimal closed-form solutions are derived for Case 1 and Case 2, while a best-effort approximation-based alternative optimization (BEA-AO) method is proposed for Case 3 to obtain sub-optimal solutions. Case 4 can be solved optimally with the barnch-and-cut algorithm within a reasonable computation time. Numerical results demonstrate that PTRIS can provide a robust and enhanced SE in LoS communications, even with arbitrary antenna rotations, compared to the scenarios without PTRIS.

In reconfigurable intelligent surfaces (RIS)-aided cognitive radio (CR) systems, the estimation of high-dimensional channel state information (CSI) with the interferences for all the cascaded channels between the RIS and any pair of the transceivers is challenging. To solve this problem, we propose a three-stage scheme of the full cascaded channel estimation based on the deep neural network (DNN). At the beginning, the protocol of the two-step pilot transmissions is designed for generating the labeled channel dataset in data preparation stage. Specifically, we propose dual-output parameter estimation (DOPE) architecture to establish and train the DNN model for full cascaded channel estimation simultaneously with a low pilot overhead in model construction and training stage. Notably, our proposed DNNbased DOPE architecture can accomplish the estimation of both the near-field and far-field cascaded channels in the RIS-aided CR system. Besides, the protocol of only one pilot transmission is introduced for online channel estimation in the model deployment stage. The simulation results show that our proposed scheme outperforms the compared benchmark estimation algorithms at the aspects of both the normalized mean square error (NMSE) performance and the cost of the pilot overhead.

This work investigates the time-dependent statistical characteristics of age of information (AoI) in the real-time Internet of Things systems with wireless periodic status updating. The periodic updating system is modeled as a discrete-time D/G/1/1 non-preemptive queue. The entire AoI process w.r.t. slot is split into a set of slot-specific AoI processes w.r.t. updating period. A Markov high-dimensional age process is introduced to track the evolution of the slot-specific AoI. Accordingly, the time-dependent AoI distribution, expected AoI (EAoI), and the time-average AoI are derived, forming a framework to study the time-dependent AoI statistical characteristics under periodic updating. Numerical results verify the effectiveness of theoretical analyses and usefulness of packet retransmission. It is found that the EAoI varies non-monotonously and greatly w.r.t. slot in an updating period; the EAoI variations are distinct for the update transmission times with different distributions; and the EAoI gains of channel enhancement differ greatly among slots.

This work studies the average Age of Information (AoI) of a remote monitoring setup in which a multi-sensor system observes independent sources and updates the status to a common monitor using orthogonal channels. Considering the limited buffer size at the sensors, we first model each sensor as a first-come-first-served M/M/1/1 queue. Leveraging tools from stochastic hybrid systems, we derive the average AoI of a homogeneous single-source multi-sensor system in which all sensors’ arrival and service rates are the same. We then extend the results to the multi-source, multi-sensor system. For a multi-source dual-sensor system, we present an approximate optimal arrival rate for a given sum arrival rate at a light load. For heterogeneous cases with different arrival and service rates at sensors, the average AoI is derived for the single-source dual-sensor and more general multi-source systems. Our analysis shows that the average AoI decreases by 16.44% and 21.44% for the dual-sensor and three-sensor systems, respectively, compared to the single-sensor system when the service rate and the total arrival rate of the sensors are normalized. Numerical results confirm that the average AoI performance of the single-source dual-sensor system outperforms the M/M/2 system at high system load.

This work studies information freshness of a V2I status updating link in IoV. The status updating link is modeled as a multi-source Ber/Geo/1/1 non-preemptive or preemptive queue. We focus on statistical characteristics of the age of information (AoI) and peak AoI (PAoI). To fully track the AoI evolutions under non-preemptive and preemptive policies, Markov three-dimensional age process (3DAP) and two-dimensional age process (2DAP) are respectively introduced. Their first element is the AoI process; The second one stands for if an update of the concerned source is in transmission and its current age; The third element of 3DAP denotes if an update of another source is in transmission. An analytical approach for studying the AoIs and PAoIs in discrete-time multi-source systems is presented. By studying the state transitions, balance equations, and stationary distributions of 3DAP and 2DAP, analytical expressions of the distributions and averages of AoIs and PAoIs under both queueing policies are derived. Moreover, the optimal probabilistic update selection mechanism (PUSM) that maximizes overall freshness is derived in closed-form for the two-source case. Numerical results validate effectiveness of the theoretical analyses and reveal usefulness of the retransmission. It is found that in terms of improving the overall freshness, the PUSM should be designed to make effective update generation probabilities of sources as close as possible.

Combining half-duplex (HD) and full-duplex (FD) is promising in improving the information transmission rate of relay channels. This work proposes a novel two-phase hybrid duplex scheme for Gaussian relay channel where the relay operates in FD mode for a fraction of time and only transmits information for the rest of time. The achievable rate of the proposed hybrid duplex scheme is characterized in detail. Based on the obtained result, a joint time division and power allocation problem is formulated to maximize the achievable rate. In particular, the formulated problem is solved through a two-step optimization method. Firstly, the optimal relay power allocation is obtained for given time division factors. Then, the achievable rate maximization problem is addressed by finding the optimal time division factors. The closed-form expression for the maximal achievable rate is derived for some specific cases. Numerical results show that the proposed two-phase hybrid duplex scheme significantly improves the achievable rate of Gaussian relay channel compared with existing benchmark schemes.

Emerging applications in industrial Internet of things (IIoT) pursue ultra-reliability, low-latency, and high data rate. While majority of the industries are in the remote areas, capability of distant ultra-reliable and low-latency communication (uRLLC) has become one of the key performance indices of IIoT which we need to make a breakthrough. While relaying provides intuitive solution for improving communication distance, the introduction of relay in distant uRLLC intensifies the conflict between reliability and low-latency which further deteriorates the throughput of the relaying-based IIoT. In this work, we adopt full-duplex relaying to enhance the performance of distant uRLLC in IIoT. Specifically, we improve the reliability at MAC layer and throughput at physical layer in full-duplex relaying-based IIoTs, through jointly optimizing the coding rate and the power allocation between the source and relay node. In particular, a low-complexity algorithm is developed to find the exact optimal coding rate and relay power under total system power constraint. Extensive numerical results validate the conclusion that the reliability and throughput of distant uRLLC in IIoT are enhanced through full-duplex relaying, power allocation, and rate adaptation.

In practical status updating systems, most decisions made at monitors are based on diverse data streams. Due to the cask effect, it can be cognised that the effectiveness of decisions is often constrained by the stalest one, i.e., the straggler among all the streams. This work studies the statistical characteristics of age of the stalest information (AoSI) which describes the timeliness of the stalest stream. The AoSI is defined as the time elapsed since the latest successfully received update of the currently stalest stream among all different streams at the monitor was generated. Peak age of the stalest information (PAoSI) is also studied for evaluating the worst cases, i.e., the peaks of AoSI process. We develop an analytical approach to derive the AoSI and PAoSI based on the per-stream age of information (AoI) and peak age of information (PAoI), for the multi-stream single-monitor system with separate status updating. In particular, to comprehensively characterize the timeliness of the stalest stream, the distributions of AoSI and PAoSI are derived in closed-form for the general multi-stream system. Moreover, we concisely derive the explicit expressions of the distributions and averages of AoSI and PAoSI, upon a typical two-stream case with the classical automatic repeat-request protocol. Finally, the accuracy of the theoretical analyses is validated by the numerical results. Appropriateness and advantages of the AoSI (PAoSI) are elaborated by comparing with the maximum average AoI (PAoI), i.e., the maximal one among the averages of all the per-stream AoIs (PAoIs).

Timely status updating is the premise of emerging interaction-based applications in the Internet of Things (IoT). Using redundant devices to update the status of interest is a promising method to improve the timeliness of information. However, parallel status updating leads to out-of-order arrivals at the monitor, significantly challenging timeliness analysis. This work studies the Age of Information (AoI) of a multi-queue status update system where multiple devices monitor the same physical process. Specifically, two systems are considered: theBasic System, which only has type-1 devices that are ad hoc devices located close to the source, and theHybrid System, which contains additional type-2 devices that are infrastructure-based devices located in fixed points compared to theBasic System. Using the Stochastic Hybrid Systems (SHS) framework, a mathematical model that combines discrete and continuous dynamics, we derive the expressions of the average AoI of the considered two systems in closed form. Numerical results verify the accuracy of the analysis. It is shown that when the number and parameters of the type-1 devices/type-2 devices are fixed, the logarithm of average AoI will linearly decrease with the logarithm of the total arrival rate of type-2 devices or that of the number of type-1 devices under specific condition. It has also been demonstrated that the proposed systems can significantly outperform the FCFS M/M/Nstatus update system.

Considering the spectrum sharing system (SSS) coexisting with multiple primary networks, we have employed a well-designed reconfigurable intelligent surface (RIS) to control the radio environments of wireless channels and relieve the scarcity of the spectrum resource. Specifically, the enhancement of the spectral efficiency of the secondary user in the considered SSS is decomposed into two subproblems which are a second-order cone programming (SOCP) and a fractional programming of the convex quadratic form (CQFP), respectively, to optimize alternatively the beamforming vector at the secondary access point (S-AP) and the reflecting coefficients at the RIS. The SOCP subproblem is shown as a concave problem, which can be solved optimally using standard convex optimization tools. The CQFP subproblem can be solved by a low-complexity method of gradient-based linearization with domain (GLD), providing a sub-optimal solution for fast deployment. Taking the discrete phase control at the RIS into account, a nearest point searching with penalty (NPSP) method is also developed, realizing the discretization of the phase shifts of the RIS in practice. The simulation results indicate that both GLD and NPSP can achieve an excellent performance.

Abundant real-time applications over Internet of Things (IoT) have imperative demands on timely information. Compared to average Age of Information (AoI), distribution of AoI characterizes the timeliness in more details. This article studies the timeliness of an IoT-based multisource status update system. By modeling the system as a multisource M/G/1/1 bufferless preemptive queue, general formulas of violation probabilities and probability density functions (p.d.f.s) of AoI and PAoI are derived based on a time-domain approach. For the case with exponentially distributed service time, the violation probabilities and p.d.f.s are obtained in closed form. To fully characterize the overall timeliness of the multisource system, the maximal violation probabilities of AoI and PAoI are proposed. To improve the overall timeliness under the resource constraint of IoT device, the arrival rate allocation is optimized to control the maximal violation probabilities. It is proved that the optimal arrival rates can be found by convex optimization. In particular, we show that the minimum of maximal violation probability of AoI (PAoI) is achieved only if all violation probabilities of AoI (PAoI) are equal. Finally, numerical results verify the theoretical analysis and show the effectiveness of the arrival rate allocation in improving the overall timeliness.

Reconfigurable intelligent surfaces (RISs) have the capability to change the wireless environment smartly Considering the attenuation of subchannels and crowding users involved in the wideband system, we introduce RISs into the multi-user multi-input single-output (MU-MISO) system with orthogonal frequency division multiplexing (OFDM) for performance enhancement. Maximizing the minimum rate of dense users in an MU-MISO-OFDM system assisted by RIS with an approximate practical model is formulated as the joint optimization problem involving subcarrier allocation, transmit precoding (TPC) matrices at the base station, and RIS passive beamforming. A coalition-game subcarrier allocation (CSA) algorithm is proposed to solve space–frequency resource allocation on subcarriers, which reforms the interference topology among dense users. Fractional programming and convex optimization method are used to optimize the TPC matrices and the RIS passive beamforming, which improves the spectral efficiency synthetically across all subchannels in the wideband system. Simulation results indicate that the CSA algorithm provides a significant gain for dense users. Besides, the proposed joint optimization method shows the considerable advantage of the RISs in the MU-MISO-OFDM system.

Age of information (AoI) is proposed to characterize the freshness of information. Since it describes the time elapsed since the information is generated, it can accurately characterize the freshness of the information. Most of the existing studies have focused on the average AoI of systems, but time-sensitive applications such as industrial control systems and sensing networks have strict requirements for information freshness. We consider the scenario of multi-terminal wireless uplink with random packet arrivals and study the system average peak AoI (PAoI) minimization and maximum PAoI minimization problem. First we derive a closed expression of the system average PAoI and sufficient and necessary conditions of the optimal policy, from which an optimal ratio based no butter policy (OR-NB) is developed. We further generalize it to a system design method to make the average PAoI of all terminals satisfy the corresponding hard constraints. In addition, a maximum expected peak AoI (EPAoI) increasing probability minimization policy is proposed to minimize the maximum PAoI, which is proved to be near-optimal.

For timeliness-sensitive applications in Internet of things (IoT) systems, it is critical to efficiently allocate transmission resources such that the freshness of information updates can be improved. This paper focuses on timely status updating in an orthogonal frequency division multiplexing-based IoT systems, in which all devices update status to one data center by sharing available bandwidth. To improve the timeliness of updates, a resource allocation optimization problem is formulated, based on finite blocklength (FBL) transmission and the age of information (AoI) metric. Two suboptimal policies, namely, fixed time slot policy and fixed blocklength policy, along with an iterative optimization algorithm, and an approximate optimal policy are presented for addressing the optimal resource allocation. By comparing the performance of different policies, it is shown that the iterative algorithm and the approximate optimal policy outperforms the other two suboptimal policies, and closely approaches the global optimal resource allocation.

As the bandwidth resource in TV white space (TVWS) is permitted to be used for the secondary users, multiple secondary networks coexisting in the same geographical area can provide multiple services without interfering with the primary service, such as the TV broadcasting. To satisfy the minimum rate requirements and maximise the sum rate of the multiple services, the problem of resource allocation can be modelled as a mixed integer non‐linear programming (MINLP). According to this model, the joint bandwidth and power allocation (JBPA) method is proposed to solve the resource allocation for multiple services. The JBPA method is sub‐optimal, which can approximate the performance of the optimal two‐step exhaustive search (TSES) method very well, especially when the number of services is larger than the number of idle channels. Compared with TSES, the JBPA method decreases the complexity from exponential level to polynomial level. Besides, compared with one channel occupied by single service, the JBPA can serve more services and provide stable performance when the number of services varies dynamically. Compared with the algorithm random bandwidth allocation, the JBPA can approximate the optimal performance provided by TSES better with the time complexity of the same order.

Combined with client pairing on nonorthogonal multiple access (CP-NOMA), carrier sense multiple access/collision avoidance (CSMA/CA) can provide more connectivity for clients in downlink phase and alleviate the low transmission efficiency from rate anomaly problem. Compared with conventional CSMA/CA system, the proposed enhanced CSMA/CA with CP-NOMA can save about half of the time cost to send signaling overhead and provide improvement in the efficiency of data transmission. Similar to saturated throughput, the long-term average rate is defined and used to illustrate the performance of the proposed method. Considering the criterion of the fairness and the received signal to noise ratio (SNR), the selection of client pairing in NOMA could be optimized to maximize the data transmission rate in NOMA. Providing the channel access for more clients, the efficiency of the downlink transmission is enhanced in the proposed scheme. In the application of Internet of Things (IoT), The enabling technology supporting more clients in connectivity really makes a big difference. Besides, the enhanced CSMA/CA with CP-NOMA is compatible with conventional CSMA/CA system.

Compared with Wireless Local Area Networks (WLANs) in the ISM band, smaller path loss of the spectrum in TV White Space (TVWS) provides larger coverage region with the same power budget. More nodes derived from the larger coverage region increase the collision probability, which damages the throughput efficiency of carrier sense multiple access#x002F;collision avoidance (CSMA#x002F;CA) protocol in 802.11af. The scheme of the Channel Access based on Frequency Contention (CAFC) exploits single sub-carrier of Filtered Bank Multi-Carrier (FBMC) to realize frequency contention. CAFC improves the system throughput efficiency by decreasing the collision probability and removing channel idle time. The set of possible frequency contention outcomes can be enlarged to further decrease the collision probability with little cost appended to the system complexity. Compared with conventional CSMA#x002F;CA in 802.11af, the simulation indicates that the CAFC scheme enhances the saturated throughput efficiency significantly. Besides, the CAFC scheme is designed to be compatible with 802.11af, which reduces the application cost in practice.

Under Service Oriented Architecture (SOA), service composition is used to integrate service components together to meet new business needs. In this paper, we propose a novel data-driven method to provide service composition guidance to implement given requirements. Based on the relations between business domain data and service domain data, we generate additional data mediations according to three composition rules. With these data relations and composition rules, we propose a Petri-net based approach to the composition of services. In our approach, all the in/output messages of the service operations are modeled as colored places, and service operations themselves are modeled as transitions with input/output places. We first generate a Service Net (SN) that contains all operations in a given service portfolio, and then use Petri-net decomposition techniques to derive a subnet of SN, and this subnet meets the need of the business requirement. Our work can be seen as an effort to bridge the gap between business and service domains.

In recent years, the interest in bistatic synthetic aperture radar (SAR) has rapidly increased and many bistatic SAR models and processing methods are presented. But some technical problems of bistatic SAR, such as synchronization (in both time and frequency) and the imaging processing of bistatic raw data, have not been resolved sufficiently. To verify bistatic SAR system synchronization plan and imaging processing algorithm, the University of Electric Science and Technology of China (UESTC) developed an Automobile-Based Bistatic SAR system because of its convenience, and carried out a series of experiments. Comparing with airborne monostatic SAR imaging processing, some special problems should be considered. In this paper, we introduce the Automobile-based Bistatic SAR system and discuss the corresponding imaging processing method.

A complete vehicleborne Bistatic Synthetic Aperture Radar (SAR) imaging experiment is presented in this paper. Some new technologies were used to solve synchronization problems. An algorithm named the Glide Window Echo CFAR was used to realize time synchronization and collect the echo. High stable local oscillator was employed to achieve frequency and phase synchronization, and the PRF was adjusted adaptively in the Data Acquisition Device in the receive station. Finally, the Range-Doppler algorithm with range migration correction was using to image the certain scene successfully.

Component based development is gaining increasing popularity for agile system development through reuse of existing asset. To make this approach effective enough to implement, the paradigm of "solution = components + composition logic" should be successfully realized. The current component composition approaches are either not flexible enough, have less visibility of the composition logic or demanding heavy platform and technology dependencies. Abstract Logic Tree is a mechanism of using a task decomposition approach based on a divide-and-conquer strategy to support composition design and execution. In this paper, the design of the Abstract Logic Tree and related methodology, the composition logic modeling capability, and the supporting framework named DynaTree are presented. The travel plan case is used to demonstrate the solution development process through the Abstract Logic Tree method.

Solution design has been more of an art than an engineering discipline. Lots of researchers and practitioners have proposed and exercised different kinds of approaches with varied success. Most of these methods seem to have focused on building new solutions from scratch. However, enterprise solutions today are mostly built on top of an existing IT infrastructure. The notion of SoA is trying to pave a way to integrate heterogeneous components together to meet new business needs. When a new requirement is given to a system developer in the form of business processes, it would be ideal if she/he can make the best of existing services for many reasons. In this paper we propose a data driven approach to provide service composition guidance to implement the given requirement. Based on the relations among business domain data and service domain data, we can generate additional data mediations according to three composition rules. With these data relations and composition rules, we give a formal approach to devise choreography of services from current service portfolio, plus additional data mediation artifacts to realize a given requirement. Our work can be seen as an effort to bridge the gap between business and service domain

In this paper, a manageable Web services hub framework and enabling technologies for e-sourcing are proposed for buyers, suppliers, service providers and trading partners to register business, user and service information as well as to provision and subscribe to services. The proposed framework enables a business to dynamically configure its business processes to integrate with existing Web services provided by other enterprises based on service requirements. Next, a multi-level security mechanism ensuring secure communications in a hub or among hubs is presented. An advanced Web services discovery mechanism is introduced after that for looking up multiple UDDI registries and aggregating results in an efficient manner. A working system of this framework, Managed e-Hub, which provides an infrastructure for enabling next generation e-utilities in a secure and controlled environment, is also presented in this paper. Some further research ideas are given at the end of the paper.

Decreasing slew rates and efforts to reduce the resistance-capacitance (RC) delays of on-chip interconnect through design and technology have resulted in the growing importance of inductance in analyzing interconnect response for timing and noise analysis. In this paper, we consider a practical approach for extracting approximate inductances of on-chip interconnect. This approach, which we call the method of return-limited inductances, is based on performing the inductance modeling of signal lines and power-ground lines independently and on taking advantage of the power and ground distribution of the chip to localize inductive coupling. A set of simple geometry-based matrix decomposition rules guide sparsification in these extractions.