ABSTRACT Diverse musical styles are crucial ways for human beings to represent their emotions and interact with each other, whereas the essentials of musical signals are a time‐lagged nonlinear dynamical system and their nonlinearity is difficult to analyze by conventional approaches. In this paper, the music is firstly framed depending on the subsections of its structure, then the Lyapunov exponent and the correlation dimension of the music signal are computationally analyzed, which reveals that the internal construction of the music signal is sophisticated with weak chaotic features. By retrieving the local characteristics of the music signal and extrapolating its holistic characteristics, the nonlinearity of the signal rendered by diverse musical styles also has a distinguishable difference. It is observed from the experiments that the maximum Lyapunov exponent of music characterized as “happy” and “relaxing” reaches 0.23, while the range of fluctuations in the correlation dimensions spans from 3.2 to 5.7. Furthermore, a discrepancy of 4.1 is noted in the correlation dimensions of music classified as “loud” and “uplifting,” indicative of the intricate nature of music signals' internal structures and the attenuation of chaotic characteristics. The M5 model exhibits an accuracy of 91.26% for classical music, representing a 2.9% enhancement over conventional methodologies. According to the aforementioned chaotic analysis, the originally designed nonlinearity extracting pattern for diverse music signals in the musical recognizing system demonstrates excellent performance.

As 6G networks actively advance edge intelligence, Federated Learning (FL) emerges as a key technology that enables data sharing while preserving data privacy and fostering collaboration among edge devices for intelligent service learning. However, the multi-dimensional heterogeneous and hierarchical network architecture brings many challenges to FL deployment, including selecting appropriate nodes for model training and designing effective methods for model aggregation. Compared with most studies that focus on solving individual problems within 6G, this paper proposes an efficient deployment scheme named hierarchical heterogeneous FL (HHFL), which comprehensively considers various influencing factors. First, the deployment of HHFL over 6G is modeled amid the heterogeneity of communications, computation, and data. An optimization problem is then formulated, aiming to minimize deployment costs in terms of latency and energy consumption. Subsequently, to tackle this optimization challenge, we design an intelligent FL deployment framework, consisting of a hierarchical aggregation deployment (HAD) component for hierarchical FL aggregation structure construction and an adaptive node selection (ANS) component for selecting diverse clients based on multi-dimensional discrepancy criteria. Experimental results demonstrate that our proposed framework not only adapts to various application requirements but also outperforms existing technologies by achieving superior learning performance, reduced latency, and lower energy consumption.

In this paper, we consider cell-free communication systems with several access points (APs) serving terrestrial users (UEs) simultaneously. To enhance the uplink multi-user multiple-input multiple-output communications, we adopt a hybrid-CSI-based two-layer distributed multi-user detection scheme comprising the local minimum mean-squared error (MMSE) detection at APs and the one-shot weighted combining at the central processing unit (CPU). Furthermore, to improve the propagation environment, we introduce multiple reconfigurable intelligent surfaces (RISs) to assist the transmissions from UEs to APs. Aiming to maximize the weighted sum rate, we formulate the weighted sum-MMSE (WMMSE) problem, where the UEs’ beamforming matrices, the CPU’s weighted combining matrix, and the RISs’ phase-shifting matrices are alternately optimized. Considering the limited fronthaul capacity constraint in cell-free networks, we resort to the operator-valued free probability theory to derive the asymptotic alternating optimization (AO) algorithm to solve the WMMSE problem, which only depends on long-term channel statistics and thus reduces the interaction overhead. Numerical results demonstrate that the asymptotic AO algorithm can achieve a high communication rate as well as reduce the interaction overhead.

The recent advances of deep learning in various mobile and Internet-of-Things applications, coupled with the emergence of edge computing, have led to a strong trend of performing deep learning inference on the edge servers located physically close to the end devices. This trend presents the challenge of how to meet the quality-of-service requirements of inference tasks at the resource-constrained network edge, especially under variable or even bursty inference workloads. Solutions to this challenge have not yet been reported in the related literature. In the present paper, we tackle this challenge by means of workload-adaptive inference request scheduling: in different workload states, via adaptive inference request scheduling policies, different models with diverse model sizes can play different roles to maintain high-quality inference services. To implement this idea, we propose a request scheduling framework for general-purpose edge inference serving systems. Theoretically, we prove that, in our framework, the problem of optimizing the inference request scheduling policies can be formulated as a Markov decision process (MDP). To tackle such an MDP, we use reinforcement learning and propose a policy optimization approach. Through extensive experiments, we empirically demonstrate the effectiveness of our framework in the challenging practical case where the MDP is partially observable.

In this paper, we investigate the uplink signal detection in cell-free massive MIMO systems with unmanned aerial vehicles (UAVs) serving as aerial access points (APs). The ground users are equipped with multiple antennas and the ground-to-air propagation channels are subject to correlated Rician fading. To overcome huge signaling overhead in the fully-centralized detection in cell-free systems, we propose a two-layer distributed uplink detection scheme, where the uplink signals are first detected in AP-UAVs by using the minimum mean-squared error (MMSE) detector based on local channel state information (CSI), and then collected and weighted combined at the CPU-UAV to obtain the refined detection. By using the operator-valued free probability theory, the asymptotic expressions of the combining weights are obtained, which only depend on the statistical CSI and show excellent accuracy compared to the exact but intractable expressions. Based on the proposed scheme, we further investigate the impacts of different deployment scenarios on the spectral efficiency (SE). Numerical results show that in urban and dense urban environments, it is more beneficial to deploy more AP-UAVs to increase SE. Nonetheless, in suburban environment, an optimal combination of the number of AP-UAVs and the number of antennas per AP-UAV exists to maximize SE.

In this paper, we investigate the multiple access technique for the aerial networks, where the multi-antenna base stations are carried by unmanned aerial vehicles (UAVs) to serve ground users. The uplink signals are transmitted by the users simultaneously, then detected and recovered by the aerial networks. On one hand, compared to the case that each UAV individually detects the signals of serving users, we aim to improve the quality of the recovered signals by using cooperative techniques that leverage the signals from multiple UAVs. On the other hand, the fully-centralized cooperation requires signaling exchange between UAVs, which incurs huge signaling overhead and latency, and is infeasible for aerial networks. Therefore, we propose a two-stage distributed minimum mean squared error (MMSE) detection with one-shot signal combining. Specifically, the users' signals are first locally detected by each UAV via the MMSE detector, and then weighted combined at the central UAV in a one-shot manner, where the combining weights are designed to minimize the MSE between the combined signals and the original signals. When only imperfect channel state information is locally available at each UAV, by using the random matrix theory, these combining weights are shown to depend on the long-term channel statistics and thus, greatly reduce the interaction overhead and latency. Numerical results show that the proposed scheme outperforms the non-cooperative detection in terms of the achievable spectral efficiency. Meanwhile, with a much smaller interaction overhead, the proposed scheme achieves comparable spectral efficiency as the fully centralized signal detection.

Mobile edge computing (MEC), extending computing services from cloud to edge, is recognized as one of key pillars to facilitate real-time services and tackle backhaul bottleneck. However, it is not economically efficient to attach intensive security appliances to every MEC node to defend application-level DDoS attacks and ensure the availability of services. Thus, we explore the elasticity of security defense among MEC nodes by proposing a COoperative DEfense (CODE) framework for MEC, referred to asCODE4MEC. CODE4MEC aims to adapt to traffic changes by coordinating container-carried defensive resources among cooperative MEC nodes in an automatic way. Towards this aim, we propose four control plane functions to enable a life-cycle management for CODE4MEC, namely, CODE triggering, scheduling, coordination and releasing. However, an effective CODE4MEC requires non-trivial algorithmic schemes, in particular for CODE scheduling and coordination functions. We thus design an online combinatorial auction mechanism for real-time CODE scheduling, and prove a tighter performance bound relative to prior arts. As for CODE coordination, a flow-based traffic and context information coordination scheme is proposed to enable classical defense schemes to work properly and efficiently. Finally, using a combination of real testbed and simulation evaluations, we validate the effectiveness of CODE4MEC.

In the future mobile edge networks, the Internet of things (IoT) applications will be latency-sensitive and computationally intensive. Given the resource limitation of IoT devices, mobile edge computing (MEC) servers are critical to support the efficient processing of IoT tasks. Since MEC servers attached to the ground base stations are generally deployed in fixed locations and vulnerable to physical damage, the unmanned aerial vehicle (UAV) and satellite-assisted MEC framework has been proposed to leverage the flexibility of UAVs and the broad coverage of satellites. However, efficient utilization of the UAV/satellite resources is challenging for the static ground IoT devices because of the dynamic in terms of aerial and space network topology and IoT task arrival rates. To adapt to the changing environment and utilize the interaction among multiple UAVs, we propose a multi-agent deep deterministic policy gradient (MADDPG) framework to jointly optimize the traveling routes of multi-UAVs and the offloading decision of IoT devices. To minimize the processing cost in terms of task processing latency and energy consumption of IoT devices, cooperative UAVs can help find the optimal task offloading location for each IoT device. Simulation results show the proposed algorithm based on MADDPG can averagely decrease 20% of the above processing cost compared with the benchmark approach.

In the emerging Internet-of-Things (IoT) paradigm, the freshness of sensory information plays a crucial role in online data-analyzing and application-level decision-making. As the tailor-made performance metric of information freshness, the age of information (AoI) depends on the data transmission efficiency and data update frequency, which are energy demanding for IoT devices with limited battery capacity. To alleviate the energy constraints of low-power IoT devices, we propose an AoI-oriented unmanned aerial vehicle (UAVs)-enabled wireless power transmission scheme, where UAVs are deployed to wirelessly charge IoT devices. With the harvested energy, the devices will upload their fresh information to UAVs. The proposed system aims for sustainable IoT networks with practical device-specific energy limitation, which has been long neglected by existing AoI optimization works. In addition, to explore the influence of dynamic time-varying channels on AoI, a practical line-of-sight (LoS)/NLoS channel model is established to accurately depict the dynamic channel characteristics and precisely capture the efficiency of both data transmission and energy harvesting. To achieve the optimal system-level AoI under dynamic channel conditions, a novel deep reinforcement learning-based proactive UAV trajectory planning (PUTP) algorithm is proposed to automatically adjust the UAV fight policy according to the channel variations and the trade-off between the energy transmission and data collection. Extensive simulation results demonstrate that the proposed PUPT algorithm can significantly reduce the AoI by approximately 20% to 65% compared to three other existing trajectory planning algorithms.

Mobile edge computing can provision hierarchical cloud resources at the edge, and efficiently reduce the distance that the remote data need to travel towards the end-users. To empower content delivery at the edge and ultimately transform “shorter distance” to “less time”, instead of focusing only on the storage aspects (e.g., allocation of limited media caches) of mobile edge, the radio aspects (e.g., interference models caused by sharing limited RBs) should be jointly considered. We hence propose a novel comprehensive analytical content caching and delivery framework for the cloud enhanced mobile edge with hierarchical radio access points. To investigate the impacts of limited radio resources (e.g., power, spectrum, and time) and storage resources, we propose a joint user scheduling and caching (JSC) scheme to optimize the end to end performance in terms of throughput (i.e., the number of successful content requests). By leveraging the backhaul links among multi-tier access points, the proposed algorithm can tap on the potential of the coded multi-casting scheme, which is designed to reduce the traffic load among the network. Simulation results demonstrate that the JSC algorithm can improve the resource utilization efficiency and provide a significant sum throughput gain.

With the capability of trading accuracy for latency on-the-fly, the technique of adaptive early-exit inference has emerged as a promising line of research to accelerate the deep learning inference. However, studies in this line of research commonly use a group of thresholds to control the accuracy-latency trade-off, where a thorough and general methodology on how to determine these thresholds has not been conducted yet, especially with regard to the common requirements of average inference latency. To address this issue and enable latency-aware adaptive early-exit inference, in the present paper, we approximately formulate the threshold determination problem of finding the accuracy-maximum threshold setting that meets a given average latency requirement, and then propose a threshold determination method to tackle our formulated non-convex problem. Theoretically, we prove that, for certain parameter settings, our method finds an approximate stationary point of the formulated problem. Empirically, on top of various models across multiple datasets (CIFAR-10, CIFAR-100, ImageNet and two time-series datasets), we show that our method can well handle the average latency requirements, and consistently finds good threshold settings in negligible time.

Over the past few decades, many research efforts have been dedicated to qualitatively and quantitatively evaluate resilience in different domains. As compared with research areas in social science and ecology, the concept of resilience in the engineering domain is relatively new. In the engineering domain, studies on resilience mostly focus on civil infrastructure. It is important to extend the concept of resilience to a broad range of engineering applications. The field environments of complex engineering systems vary with different applications. Even with the same component/system applied in different field environments, the ability, time, and resources required by failure detection, diagnosis, and restoration can be different. Hence, it is critical to introduce a new dimension, random field environment (RFE), into the development of the mathematical model for quantifying resilience. This article first introduces a new definition of resilience and then proposes a general RFE-based multidimensional time-dependent resilience model connecting reliability, vulnerability, and recoverability. Besides, we present a specific RFE-based multidimensional time-dependent resilience model by considering the specified functions of the impact of the RFE on system performance and recovery. Furthermore, we extend the proposed resilience model by incorporating multiple failure paths of complex systems. Finally, we apply the proposed resilience model to vehicular edge computing networks to evaluate the vehicular network resilience with the disruptive events on the communication links.

With convenient Internet access and ubiquitous high-quality sensors in end-user devices, a growing number of content consumers are engaging in the content creation process. Meanwhile, mobile edge computing (MEC) can provision distributed computing resources for local data processing. The MEC-enhanced video crowdsourcing application will gather user-generated video contents and collectively distribute them to the viewers of interest. To empower the crowdsourced video streaming at the edge, we investigate how to efficiently transmit data from content generators to the viewers. In particular, for a group of collaborative mobile users willing to share their data with the viewers, the content generation and delivery scheme is designed by considering the cost incurred by the crowdsourcing application. By leveraging the cloud resources available at the wireless base stations, the uploading or downloading server site is chosen for each user. To minimize the system makespan, i.e., the overall data transmission time among the generators and viewers, the user association scheme is also designed to efficiently utilize the diverse wireless radio resources. As compared with traditional centralized/distributed content delivery schemes, the proposed algorithm can improve the cost-effectiveness of distributed radio/cloud resources deployed at the mobile edge.

Mobile devices make up the bulk of clients that stream video content over the internet. Improving one of the most popular services, i.e., mobile video streaming, has the potential to make the most market impact. Video streaming giants like YouTube, Netflix, Hulu, and Amazon video aim to provide the best quality service and expand market share. The problem of selecting the best server is critical for ensuring the qualified experience for video streaming on a mobile device. Traditional server selection strategies use proximity as a server selection rule. Improved strategies select servers by considering more factors that also impact the quality of experience (QoE). Currently, reinforcement learning is being used to maximize QoE when selecting servers. This paper seeks to further develop an RL agent that performs better on mobile devices. The result is an RL agent that quickly learns to select servers that offer the best QoE.

In this paper, we propose a novel Adaptive Transmission Strategy to improve energy efficiency (EE) in a wireless point-to-point transmission system with Quality of Service (QoS) requirement, i.e., delay-outage probability considered. The transmitter is scheduled to use the channel that has better coefficients, and is forced into silent state when the channel suffers deep fading. The proposed strategy can be easily implemented by applying two-mode circuitry and is suitable for massive machine type communications (MTC) scenarios. In order to enhance EE, we formulate an EE maximization problem, which has a single optimum under a loose QoS constraint. We also show that the maximization problem can be solved efficiently by a binary search algorithm. Simulations demonstrate that our proposed strategy can obtain significant EE gains, hence confirming our theoretical analysis.

In concert with advances of wireless technologies in facilitating internet connectivity of Internet of Things (IoT) devices, mobile edge computing can provision and distribute computing resources at the cloudlets to efficiently process a high volume of IoT data. Among the IoT applications, multi-party data sharing among IoT devices, wireless access nodes and cloudlets is becoming increasingly critical, not only because the data collected by each single IoT device will often stay unmined, but also because of the security concern. As IoT applications' dependence on the cloud environment grows, the rich resources at cloudlets often become the attack targets, and the IoT data that are stored or processed using the cloud resources will be jeopardized. For the internet of important things, we have investigated how to efficiently and securely share the data among multi-party. In particular, for a group of cooperative IoT devices, by leveraging the cloud resources available at the wireless access points, a secure cache site with fast data uploading rate is chosen for each user. To minimize the overall data downloading time, the multi-party multi-path data delivery scheme is also designed such that each user can efficiently retrieve the data belonging to other parties.

To facilitate wireless transmission of multimedia content to mobile users, we propose a content caching and distribution framework for smart grid enabled OFDM networks, where each popular multimedia file is coded and distributively stored in multiple energy harvesting enabled serving nodes (SNs), and the green energy distributively harvested by SNs can be shared with each other through the smart grid. The distributive caching, green energy sharing, and the on-grid energy backup have improved the reliability and performance of the wireless multimedia downloading process. To minimize the total on-grid power consumption of the whole network, while guaranteeing that each user can retrieve the whole content, the user association scheme is jointly designed with consideration of resource allocation, including subchannel assignment, power allocation, and power flow among nodes. Simulation results demonstrate that bringing content, green energy, and SN closer to the end user can notably reduce the on-grid energy consumption.

With the development of green energy technologies, base stations (BSs) can be readily powered by green energy in order to reduce the on-grid power consumption, and subsequently reduce the carbon footprints. As smart grid advances, power trading among distributed power generators and energy consumers will be enabled. In this paper, we investigate the optimization of smart grid-enabled mobile networks, in which green energy is generated in individual BSs and can be shared among the BSs. In order to minimize the on-grid power consumption of this network, we propose to jointly optimize the BS operation and the power distribution. The joint BS operation and power distribution optimization (BPO) problem is challenging due to the complex coupling of the optimization of mobile networks and that of the power grid. We propose an approximate solution that decomposes the BPO problem into two subproblems and solves the BPO by addressing these subproblems. The simulation results show that by jointly optimizing the BS operation and the power distribution, the network achieves about 18% on-grid power savings.

To facilitate content delivery to mobile users, we propose a content caching and distribution framework for the heterogeneous OFDM networks, where a library of files available at the macro base station (MBS) can be distributively cached in multiple serving nodes (SNs). SNs are capable of both receiving unstored files from MBS and transmitting files to the associated users. For a given group of file downloading requests, the user scheduling scheme is jointly designed with the content caching scheme so that the number of served users is maximized for a given amount of spectrum and time. First, the corresponding downlink throughput maximization problem is shown to be NP-hard. Then, for the system with one MBS and one SN, the design of the joint user scheduling and caching scheme is transformed into a binary linear programming problem. For the system with one MBS and two SNs, the joint scheduling and caching (JSC) algorithm has been proposed to tap on the potential of the coded multicasting scheme between MBS and SNs. The proposed algorithm can be extended to networks with arbitrary number of SNs. Simulation results demonstrate that the JSC algorithm provides a significant sum throughput gain.

Energy harvesting (EH) enabled relaying has attracted lots of interests recently, as the network energy consumption can be reduced and the coverage range can be extended simultaneously. In most existing literatures, the Harvest-Store-Use (HSU) model is utilized to describe the energy flow behavior of the EH system. However, the half-duplex (HD) constraint of HSU that harvested energy can only be used for powering load after being temporally stored in energy storage unit may reduce the effective transmission time. Thus, we first model the full-duplex (FD) energy flow behavior of the EH system where harvested energy can be tuned to power load and being stored simultaneously, and then prove the FD model is equivalent to the HSU model when time interval is small enough. With consideration of some key physical variabilities, e.g., the wireless channel and the amount of harvested energy, and the energy consumption difference between FD and HD relaying protocols, we further model the transmission optimization problem to improve the utilization of harvested energy by optimizing the short-term throughput. Finally, to numerically obtain the optimized short-term throughput, we propose the joint power adaption, relay selection and transmission protocol switching algorithm. Results show that the performance of the proposed algorithm outperforms that of fixed relaying algorithms, e.g., the short-term throughput of the proposed algorithm is improved by about 40% comparing with fixed HD relaying algorithm, with 20 user equipments, and loop interference power and EH rate equal to 23 dB and 120 J/s, respectively.

To advance green communications, we propose an orthogonal frequency division multiplexing (OFDM) based cooperative relay system, where the relay node not only can forward the data to the destination node, but is also capable of transferring energy to the source node. In particular, to maximize the overall system capacity in multiple subchannels and multiple time slots while meeting the power constraints, a power allocation optimization problem is formulated and solved in three steps. First, at each data transmission and data forwarding cycle, we split the total transmission power of relay into two parts, one for data forwarding and the other as power supplement for the source node. Then, our analysis indicates that at each cycle, once all of the subchannels are sorted in a certain order, the relay node will only provide forwarding power to the subchannels with index greater than a certain value. Meanwhile, the incentive for the relay node to provide power supplement should be strong enough such that relay chooses not to simultaneously transmit data and energy. Then, an equivalent convex constrained optimization problem is formulated and the solution is derived by solving the Lagrange function. The solution takes the form of water-filling in combination with a cooperative feature. Numerical results demonstrate that energy cooperation notably improves the system capacity.

Green communications has received much attention in recent years. In cellular networks, base stations (BSs) account for more than 50 percent of the energy consumption. Reducing energy consumption of BSs is essential to realizing green cellular networks. Utilizing green energy to power BSs is a promising way to reduce the on-grid energy consumption. Maximizing the utilization of green energy has thus been proposed to furthest save the on-grid energy. In this paper, we propose a green energy driven user-BS association with dual battery system to maximize the utilization of green energy at BSs. The BSs of cellular networks are powered by both on-grid energy and green energy. The optimal usage of green energy is achieved by balancing the mobile users among BSs according to the amount of residual green energy in their batteries. This green energy driven user association optimization problem is NP-hard. Hence, we propose some heuristics to maximize the green energy utilization and approximate the optimal user association with low computational complexity. Finally, we validate the performance of the proposed algorithm through extensive simulations.

Energy efficiency is a growing concern for wireless networks, not only due to the emerging traffic demand from smart devices, but also because of the dependence on the traditional unsustainable energy and the overall environmental concerns. The urgent call for reducing power consumption while meeting system requirements has motivated increasing research efforts on green radio. In this paper, we investigate a new joint spectrum and power allocation scheme for a cooperative downlink multi-user system using the frequency division multiple access scheme, in which arbitrary M base stations (BSs) coordinately allocate their resources to each user equipment (UE). With the assumption that multi-BS UE (user being served by multi-BS) would require the same amount of spectrum from these BSs, we conclude that when the number of multi-BS UEs is limited by M-1, the resource allocation scheme can always guarantee the minimum overall transmit power consumption while meeting the throughput requirement of each UE and also each BS's power constraint. Then, to decide the clusters of multi-BS UEs and the clusters of individual-BS UEs (users being served by individual BSs), we propose a UE-BS association scheme and a complexity reduction scheme. Finally, a novel joint spectrum and power allocation algorithm is proposed to minimize the total power consumption. Simulation results are presented to verify the optimality of the derived schemes.

Green communications has received much attention recently. Utilizing green energy in wireless cellular networks is promising to reduce the main grid electricity consumption, and thus to reduce the CO2footprint. However, owing to the fluctuating nature of green energy, it is challenging to use green energy in cellular networks. In this paper, we propose an energy agile packet scheduler which maximizes the utilization of green energy by optimizing the packet scheduling. The packet scheduling optimization problem is NP-hard in the strong sense. The energy agile scheduler approximates the optimal packet scheduling solution in two steps. First, the energy agile scheduler balances the BS's energy consumption in transmitting packets among time slots. Second, within each time slot, the energy agile scheduler optimizes the bandwidth allocations to minimize the BS's energy consumption. Simulation results demonstrate that the proposed energy agile scheduler achieves significant main grid energy savings.

Coordinated multi-point transmission/reception (CoMP) has been considered in 3GPP LTE-Advanced to improve system performance, especially cell edge throughput. The conventional uplink power control (PC) scheme cannot work well since a UE can be served by multiple cells. This paper analyzes uplink PC issues in detail, and proposes an effective scheme aiming to obtain the reception diversity gain from CoMP. System-level simulation results have shown that CoMP systems with both the conventional scheme and the proposed scheme can achieve a better cell edge performance, compared with non-CoMP systems. Furthermore, the proposed scheme considerably outperforms the conventional scheme, it can bring an additional cell average throughput gain up to 15.78% and an additional cell edge throughput gain up to 69.22% over the conventional scheme, thus is recommended to be adopted in CoMP systems.

Most timing analyzers rely upon a linear approximate interconnect model, typically an RC tree, to estimate efficiently the propagation delays for digital MOS integrated circuits. RC tree methods are adequate to analyze a large class of MOS circuits, but are not sufficient in general for high speed, dynamic and precharge MOS circuits. In addition bipolar logic and board level digital systems can have interconnect models which may not be compatible with RC tree topologies. In this paper we describe AWEsim, a variable refinement waveform estimator for generalized linear RLC approximate interconnect models.