In LEO satellite handover under urban mobility, ephemeris, elevation, and field-of-view (FoV) constraints can potentially identify a reachable satellite, but they do not indicate whether the satellite's projected path in the local sky of the user terminal (UT) will remain usable after the handover decision. While present-time visibility can reject a path that is already blocked, it cannot warn that a currently reachable satellite is losing clearance near a building, canopy, or bridge boundary. The resulting gap for LEO satellite handover is thus not just candidate discovery, but candidate ranking under future local obstruction. This paper aims to address this gap based on future local-sky clearance, the path-level margin between each candidate satellite projection and the predicted terrain or skyline boundary. We propose SkyMRT, a future-skymask rollout model that estimates boundary motion from recent binary skymasks and UT motion, as well as SMASH, a deterministic selector that checks the incumbent and ranks candidates by worst-case clearance, serviceable fraction, and near-boresight priority. Our evaluations on an urban digital-twin replay with Starlink TLE (two-line element) propagation and packet-level ns-3 replay show that the resulting selector reduces blocked exposure by 5x compared with a geometry-and-FoV selection baseline. Against a same-cadence present-time visibility baseline, it reduces packet error rate by 2.2x and transition time by 10.2x. These results show that future local-sky clearance can indeed change urban LEO satellite selection from late blockage repair to early ranking of future-serviceable candidates.

Low Earth Orbit (LEO) satellites have recently attracted attention as solutions for enabling global connectivity because of the low propagation latency and low path loss compared to other satellite systems. In the meantime, however, the high orbital speed as well as the low production cost have rendered power consumption minimization as one of the most critical issues for performance optimization in LEO satellite communications. In this paper, we investigate energy-efficient beamforming design for LEO satellites that support multigroup multicast downlink communications. Different from related work that assumes availability of instantaneous channel state information (CSI), our design relies only on the slow-varying statistical CSI (sCSI). The formulated problem aims to maximize energy efficiency while meeting the target data rate requirements. To solve the problem, we first approximate the average rate function by applying a closed-form tight upper bound. We then use the Dinkelbach's algorithm to transform the fractional function for energy efficiency into a concave function. We finally adopt the Convex-Concave Procedure (CCCP) to solve the problem. Numerical results show that the proposed algorithm is able to achieve higher energy efficiency than existing approaches for multicast LEO satellite communications.

Pose estimation based on WiFi channel state information (CSI) has gained popularity in recent years. Most existing works, however, focus only on scenarios with a single user. For those research endeavors on multi-user pose estimation, on the other hand, they suffer from the robustness problem when environment changes since most of them rely on the use of environment-specific features such as CSI amplitude and phase. In this paper, we propose to use both spatial and temporal features for multi-user pose estimation that can show resilience to environment changes. The features we use combine angle of arrival (AoA), time of flight (ToF), and Doppler frequency shift to capture the location and motion information of the users. Unlike existing methods that extract such features along the time or frequency axis based on a particular packet, we propose three methods to jointly estimate AoA-ToF and AoA-Doppler heatmaps from consecutive packets across multiple subcarriers to increase the resolutions of the desired features. We use mathematical analysis to show the performance benefits of the proposed methods, along with ray-tracing-based simulation and real-life testbed experiments. The simulation shows that the proposed methods can systematically suppress noises and increase the resolutions of desired features compared to existing methods. In addition, the results based on the testbed experiments show that our system outperforms the existing model by 12 when layout of the environment changes, thus substantiating the benefits of using both spatial and temporal features for robust multi-user pose estimation.

While Poisson Cluster Process (PCP) has been used extensively in the literature for analyzing large-scale clustered wireless networks, related work differs in terms of how the BS (Base Station) distribution and UE (User Equipment) association strategy are modeled in this context. Different from related work that places BSs via Poisson Point Process (PPP) independent of the UE distribution, we consider a more practical scenario where the BSs are located at the parent points of PCP. Furthermore, while a lot of analysis often assumes each UE to be associated with the BS at the parent point of the cluster it belongs to, such a model may result in bias for dense networks where clusters of UEs may overlap with each other. To address such a pitfall, in this work we consider “nearest-BS” association such that a UE may be associated with a nearby BS that is the parent point of another cluster. While there does exist analysis on downlink transmissions for such a network scenario, we find that analysis for uplink performance is more challenging and has yet to be developed in the literature. To proceed, we start from the analytical framework established by related work but derive new expressions for the aggregate uplink interference from different UE clusters in the network. We derive accurate analytical upper and lower bounds for the transmission success probability and we are able to arrive at a closed-form expression for the special case with a path loss exponent of 4. Furthermore, we derive the asymptotic performance bound for ultra-dense networks and investigate the problem of optimizing the area spectral efficiency (ASE) with respect to the design of the signal-to-interference-plus-noise ratio (SINR) threshold. By leveraging the closed-form expression that we have derived, the problem can be solved effectively to obtain the optimal ASE in ultra-dense networks. Evaluation results show that our analysis is correct and the derived bounds are accurate, thus motivating further investigation based on the derived results.

Pose estimation based on WiFi channel state information (CSI) has gained popularity in recent years. Most existing works, however, focus only on scenarios with a single user. For those research endeavors that can handle multi-user scenarios, on the other hand, they suffer from the robustness problem against environment changes due to their reliance on the use of domain-specific features such as CSI amplitude and phase. In this paper, we propose to use both spatial and temporal features for multi-user pose estimation that can show resilience to environment changes. The features we use combine the angle of arrival (AoA), time of flight (ToF), and Doppler shift for capturing the location and motion information of multiple users. Unlike existing feature extraction methods that only take CSI either along the time axis or across different frequency subcarriers, we propose new methods to jointly estimate AoA-ToF and AoA-Doppler heatmaps from consecutive CSI samples and subcarriers for increasing the resolutions of the desired features. An experiment testbed is set up to evaluate the performance of the proposed system. Results show that our system outperforms the existing model by 12% in precision across different scenarios with changes in the environment, thus substantiating the benefits of using both spatial and temporal features for multi-user pose estimation.

Current wireless volumetric video streaming faces multiple challenges, including high bandwidth consumption, large decoding overhead on the client device, and low view reconstruction quality perceived by the user. In this paper, we explore an edge-assisted streaming system, where 3D contents of volumetric video are first transcoded by the edge server based on predicted user positions and then transmitted to the client to substantially reduce the bandwidth consumption and decoding overhead. In such a system, however, inaccuracy in position prediction could lead to displacement between the transcoded reference view and the actual view required by the client. To mitigate this problem, we task the edge server to transcode multiple views and formulate the problem of multiview generation as an optimal quantization problem. Rather than using distance-based distortion metrics, our formulation considers the actual distortion perceived by the user for solving the general problem of positioning reference views under general position error distribution caused by position predictors. Our evaluations show significant improvements over state-of-the-art techniques by reducing quality degradation from 17% to 28% in terms of the 75-th and 95-th percentiles of distortion perceived by users.

Wireless virtual reality (VR), aiming to provide an untethered immersive experience through 360° videos, could be facilitated by viewport-guided streaming with the help of viewport prediction. Although many recent viewport predictors can output a series of predictions over upcoming frames, most existing work on video streaming does not fully utilize the capability of these predictors. In this paper, we investigate the problem of 360° video streaming by incorporating the complete series of viewport predictions for maximizing the quality of experience (QoE) through cross-frame resource allocation. To address the problem of viewport prediction errors that could result in erroneous estimation of QoE contribution of tiles in upcoming frames, we develop a novel approach based on contextual multi-armed bandit (CMAB) to “learn” online the viewing behavior of the user and the capability of the predictor such that resource can be preferentially allocated to tiles with significant QoE contribution. Further, to address the problem of transmission failures during wireless streaming, we formulate a constrained Markov decision process (CMDP) and apply model predictive control (MPC) to account for resource competition among reactive and proactive transmissions as well as retransmissions of tiles. The performance of the proposed streaming system is evaluated using a real-world VR dataset, state-of-the-art viewport predictors, and realistic mmWave channel models. An improvement of 5.68% in QoE and a reduction of 23.0% in resource waste are achieved across various videos, users, and predictors. Simulation results substantiate that the context-aware QoE learned by the proposed CMAB effectively addresses prediction errors for tiles with different temporal and spatial contexts, and the proposed CMDP can achieve the desired performance even under high viewport prediction error and channel error.

Many research endeavors to optimize the performance of NOMA (non-orthogonal multiple access) have focused on mobile broadband applications, where transmissions typically occur in the downlink with full-buffered traffic and the primary performance metric is the sum date rates. Machine-type communications, however, are distinctly different, where transmissions typically occur in the uplink and traffic load from individual machines is low with short payloads. To optimize NOMA performance for resource-constrained cellular IoT (Internet of Things) networks, in this paper we investigate a problem to minimize total radio resource used by all IoT devices for sending the collected data to the base station. By employing distributed source coding (DSC) between the two nodes in a NOMA pair, we first solve the resource optimization problem of a two-node pair through joint data and power allocation. With the calculated resource usage of two nodes in OMA and NOMA, we then construct a weighted graph and investigate maximum weight matching for pairing IoT devices in the network with minimum total resource usage. We compare different pairing algorithms for solving the problem while striking a good balance between complexity and optimality. Simulation results show that DSC can achieve significant performance gain for NOMA resource usage compared to the baseline approaches in cellular IoT networks.

In this paper, we consider the problem of minimizing the queue length of wireless sensors involved in data gathering. Unlike conventional approaches, we focus on the received data quality at the collector for optimizing scheduling design. While meeting the minimum data fidelity requirement from the application, we leverage correlation among gathered data to allow proactive data dropping before queue is full and reduce radio resource usage. We first formulate the problem and then transform the time-average resource allocation problem into a scheduling problem based on the Lyapunov optimization framework. To solve the problem, we investigate two heuristic algorithms called allocation-first and drop-first algorithms in addition to the optimal algorithm. Evaluation results show that data-centric algorithms can effectively reduce resource usage and support more sensors compared to the conventional scheduling algorithm while meeting the requirement on data quality.

In many IoT (Internet-of-Things) applications, IoT devices (machines) are deployed to collectively gather data required by the target application, and the data gathered by individual machines is often correlated. Leveraging the fact that it is the quality of the data that matters to the application rather than the link qualities of individual machines, data-centric machine-to-machine (M2M) communications prioritize machines based on the importance of data they carry to optimize system design. In this paper, we investigate the use of non-orthogonal multiple access (NOMA) technique for data-centric M2M wireless networks. In particular, we focus on the problem of how machines should be paired for resource sharing during transmission scheduling. We have found that the conventional NOMA scheduling strategy to maximize the sum data rates of co-scheduled users can result in worse performance than OMA (orthogonal multiple access) for data-centric communications. To address the problem, we propose a scheduling strategy to minimize the waiting time among co-scheduled users by taking into consideration the amount of data to transmit and achievable data rates of NOMA users. Evaluation results show that such a scheduling strategy performs much better than sum-rate maximization scheduling for data-centric M2M networks.

Recent studies show that Non-Orthogonal Multiple Access (NOMA) can outperform conventional Orthogonal Multiple Access (OMA) in terms of both throughput and fairness. However, most of existing studies focus primarily on wideband scheduling without leveraging subband CQIs reported from users that reflect performance mismatch across difference frequency subbands. One challenge towards NOMA subband scheduling is the high complexity due to the need to jointly consider resource allocation for multiple user pairs across multiple subbands. In this paper, we propose a subband scheduling algorithm for NOMA based on the cross-entropy (CE) method to reduce computation complexity. The proposed solution utilizes subband CQIs reported from users that indicate SINR variations in the frequency domain to optimize the performance of all users across all resource blocks. We further implement subband scheduling for NOMA in the Vienna LTE-A downlink system-level simulator to substantiate the performance gain of subband scheduling against wideband scheduling on the well-tested evaluation platform.

In this paper, we tackle the practical error propagation and MCS (modulation and coding scheme) selection problem for non-orthogonal multiple access (NOMA) based on multi-user superposition transmission (MUST). Our formulation involves proportional-fair allocation of resource blocks to a set of users with guaranteed bounds of error rates. Since a majority of MCSs used in existing communication systems do not have closed-form expressions to evaluate the bit error rates of co-allocated NOMA users, we propose a method to integrate link-level NOMA simulation for solving the network optimization problem. By constructing an “MCS map” as the output of the NOMA simulator, the resource allocation algorithm can perform system-level allocation without involving link-level simulation on a bit-by-bit basis. Through evaluation results, we show that the proposed method based on the MCS map can outperform baseline approaches based on estimation of post-processing SINR of NOMA users. We also find that NOMA can indeed achieve significant gain over OMA, but the gain does not increase proportionally to the number of users allowed to share each resource block. Such diminishing returns suggest further optimization for NOMA in this direction.

While clustered communication has been considered as one key technology for wireless sensor networks, existing work on cluster formation predominantly takes a pure graph-theoretic approach with the goal of optimizing the performance of individual machines. Since the radio resource available for M2M communications is typically limited yet the amount of data to transport is large, such “resource-agnostic” and “data-agnostic” clustering techniques could lead to sub-optimal performance. To address this problem, we propose “data-centric” clustering in a resource-constrained M2M network by prioritizing the quality of overall data over the performance of individual machines. We first formulate an optimization problem to minimize the amount of radio resource needed for supporting two-tier clustered communications. We then partition the formulated problem into the inner power control and outer cluster formation sub-problems and propose algorithms for solving the problems. While power control can be optimally solved for any given cluster structure by the proposed algorithm, cluster formation is an NP-hard problem. Hence, we propose an anytime, guided, stochastic search algorithm to find a reasonably good cluster structure without incurring prohibitive computation complexity. Compared with baseline approaches, our evaluation results show that data-centric clustering can achieve noticeable performance gain by selecting only important machines and forming a cluster structure that can balance the radio resource usage of the two tiers. We therefore motivate data-centric clustering as a promising communication model for resource-constrained M2M networks.

Interference-aware spectrum sensing extends conventional interference-agnostic sensing by exploring the fact that missed detection does not necessarily result in outage or intolerable interference on the primary user. While related work has motivated and demonstrated the benefits of interference-aware spectrum sensing for spectrum hole discovery, the inherent conflict of interests among the set of cooperative users with interference-aware spectrum detectors has not been properly formulated and addressed. In this paper, we aim to bridge the gap by considering a coalition-based model, where the set of secondary users is to be partitioned into multiple coalitions for cooperative spectrum sensing and access. The goal is to maximize the utility sum of all secondary users while observing the protection requirement of the primary user. Since the user with the largest interference probability in a coalition critically limits the detection performance of the coalition, there is a trade-off in determining the optimal coalition structure in the network. To proceed, we first formulate a joint threshold detection and coalition formation problem under the target cooperative model, and then explore important properties of the target problem. Our proposed algorithms based on polyblock approximation and search space partition can effectively solve the formulated problem with significant performance gains and complexity reduction against baseline approaches proposed in related work.

Existing wireless networks have predominantly adopted orthogonal multiple access (OMA) such as OFDMA as the underlying multiple access technology. To further improve spectrum efficiency in next-generation wireless networks, however, a promising direction is to shift to non-orthogonal multiple access (NOMA). To address the new technical challenges brought forth by NOMA, in this paper we investigate the problem of scheduling multiple NOMA users in the same resource block previously dedicated to a single user in OFDMA. Unlike related work that relies on the ideal link capacity model for profiling the performance gain of NOMA, we start by implementing a more practical NOMA simulator to investigate problems such as modulation/coding scheme (MCS) selection, power allocation, and error propagation along with transmission scheduling. We formulate an optimization problem for transmission scheduling with the goal of providing proportional fairness to the set of users served by a base station. We then propose a method to integrate physical-layer simulation into a meta-heuristic search algorithm for solving the joint optimization problem. Evaluation results show that the proposed scheduling algorithm can effectively solve the problem in the target scenario and NOMA can achieve significant performance benefits over OMA, thus motivating further investigation along this direction.

In machine-to-machine communications, several machines located close to one another can form a cluster to leverage spatial reuse gains and energy savings. We investigate a machine selection algorithm where only a machine in each cluster transfers its data to the cellular user via device-to-device communication and then the cellular user forwards it to the base station. Unlike the previous works that focus on data rate or channel condition as the selection metrics, this paper proposes a correlation-aware selection algorithm which maximizes the joint entropy extracted from the data delivered from the selected machines. Our evaluation results show the proposed selection scheme reaps a significant gain and is near-optimal.

Coexistence between cellular-mode and D2D-mode users that share the same radio resource is one key problem for D2D communications. While related work has investigated transmission power control for interference management, most approaches have considered only the long-term channel gain without specifically addressing the stochastic fluctuations of the channel. In this paper, we investigate interference management under Rayleigh channel fading through stochastic optimization. We first transform the objective and constraint functions in stochastic forms into equivalent yet deterministic forms, and then we propose a low-complexity method to solve the formulated nonlinear problem. The proposed method relaxes and separates the constraint functions into simpler ones, and then solves the linearized problem using an iterative algorithm while simultaneously shrinking the search space. Simulation results demonstrate that the outage probability of the cellular- mode user can be maintained below the desired threshold despite the uncertainty of channel conditions, while the sum rate of D2D- mode users outperforms baseline methods under the same constraint.

Most related work on cluster formation has modeled the cluster structure from a purely graph-theoretic perspective with predefined communication links and data rates among the set of nodes under consideration. Failure to accurately model inter- cluster interference among concurrent transmissions, however, results in sub-optimal performance for supporting M2M communications in cellular networks with limited radio resource and tight interference control. In this paper, we investigate the problem of energy-efficient clustering by jointly considering cluster formation, transmission scheduling, and power control. We specifically take the communication constraint into consideration to ensure the subset of machines scheduled and the transmission powers used allow concurrent, reliable transmissions in the cluster structure. Based on the evaluation for a semi- realistic camera surveillance network, the proposed approach can result in minimum powers for tier-1 and tier-2 transmissions while collecting the required amount of data for M2M applications.

Many applications involving machine-to-machine (M2M) communications are characterized by the large amount of data to transport. To support these M2M applications, we argue in this article that instead of focusing on serving individual machines with better quality, one should focus on solutions that can better serve the data itself. To substantiate, we consider the application of data gathering from a set of machines that communicate directly to an aggregator. Since the aggregator has limited radio resources, the problem arises as to how the resource can be effectively utilized for supporting such an application. We investigate “data-centric” resource allocation that aims to maximize information entropy of data collected through selecting the subset of machines to transmit, determining the amount of resources to allocate, and scheduling the sequence of transmissions. We present two instantiations of the problems when machines can perform distributed source coding or dependent source coding based on the data overheard from neighboring machines and then propose algorithms for solving the joint optimization problems. Evaluation results show that compared to conventional “machine-centric” resource allocation that aims to maximize the aggregate data rates or number of supported machines, “data-centric” resource allocation exhibits significant performance gain in terms of the quality of data that can be collected for the given amount of radio resources.

We consider the correlated data gathering problem in machine-to-machine communications. The machines implement distributed source coding and transmit their gathered data to the data aggregator. The data aggregator has limited radio resources and thus only a subset of machines are selected for transmission. Missing data from nonselected machines are reconstructed at the aggregator by exploiting data correlation. We first propose a data distortion measure based on information loss to characterize the reconstruction, and derive its relationship with the traditional mean squared error distortion analytically. Then, we formulate the machine selection problem with the objective of minimizing the overall data distortion given some resource constraints. We decouple the problem into subproblems and solve them by the proposed algorithm based on the cross entropy method. Numerical results demonstrate improved data fidelity by implementing distributed source coding, and better network coverage and energy efficiency for the proposed machine selection scheme.

In this paper, we investigate the problem of joint coordinated resource allocation and power control for LTE-A heterogeneous networks (HetNets) with low-power remote radio heads (RRHs). The scenario we consider is the configuration when RRHs share the same cell ID with the macro BS such that coordinated multi-point (CoMP) operations among transmission points can be performed in a finer granularity without undesirably triggering frequent handover operations. We first formulate a mixed-integer non-linear (MINLP) optimization problem involving multiple transmission points and a set of users demanding fair service. To reduce problem complexity, we transform the formulation into a coordinated scheduling problem with transmission power control. We then propose a two-phase iterative algorithm involving sub-channel resource allocation and co-channel power allocation for solving the target problem. Simulation results show that RRHs with CoMP operations do provide a promising approach for enhancing the performance of users in the macrocell and the proposed algorithm can effectively solve the problem with noticeable performance gain.

Energy-efficient base station (BS) operation is a key design goal in green cellular networks. An effective way for energy conservation of BSs is to switch BSs on/off according to the traffic profile. However, such operations may create coverage holes in the network. In this paper, we aim to minimize the total power consumption of the network by switching BSs on/off adaptively while maintaining the network coverage. We find that the BS activation problem for minimal network power consumption with full network coverage preservation is an NP-hard problem. To address the problem, we first derive the optimal cell size for minimizing BS power consumption per unit coverage area and propose a polynomial-time algorithm for energy-efficient BS activation. The simulation results show that our algorithm can approach the minimum network power consumption and adapt to network traffic load under non-uniform traffic load distributions. More importantly, we demonstrate that network densification with small cells for bursting throughput in hot spot areas can also be beneficial in saving network energy during the low traffic load period.

Femtocell technology has shifted beyond indoor residential applications to cover a wider range of scenarios including metropolitan and rural areas. The term “small cell” has hence been used to denote such low-power transmission points deployed for enhancing macrocell coverage and/or capacity. While deployment of femto BSs has typically followed the bottom-up paradigm driven by the ad hoc demand of users, more and more studies have prompted a move toward a more managed deployment model for better tradeoff between performance and cost. In this paper, we investigate an optimization problem for femtocell deployment in a dense network with arbitrary topology. The goal is to determine deployment locations and operation parameters of femtocells for maximizing the number of customers supported with QoS constraints. Since the formulated problem belongs to mixed-integer non-linear programming (MINLP), we propose an anytime algorithm that transforms the joint problem into a cluster formation sub-problem (involving location selection and cell coverage) and a resource management sub-problem (involving power control and resource allocation) for effectively solving all optimization variables in an iterative fashion. Compared with other approaches for femtocell deployment, our evaluation results show that the proposed algorithm can effectively solve the target problem while striking a better performance tradeoff between computation complexity and solution quality.

In this paper, we consider the problem of correlated data gathering in M2M (machine-to-machine) wireless networks with a large number of machines. Since machines communicate directly with the aggregator, the limited radio resources at the aggregator become the bottleneck for supporting all machines. Unlike related work that employs distributed source coding for minimizing resource usage, we assume that machines only perform local source coding. However, machines can leverage data overheard from transmissions of other machines for removing redundancy based on “dependent” source coding. To explore the performance tradeoffs of overhearing, we formulate a joint optimization problem involving node selection, resource allocation, and transmission scheduling, and then solve the problem based on the cross entropy method. Evaluation results show that without incurring the complexity of distributed source coding, dependent source coding via overhearing can achieve noticeable performance gain compared to independent source coding - even if the overhearing range and time are limited due to energy consideration. The results thus motivate further investigation for leveraging overhearing opportunities in M2M networks with limited radio resources.

We consider the problem of data gathering from a set of machines deployed arbitrarily in a source field. Machines are assumed to communicate directly with the aggregator (sink) using the allocated radio resource. Since the aggregator has limited radio resources to allocate for machine communications, only a subset of machines can be selected for uplink transmissions. Missing data from unselected machines is reconstructed by the aggregator through exploiting correlation of gathered data. To further reduce resource usage, each selected machine performs local source coding before the data is transmitted to remove redundant information that it overhears from other machines. In such a scenario, the aggregator needs to optimally select the subset of machines for resource allocation and then schedule their orders of transmissions to minimize the overall data distortion. We first formulate a joint optimization problem for the target scenario and then propose an algorithm based on the cross entropy method to solve the problem. Evaluation results show that dependent source coding based on overhearing can achieve significant performance gain compared to independent source coding without overhearing. The gain is still noticeable even if the overhearing time is limited to due energy consideration.

In this paper, we investigate the problem of opportunistic spectrum sharing in cognitive radio networks through transmission power control. Motivated by the random nature of Rayleigh channel fading, we model the QoS constraint function under a probabilistic form and then propose a method to convert it into an equivalent yet deterministic form. To solve the formulated problem, we introduce an algorithm based on differential evolution (DE). Simulation results show that the SINR at the primary receiver can be maintained under the proposed power control mechanism despite the fluctuations of channel conditions. The proposed algorithm also implies a better trade-off in terms of satisfying the probability constraint and maximizing the objective function compared to the baseline approach.

We consider an LTE-A heterogeneous network involving a set of low-power remote radio heads (RRHs) connected to the macro BS through optical fibers. RRHs share the same cell ID with the macro BS such that coordinated multi-point (CoMP) operations can be performed in a finer granularity without triggering frequent handover operations. We first formulate an optimization problem for coordinated scheduling from multiple transmission points to a set of users demanding fair service. Since the problem incurs high complexity, we transform the formulation into an iterative scheduling problem for each scheduling time slot. To solve the non-linear binary integer problem, we propose an algorithm that relaxes the discrete variables into continuous variables while imposing proper penalty and smooth functions for minimizing the chance of the solution falling into local optimum. Simulation results show that the proposed algorithm can effectively solve the target problem with noticeable performance gain compared to related approaches.

Heterogeneous network with small cells has recently been regarded as a promising scenario in LTE-Advanced systems. In particular, transmission point selection for heterogeneous networks with low-power nodes has drawn attention. We consider in this paper a scenario where a set users is admitted to a macrocell, but it is yet to be determined how each user is served solely or cooperatively by the set of subordinate transmission points in the cell. Unlike related work that focuses on maximizing the system throughput, we formulate a joint optimization problem of transmission point selection and resource allocation to minimize the total transmission delay of users in the cell. The formulated problem is NP-hard, and thus we propose an algorithm based on overlapping clustering and Gibbs sampler for solving the problem. Simulation results show that, compared to related approaches, the total transmission delay can be reduced by 34% and the Jain's fairness index can be increased to 0.9 on average.

Spectrum sensing is an important step toward enabling dynamic spectrum access in cognitive radio networks. To ensure that primary users are properly protected while maximizing the performance of secondary users, most related work considers the metrics of probabilities of missed detection and false alarm for determining optimal spectrum sensing parameters. In this paper, we argue that spectrum sensing based entirely on the two metrics is unable to maximize spectrum utilization for dynamic spectrum access. We show that, to meet the requirement of the probability of missed detection, conventional spectrum sensing techniques can unnecessarily increase the probability of false alarm in scenarios with good spectrum reuse opportunity, thus lowering the ability to leverage spectrum holes. To address this problem, we define the probability of interference and propose a new metric for spectrum sensing to consider both the probabilities of interference and missed detection. We first investigate the problem of optimal spectrum hole discovery for a single secondary user based on the proposed metric, and then extend to the problem of cooperative spectrum sensing among a group of secondary users. Compared against conventional sensing techniques presented in related work, we show through simulations that interference-aware spectrum sensing can potentially result in better utilization of the spectrum by allowing the secondary user to maximize its transmission opportunity without sacrificing the desired degree of protection for primary users.

Many applications involving machine-to-machine (M2M) communications are characterized by the large amount of data to transport. To address the “big data” problem introduced by these M2M applications, we argue in this paper that instead of focusing on serving individual machines with better quality, one should focus on solutions that can better serve the data itself. To substantiate this concept, we consider the scenario of data gathering in a wide area by machines that are connected to a central aggregator through direct wireless links. The aggregator has limited radio resources to allocate to machines for uplink transmission of collected data, and hence the problem arises as to how the resources can be effectively utilized for supporting such an M2M application. In contrast to conventional approaches on maximizing the number of machines that can access the radio resources, we investigate an approach that takes into consideration “useful” information content that individual machines can provide for prioritization of resource allocation. Numerical results based on the proposed algorithms show that although the number of machines that can be supported is not maximized, the data so collected at the aggregator does exhibit significant quality gain for the target M2M scenario, thus motivating further investigation along this direction.

Clustered communication has been considered as one key technology for supporting machine-to-machine (M2M) wireless networks with a large number of communicating devices. Unlike related work that focuses on clustering with simple or no wireless interference model at the physical layer, in this paper we investigate the optimization problem of cluster formation and power control for interference-limited M2M communications. We consider a scenario where machines that form in clusters are allowed to reuse the spectrum occupied by human devices through proper transmission power control. To maximize the number of machines that can communicate while meeting the data rate constraints of human devices and machines themselves, we formulate a mixed-integer non-linear programming (MINLP) problem. Since the MINLP problem becomes too complex when the number of machines increases, we propose an algorithm that transforms the problem into a coalition structure generation sub-problem embedded with a linear power control sub-problem. The proposed algorithm is an anytime algorithm and hence the length of the running time can be arbitrarily controlled while yielding a feasible solution with the desired quality. Compared with other approaches for solving the original MINLP problem, we show through numerical results that the proposed algorithm can effectively solve the target problem and allow machines to achieve better spatial reuse with human devices in interference-limited M2M communications.

Recently, there has been an increasing interest in the deployment and management of femto base stations (BSs) to optimize the overall system performance in macro-femto heterogeneous networks. While deployment of femto BSs is typically not as planned as that of pico BSs, given a number of femto BSs to be distributed to candidate customer sites, questions regarding the optimal deployment locations and transmission configurations still need to be answered. In this paper, we formulate a joint optimization problem involving deployment location, cell selection, and power control to maximize the number of users that can be supported for a given number of femto BSs to be deployed in the macro cell. Since the formulated problem belongs to mixed-integer non-linear programming (MINLP), we propose an anytime algorithm that can yield a desirable solution within proper time limit. Specifically, based on the concept of coalition structure generation, the algorithm decouples the problem into the cluster formation sub-problem and power control sub-problem to find the optimal cluster head (femto BS location), cluster membership (cell selection), and transmission power in an iterative fashion. Evaluation results presented in this paper show that the proposed algorithm can effectively solve the problem with better complexity-optimality tradeoffs compared to baseline approaches.

Clustering of machines for better spatial reuse has been considered as one key technology for supporting machine-to-machine (M2M) communications with a large number of communicating devices. Unlike related work that focuses on greedy clustering algorithms without interference control, in this paper we consider a scenario where machines through joint cluster formation and power control are allowed to opportunistically use the spectrum occupied by human devices for interference-limited M2M communications. To maximize the number of machines that can communicate without violating the QoS constraint of the human device, we formulate a mixed-integer non-linear programming (MINLP) problem to determine the optimal cluster structure and power control. We then propose an anytime algorithm based on simulated annealing to solve the MINLP problem under a high density of machines. Compared with the approach of directly solving the MINLP problem and the approach of separately performing cluster formation and power control, we show through numerical results that the proposed algorithm can effectively solve the target problem while striking a better performance tradeoff between complexity and optimality.

In the paper, we investigate a distortion-optimized resource allocation problem among a group of users with unicast video transmission in OFDMA networks. Since video distortion results from both encoding errors due to rate limitation and transmission errors due to packet losses, to minimize distortion we also consider joint optimization of the selection of the modulation and coding scheme (MCS) for each allocated resource unit. To proceed, we formulate a mixed-integer non-linear programming (MINLP) problem for joint resource allocation and MCS selection with the objective to minimize overall video distortions from all users. To solve the formulated problem, we propose a two-stage algorithm, where the Hungarian algorithm is used in the first stage to optimally assign the minimum resource units required for individual users based on their channel conditions. In the second stage, additional resource units are assigned to the most needed users with the greatest potential to minimize the overall distortions. As more resource units are allocated to each user, the MCS is adjusted accordingly to avoid biased selection from the initial resource unit. Simulation results show that the proposed algorithm achieves performance gain of about 16%-55% compared to the conventional approach of separate resource allocation and MCS selection.

Transmission power control is one of the key enabling technologies in opportunistic spectrum sharing for secondary users to optimize their performance without incurring undesirable interference on primary users. Various optimization models and algorithms for different scenarios and design objectives have hence been proposed in related work. While ideally these algorithms can find optimal solutions for power control, in practice it is very likely that the output powers are suboptimal or even infeasible if these algorithms are applied in a distributed environment. The reasons are due to various practical considerations such as the overheads of power training, use of the control channel, and dynamics of primary user activity. To address the problem of unfit outputs thus obtained, we investigate in this paper low-complexity algorithms that can be used in tandem with these distributed algorithms by quickly adapting undesirable solutions for use by secondary users such that feasibility is restored and/or optimality is improved. Compared with the approach of finding a new solution based on linear approximation of the optimization problem, we show through evaluations that the proposed algorithm is simple yet effective in achieving the desired goal.

In this paper, we investigate the problem of opportunistic spectrum sharing through joint optimization of spectrum hole detection and transmission power control. Unlike conventional spectrum sensing models that classify the state of the primary user as being idle or active, we consider a multi-state spectrum sensing model where there exist multiple states to be chosen as the detection decision. Different states represent the degrees of certainty at the detector regarding the presence of the primary user, and hence are mapped to different levels of transmission powers to be used by the secondary user for spectrum access. Our goal thus is to jointly decide the optimal detection thresholds (state boundaries) and transmission powers such that the achieved capacity at the secondary user is maximized subject to the interference temperature limit constraint at the primary user. We first formulate a non-convex optimization problem based on the system models and then propose an algorithm for solving the problem. By varying the number of states in the multi-state sensing model, we compare the performance of the conventional two-state hard sensing model and the infinite-state soft sensing model, thus motivating further investigation on multi-state spectrum sensing for dynamic spectrum access.

As IP telephony gains more popularity, interworking with conventional PSTN telephony has also gained more importance. In particular, an increasing number of new telephony services now involves both packet-switched (IP telephony) and circuit-switched (PSTN telephony) voice legs in one call session. One common problem that arises for enabling such new services is the need for synchronization of voice streams that traverse through heterogeneous telephony systems. In this paper, we first identify the key role of voice synchronization across heterogeneous telephony systems for services such as seamless handover between WLAN and cellular networks and multi-party audio conferencing with video overlay. We then explain the challenges in synchronizing circuit-switched and packet-switched voice streams, including codec distortion, packet losses, line noises, and overlapping utterances. To achieve voice synchronization, we proceed to investigate three different approaches based on digital speech processing techniques in the waveform, cepstrum, and spectrum domains. Finally, we compare the performance benefits and tradeoffs of different approaches, thus motivating further research along this direction.

A key issue of dynamic spectrum access in cognitive radio networks is to ensure that the interference incurred on primary users is under control. While interference models and optimization algorithms exist for spectrum sharing in cognitive radio networks, the study on network protocol design is still preliminary. In this paper, we aim to propose a distributed power control protocol for enabling effective spectrum sharing between primary and secondary users. The goal of power control is to maximize the aggregate capacity of the secondary network while ensuring that the cumulative interference incurred on primary users is within their interference temperature limit. We start by formulating the problem using network optimization, and then propose a distributed algorithm for solving the optimization problem using game theory. Based on the proposed distributed algorithm, we then design a network protocol for achieving distributed power control in cognitive radio networks. We find that while the network protocol can indeed achieve the desired performance of the power control game, it incurs significant protocol overheads during the convergence of the game. We therefore propose a hybrid protocol for better trade-offs between network optimality and protocol complexity. Evaluation results show the benefits of the proposed protocol for power control in cognitive radio networks.

To conduct collaborative beamforming in wireless ad hoc or sensor networks, several protocols must be executed, including the localization protocol, time synchronization protocol, and data dissemination protocol. In practice, however, these protocols are often limited by their complexities for achieving the ideal perfect performance. Therefore, protocol defects such as location errors, time synchronization errors, and message losses often appear in collaborative beamforming with distributed operations. In this paper, we introduce an analytical framework to analyze the impact of protocol defects on the performance of collaborative beamforming. We show numerical results of the proposed model, and explain how the proposed model can be used to mitigate the impact of protocol defects for collaborative beamforming in wireless networks.

In this paper, we investigate the problem of primary receiver protection in a cell-based network after the presence of the primary transmitter has been detected by cognitive radio. Since the primary transmitter may unicast, multicast or broadcast data to receivers anywhere in the cell, our goal is to protect the entire cell so the received SINR anywhere in the cell is maintained above the target QoS constraint. We formulate the problem using network optimization, and investigate an iterative algorithm for solving the problem. A solution based on partial sampling of monitoring points in the view angles of individual secondary transmitters is then investigated. Numerical results show the benefits of the proposed solution.

Transmitting real-time multimedia data has been a big challenge for wireless communications. The QoS experienced by the multimedia traffic is subject to the time-variant characteristics of the wireless channels. In this paper, a cross-layer algorithm is proposed to combat the wireless channel variation by adjusting the multimedia codec settings according to the MAC frame error rate in real-time. The proposed algorithm is computational efficient and the numerical experiments show that the cross-layer algorithm indeed achieves better performance even for the wireless channels in severe conditions.

In this paper we investigate the problem of voice communications across heterogeneous telephony systems on dual-mode (WiFi and GSM) mobile devices. Since GSM is a circuit-switched telephony system, existing solutions that are based on packet-switched network protocols cannot be used. We show in this paper that an enabling technology for seamless voice communications across circuit-switched and packet-switched telephony systems is the support of digital signal processing (DSP) techniques during handoffs. To substantiate our argument, we start with a framework based on the session initiation protocol (SIP) for vertical handoffs on dual-mode mobile devices. We then identify the key obstacle in achieving seamless handoffs across circuit-switched and packet-switched systems, and explain why DSP support is necessary in this context. We propose a solution that incorporates time alignment and time scaling algorithms during handoffs for supporting seamless voice communications across heterogeneous telephony systems. We conduct testbed experiments using a GSM-WiFi dual-mode notebook and evaluate the quality of speech when the call is migrated from WiFi to GSM networks. Evaluation results show that such a cross-disciplinary solution involving signal processing and networking can effectively support seamless voice communications across heterogeneous telephony systems.

In this paper, we investigate the problem of spectrum sensing in cognitive radio networks. Compared with related work that aims to propose techniques at different layers of the network protocol stack for detecting primary users, we aim to investigate the capabilities and limitations of different primary user detection techniques from the perspective of network optimization. The goal is to understand the fundamental performance tradeoffs of different primary user detection techniques without being limited by existing cognitive radio software and hardware platforms. To proceed, we first identify several dimensions for designing primary user detection techniques in cognitive radio networks, and then formulate primary user detection techniques using mixed- integer nonlinear programming (MINLP). Evaluation results show the benefits of using the proposed optimization framework for profiling the fundamental characteristics of primary user detection techniques.

In this paper, we consider a university campus that has an established infrastructure for supporting SIP-based VoIP service through the campus wireless data network. The campus WLAN, however, does not have 100% full coverage, and hence users cannot make untethered VoIP calls anywhere on campus. The goal of this paper is to overcome the limitations of such WLAN dead spots and improve user experience when making VoIP calls. Different from related work that relies on peer-to-peer communication for multi-hop relay, we propose an approach called ldquodual-mode communicationrdquo to leverage the availability of dual-mode handsets for ubiquitous communication on campus. We implement the proposed approach and evaluate its performance in the campus testbed environment. We find that an opportunistic usage of dual communication modes on mobile handsets does allow ubiquitous voice communication in WLAN dead spots. However, it has one problem as the potential lack of voice call continuity during hand-off between the two modes that can cause degradation of the speech quality. We adopt a cross-layer solution based on signal processing algorithms to address the problem, thus achieving seamless voice call continuity while enabling ubiquitous voice communication on campus. Testbed evaluations show promising results for future research along the proposed direction.

In this paper, we investigate the problem of primary user detection in cognitive radio networks. Compared with related work that aims to propose techniques at different layers of the network protocol stack for detecting primary users, we aim to investigate the capabilities and limitations of different primary user detection techniques from the perspective of network optimization. The goal is to understand fundamental performance tradeoffs of these techniques without being limited by existing cognitive radio software and hardware platforms. To proceed, we first identify several dimensions for designing primary transmitter detection techniques in cognitive radio networks, including transmitter side vs. receiver side detection, and collaborative vs. non-collaborative detection. We then formulate primary transmitter detection techniques along these dimensions using mixed-integer nonlinear programming (MINLP). Evaluation results show the benefits of using the proposed optimization framework to profile the fundamental characteristics of primary transmitter detection techniques, thus motivating future research along this direction.

In this paper, we consider multi-mode, multi-radio wireless mesh networks and investigate the impact when multiple wireless mesh networks overlap in service area. We formulate the problem of resource sharing as a network optimization problem, and present a general LP (linear programming) formulation for modeling the problem. We first find that in a system with multiple wireless mesh networks in overlap, individual mesh networks could suffer from capacity degradation if no form of inter-domain coordination is present. Therefore, it is desirable to "interwork" these wireless mesh networks by allowing inter-domain traffic relay through provisioning of "bridge" nodes. If bridge nodes are chosen arbitrarily without any careful planning, however, serious inefficiency and unfairness problem may result. We use the proposed LP formulation to show the impact of bridge node selection and performance tradeoffs between throughput unfairness and network capacity when interworking multiple wireless mesh networks. Based on simulation results, we conclude that if proper interworking is provided, significant performance gain can be obtained for overlapping wireless mesh networks.

Existing works have approached the problem of reliable transport in ad-hoc networks by proposing mechanisms to improve TCP's performance over such networks. In this paper we show through detailed arguments and simulations that several of the design elements in TCP are fundamentally inappropriate for the unique characteristics of ad-hoc networks. Given that ad-hoc networks are typically stand-alone, we approach the problem of reliable transport from the perspective that it is justifiable to develop an entirely new transport protocol that is not a variant of TCP. Toward this end, we present a new reliable transport layer protocol for ad-hoc networks called ATP (ad-hoc transport protocol). We show through ns2 based simulations that ATP outperforms both default TCP and TCP-ELFN.

A recent class of approaches for enhancing the performance of cellular wireless data networks has focused on improving the underlying network model. It has been shown that using the peer-to-peer network model, a mode of communication typically seen in ad hoc wireless networks, can result in performance improvements such as increased data rate, reduced transmission power, better load balancing, and enhanced network coverage. However, the true impact of adopting the peer-to-peer network model in such an environment is yet to be fully understood. In this paper, we investigate the performance benefits and drawbacks of using the peer-to-peer network model for Internet access in cellular wireless data networks. We find that, although the peer-to-peer network model has significantly better spatial reuse characteristics, the improved spatial reuse does not translate into better throughput performance. Instead, we observe that using the peer-to-peer network model as-is might actually degrade the throughput performance of the network. We identify and discuss the reasons behind these observations. Using the insights gained through the performance evaluations, we then propose two categories of approaches to improve the performance of the peer-to-peer network model: approaches that leverage assistance from the base station and approaches that leverage the relaying capability of multihomed hosts. Through simulation results, we show that using the peer-to-peer network model in cellular wireless data networks is a promising approach when the network model is complemented with appropriate mechanisms.

Numerous transport protocols have been proposed in related work for use by mobile hosts over wireless environments. A common theme among the design of such protocols is that they specifically address the distinct characteristics of the last-hop wireless link, such as random wireless errors, round-trip time variations, blackouts, handoffs, etc. In this paper, we argue that due to the defining role played by the wireless link on a connection's performance, locating the intelligence of a transport protocol at the mobile host that is adjacent to the wireless link can result in distinct performance advantages. To this end, we present a receiver-centric transport protocol called RCP (Reception Control Protocol) that is a TCP clone in its general behavior, but allows for better congestion control, loss recovery, and power management mechanisms compared to sender-centric approaches. More importantly, in the context of recent trends where mobile hosts are increasingly being equipped with multiple interfaces providing access to heterogeneous wireless networks, we show that a receiver-centric protocol such as RCP can enable a powerful and comprehensive transport layer solution for such multi-homed hosts. Specifically, we describe how RCP can be used to provide: (i) a scalable solution to support interface specific congestion control for a single active connection; (ii) seamless server migration capability during handoffs; and (iii) effective bandwidth aggregation when receiving data through multiple interfaces, either from one server, or from multiple replicated servers. We use both packet level simulations, and real Internet experiments to evaluate the proposed protocol.

Existing works have approached the problem of reliable transport in ad-hoc networks by proposing mechanisms to improve TCP's performance over such networks. In this paper we show through detailed arguments and simulations that several of the design elements in TCP are fundamentally inappropriate for the unique characteristics of ad-hoc networks. Given that ad hoc networks are typically stand-alone, we approach the problem of reliable transport from the perspective that it is justifiable to develop an entirely new transport protocol that is not a variant of TCP. Towards this end, we present a new reliable transport layer protocol for ad-hoc networks called ATP (ad-hoc transport protocol). We show through ns2 based simulations that ATP outperforms both default TCP and TCP-ELFN.

We propose a hybrid network model called Sphinx for cellular wireless packet data networks. Sphinx uses a peer-to-peer network model in tandem with the cellular network model to achieve higher throughput and lower-power consumption. At the same time, Sphinx avoids the typical pitfalls of the pure peer-to-peer network model including unfair resource allocation, and throughput degradation due to mobility and traffic locality. We present simulation results showing that Sphinx outperforms the cellular network model in terms of throughput and power consumption, and achieves better fairness and resilience to mobility than the peer-to-peer network model.

The TCP transport layer protocol is designed for connections that traverse a single path between the sender and receiver. However there are several environments in which multiple paths can be used by a connection simultaneously. We consider the problem of supporting striped connections that operate over multiple paths. We propose an end-to-end transport layer protocol called pTCP (parallel TCP) that allows connections to enjoy the aggregate bandwidths offered by the multiple paths, irrespective of the individual characteristics of the paths. We show that pTCP can have a varied range of applications through instantiations in three different environments: (a) bandwidth aggregation on multi-homed mobile hosts; (b) service differentiation using purely end-to-end mechanisms; (c) end-systems based network striping. In each of the applications, we demonstrate the applicability of pTCP and how its efficacy compares with existing approaches through simulation results.

We study the performance trade-offs between conventional cellular and ad-hoc peer-to-peer wireless networks. We compare, through simulations, the performance of the two network models in terms of throughput, delay, power consumption, per-flow fairness, impact of mobility, impact of traffic locality, and impact of node distribution on the network performance. The simulation results show that while peer-to-peer networks perform better in terms of throughput, delay, and power, they suffer from unfairness, and poor performance in the event of mobility and low traffic locality. We discuss the trade-offs involved in the performance of the two network models and contend that the trade-offs preclude the adoption of either of the network models as a clear solution for future wireless packet data networks. Thus, we present a simple hybrid wireless network model that uses peer-to-peer network and conventional cellular network models in tandem. It supports a dual mode of operation and has the combined advantages of cellular and peer-to-peer wireless networks without suffering from the disadvantages of either. We present simulation results showing that the hybrid network model outperforms the conventional cellular network model in terms of throughput, delay, and power consumption, and achieves better fairness and resilience to mobility than the peer-to-peer network model.

Due to the availability of a wide variety of wireless access technologies, a mobile host can potentially have subscriptions and access to more than one wireless network at a given time. In this paper, we consider such a multi-homed mobile host, and address the problem of achieving bandwidth aggregation by striping data across the multiple interfaces of the mobile host. We show that both link layer striping approaches and application layer techniques that stripe data across multiple TCP sockets do not achieve the optimal bandwidth aggregation due to a variety of factors specific to wireless networks. We propose an end-to-end transport layer approach called pTCP that effectively performs bandwidth aggregation on multi homed mobile hosts. We show through simulations that pTCP achieves the desired goals under a variety of network conditions.

While several approaches have been proposed in literature for improving the performance of wireless packet data networks, a recent class of approaches has focused on improving the underlying wireless network model itself. Several of such approaches have shown that using peer-to-peer communication, a mode of communication used typically in ad-hoc wireless networks, can result in performance improvement in terms of both throughput and energy consumption. However, the true impact of using the ad-hoc network model in wireless packet data networks has neither been comprehensively studied, nor characterized. In this paper, we investigate the benefits of using an ad-hoc network model in cellular wireless packet data networks. We find that while the ad-hoc network model has significantly better spatial reuse characteristics, the improved spatial reuse does not translate into better throughput performance. Furthermore, although considerable improvement is seen in energy consumption performance, we observe that using the ad-hoc network model as-is might actually degrade the throughput performance of the network. We identify and discuss the reasons behind these observations. Finally, using the insights gained through our performance evaluations, we discuss strawman versions of three techniques which when used in tandem with the ad-hoc network model result in better throughput, energy consumption, fairness, and mobility-resilience characteristics. Through our simulation results, we motivate that using the ad-hoc network model in conventional wireless packet data networks is a promising approach when the network model is complemented with appropriate mechanisms.

This paper presents a new approach to use prosodic information for the integration of acoustic and linguistic knowledge in continuous Mandarin speech with very large vocabulary.Since the overhead computation incurred from unification of search space is confined to the syllable boundaries, the use of prosodic information to reduce the syllable boundary hypotheses as well as the syllable matching length is shown to be effective.The inherent complexity with the very large vocabulary is also reduced by the use of phrase boundary hypotheses conjectured via the phrase-final lengthening.Experimental results show a 47.2% recognition time save with only 5.67% error rate increase using the syllable and phrase boundary hypotheses conjectured from prosodic information.

This paper presents a prototype prosodic-segment-based Mandarin dictation machine for the Chinese language with very large vocabulary. It accepts utterances continuous within a prosodic segment which is composed of one or a few word(s). It also possesses various on-line learning capabilities for fast adaptation to a new user in acoustic, lexical and linguistic levels. The overall system is implemented on an IBM/PC with an additional DSP card including a Motorola DSP 96002 chip. The word accuracy can achieve nearly 90% for a new user after he produces about 10 minutes of speech to train the system, and the accuracy can be further improved with the on-line learning functions.