Schatten p-norm inequalities related to a characterization of inner product spaces

Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. Moreover, \sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch.Comment: Minor revision, to appear in Math. Inequal. Appl. (MIA

On Modeling and Optimizing LTE/Wi-Fi Coexistence with Prioritized Traffic Classes

© 2018 IEEE. The dramatic growth in demand for mobile data service has prompted mobile network operators (MNOs) to explore new spectrum resources in unlicensed bands. MNOs have been recently allowed to extend LTE-based service called LTE-LAA over 5 GHz U-NII bands, currently occupied by Wi-Fi. To support applications with diverse QoS requirements, both LTE and Wi-Fi technologies introduce multiple priority classes with different channel contention parameters for accessing unlicensed bands. How these different priority classes affect the interplay between coexisting LTE and Wi-Fi technologies is still relatively under explored. In this paper, we develop a simple and efficient framework that helps MNOs assess the fair coexistence between MNOs and Wi-Fi operators with prioritized channel access under multi-channel setting. We derive an approximated close-form solution for each MNO to pre-evaluate the probability of successful transmission (PST), average contention delay, and average throughput when adopting different priority classes to serve different traffics. MNOs and Wi-Fi operators can fit our model using measurements collected offline and/or online, and use it to further optimize their systems' throughput and latency. Our results reveal that PSTs computed with our approximated closed-form model approach those collected from system-level simulations with around 95% accuracy under scenarios of dense network deployment density and high traffic intensity

Optimizing inter-operator network slicing over licensed and unlicensed bands

© 2018 IEEE. Network slicing has been considered as a key enabling technology for 5G due to its ability to customize and "slice" a common resource to support diverse services and verticals. This paper introduces a novel inter-operator network slicing framework in which multiple mobile network operators (MNOs) can cooperate and jointly slice their accessible spectrum resources in both licensed and unlicensed bands. For the licensed band slicing, we propose the inter-operator spectrum aggregation method which allows two or more MNOs to cooperate and share their licensed bands to support a common set of service types. We then consider the sharing of unlicensed bands. Since all MNOs enjoy equal rights to access unlicensed bands, we introduce the concept of right sharing for MNOs to share and trade their spectrum access rights. We develop a modified back-of-the-envelop method for the MNOs to evaluate their value of rights when coexisting with other wireless technologies. We develop a network slicing game based on the overlapping coalition formation game to investigate the possible cooperation between MNOs. We prove that our proposed game always has at least one stable slicing structure that maximizes the social welfare. To evaluate the practical performance of our proposed framework, we develop a C++-based discrete-event simulator and simulate a possible implementation of our proposed framework over 400 base station locations deployed by two primary cellular operators in the city of Dublin. Numerical results show that our proposed framework can almost double the capacity for all supported services for each operator under certain conditions

Intelligent Tracking of Network Dynamics for Cross-Technology Coexistence Over Unlicensed Bands

Unlicensed bands offer great opportunities for numerous wireless technologies, including IEEE 802.11-based systems, 4G Licensed-Assisted-Access (LAA), and 5G New Radio Unlicensed (NR-U) networks. Achieving harmonious coexistence between these technologies requires real-time adaptation of their channel access, which can be facilitated by artificial intelligence (AI) and machine learning (ML) techniques. However, to leverage such techniques, we need to characterize the state of unlicensed wireless channel and the dynamics of the coexisting systems. In this paper, we introduce the concept of Sensing Fingerprint (SF) profile to characterize the state of coexisting networks and track their dynamics over unlicensed bands. We conduct extensive experiments to show the effectiveness of SF profile in tracking key network dynamics, including sensitivity thresholds of contending devices, their mobility, traffic loads, and other channel access parameters. AI-and ML-based controllers can utilize this tool to model the state of coexisting networks and track their dynamics

Sense-Bandits: AI-based Adaptation of Sensing Thresholds for Heterogeneous-technology Coexistence Over Unlicensed Bands

In this paper, we present Sense-Bandits, an AI-based framework for distributed adaptation of the sensing thresholds (STs) over shared spectrum. This framework specifically targets the coexistence of heterogenous technologies, e.g., Wi-Fi, 4G Licensed-Assisted Access (LAA), and 5G New Radio Unlicensed (NR-U), over unlicensed channels. To access the channel, a device compares the measured power with a predefined ST value and accordingly decides if the channel is idle or not. Improper setting of the ST values creates asymmetric sensing floors, resulting in collisions due to hidden terminals and/or reduction in the spatial reuse due to exposed terminals. Optimal ST setting is challenging because it requires global knowledge of mobility, traffic loads, and channel access behavior of all contending devices. Sense-Bandits tackles this problem by employing a clustering-based multi-armed bandit (MAB) algorithm, which adapts its learning behavior based on network dynamics. Clustering allows the algorithm to track network changes in real-time, ensuring fast learning of the best ST values by classifying the state and dynamics of coexisting networks. We develop a C++-based network simulator that implements Sense-Bandits and we apply it to evaluate the coexistence of Wi-Fi and 5G NR-U systems over the unlicensed 5 GHz U-NII bands. Our simulation results indicate that ST-adaptive devices employing Sense-Bandits do not harm neighboring devices that adopt a fixed ST value

Provisioning QoS in Wi-Fi Systems with Asymmetric Full-Duplex Communications

© 2015 IEEE. The traffic volume carried by wireless local area networks (WLANs) continues to increase at a rapid pace. Full-duplex communication is a key solution for satisfying the growing traffic demand, enhancing spectrum efficiency, and reducing latency for WLAN users. In this paper, we consider the application of asymmetric full-duplex (AFD) communications in WLANs, exemplified by a Wi-Fi system. Our system model relies on a full-duplex-enabled Wi-Fi access point to simultaneously transmit uplink and downlink to a pair of half-duplex Wi-Fi stations. Providing QoS guarantees in WLANs with AFD communication capabilities is challenging due to inter-node as well as residual self-interference. The heterogeneity of the QoS requirements between paired uplink and downlink stations further complicates the problem. To tackle these challenges, we introduce a framework called AFD-QoS, which incorporates AFD communications in WLANs and supports QoS. AFD-QoS consists of three components: 1) AFD-enabled uplink/downlink station-pair selection algorithm; 2) AFD-enabled block-acknowledgment session initiation/termination protocol; and 3) joint transmission rate/AFD communication mode adaptation scheme. Our adaptation scheme relies on intelligent and cognitive approaches to improve Wi-Fi networks awareness about channel dynamics as well as inter-node and self-interference. We introduce new intelligent MAC-layer procedures for supporting QoS services in AFD communications, and cast light on many challenges and their solutions. Our simulation results indicate that AFD-QoS outperforms classical half-duplex frameworks and achieves up to 90% of the optimal AFD performance

MatchMaker: An Inter-operator Network Sharing Framework in Unlicensed Bands

© 2019 IEEE. In this paper, we consider the scenario in which mobile network operators (MNOs) share network infrastructure for operating 5G new radio (NR) services in unlicensed bands, whereby they reduce their deployment cost and extend their service coverage. Conserving privacy of MNOs' users, maintaining fairness with coexisting technologies such as Wi-Fi, and reducing communication overhead between MNOs are among top challenges limiting the feasibility and success of this sharing paradigm. To resolve above issues, we present MatchMaker, a novel framework for joint network infrastructure and unlicensed spectrum sharing among MNOs. MatchMaker extends the 3GPP's infrastructure sharing architecture, originally introduced for licensed bands, to have privacy-conserving protocols for managing the shared infrastructure. We also propose a novel privacy-conserving algorithm for channel assignment among MNOs. Although achieving an optimal channel assignment for MNOs over unlicensed bands dictates having global knowledge about MNOs' network conditions and their interference zones, our channel assignment algorithm does not require such global knowledge and maximizes the cross-technology fairness for the coexisting systems. We let the manager, controlling the shared infrastructure, estimate potential interference among MNOs and Wi-Fi systems by asking MNOs to propose their preferred channel assignment and monitoring their average contention delay overtime. The manager only accepts/rejects MNOs' proposals and builds contention graph between all colocated devices. Our results show that MatchMaker achieves fairness up to 90% of the optimal alpha-fairness-based channel assignment while still preserving MNOs' privacy

Full-duplex spectrum sensing and fairness mechanisms for Wi-Fi/LTE-U coexistence

© 2016 IEEE. In this paper, we investigate the coexistence problem between Wi-Fi and a pre-standard form of LTE over unlicensed bands, namely, LTE-Unlicensed (LTE-U). We address two coexistence problems. First, the different access mechanisms for Wi-Fi and LTE-U can lead to an increase in the collision rate and higher latency for both systems. We propose a modified Wi-Fi operation mode, whereby Wi-Fi stations (STAs) carry out simultaneous spectrum sensing and transmission to reduce the time required for collision detection. Specifically, we propose and analyze a full-duplex (FD) based detection framework that can differentiate between Wi-Fi and LTE-U signals while taking into account residual self- interference. Second, the ability to differentiate between Wi-Fi and LTE-U signals motivates the idea of adapting the clear channel assessment (CCA) threshold according to the type of the detected signal. Inspired by upcoming Wi-Fi standards (e.g., IEEE 802.11ax), we propose a CCA threshold adaptation scheme and study via simulations its optimal setting so as to maximize the spatial reuse while maintaining fairness between LTE-U and Wi-Fi systems

Intelligent-CW: AI-based Framework for Controlling Contention Window in WLANs

© 2019 IEEE. The heterogeneity of technologies that operate over the unlicensed 5 GHz spectrum, such as LTE-Licensed-Assisted-Access (LAA), 5G New Radio Unlicensed (NR-U), and WiFi, calls for more intelligent and efficient techniques to coordinate channel access beyond what current standards offer. Wi-Fi standards require nodes to adopt a fixed value for the minimum contention window (CW{min}), which prohibits a node from reacting to aggressive nodes that set their CWmin to small values. To address this problem, we propose a framework called Intelligent-CW (ICW) that allows nodes to adapt their CWmin values based on observed transmissions, ensuring they receive their fair share of the channel airtime. The CWmin value at a node is set based on a random forest, a machine learning model that includes a large number of decision trees. We train the random forest in a supervised manner over a large number of WLAN scenarios, including different misbehaving and aggressive scenarios. Under aggressive scenarios, our simulation results reveal that ICW provides nodes with higher throughput (153.9% gain) and 64% lower frame latency than standard techniques. In order to measure the fairness contribution of individual nodes, we introduce a new fairness metric. Based on this metric, ICW is shown to provide 10. 89 times improvement in fairness in aggressive scenarios compared to standard techniques

Harmonious Cross-Technology Coexistence with Heterogeneous Traffic in Unlicensed Bands: Analysis and Approximations

IEEE The dramatic growth in demand for mobile data has prompted mobile network operators (MNOs) to explore spectrum sharing in unlicensed bands. MNOs have been allowed recently to operate their LTE services over the 5 GHz Unlicensed National Information Infrastructure (U-NII) bands, currently occupied by Wi-Fi. The unlicensed LTE operation has been standardized by 3GPP under the name Licensed Assisted Access (LAA). Unlicensed 5G New radio (NR) operation over the U-NII bands, a.k.a., NR-Unlicensed (NR-U), is also being explored. To support applications with diverse quality of service requirements, LAA, NR-U, and Wi-Fi technologies offer multiple priority classes with different contention parameters for accessing an unlicensed channel. How these different classes affect the interplay between coexisting MNOs and Wi-Fi systems is still a relatively under-explored topic. In this paper, we develop a simple yet efficient framework for fair coexistence between LTE MNOs and Wi-Fi systems, each with multiple priority classes. We derive approximate closed-form solutions for the probability of successful transmission (PST), average contention delay, and average throughput under different LAA and Wi-Fi priority classes. LTE and Wi-Fi operators can fit these solutions to offline and/or online measurements, and use them to further optimize their system throughput and latency. Our results reveal that PSTs computed with our approximate models are within 5% of these obtained via simulation under dense network deployments and high traffic loads