arXiv subjects
Publications and source records attributed to H. Vincent Poor.
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition for the equality is established by making a connection to the famous Cauchy functional equation.
In this report, the fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) with and without feedback are fully characterized. More specifically, all the achievable information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. Furthermore, the fundamental limits on the individual and sum- rates given a minimum energy rate ensured at an energy harvester are also characterized. In the case without feedback, an achievability scheme based on power-splitting and successive interference cancellation is shown to be optimal. Alternatively, in the case with feedback (G-MAC-F), a simple yet optimal achievability scheme based on power-splitting and Ozarow's capacity achieving scheme is presented. Finally, the energy transmission enhancement induced by the use of feedback is quantified. Feedback can at most double the energy transmission rate at high SNRs when the information transmission sum-rate is kept fixed at the sum-capacity of the G-MAC, but it has no effect at very low SNRs.
Finite resolution analog beamforming (FRAB) has been recognized as an effective approach to reduce hardware costs in massive multiple-input multiple-output (MIMO) and millimeter-wave networks. However, the use of FRAB means that the beamformers are not perfectly aligned with the users' channels and multiple users may be assigned similar or even identifical beamformers. This letter shows how non-orthogonal multiple access (NOMA) can be used to exploit this feature of FRAB, where a single FRAB based beamformer is shared by multiple users. Both analytical and simulation results are provided to demonstrate the excellent performance achieved by this new NOMA transmission scheme.
Non-orthogonal multiple access (NOMA) schemes have been proposed for the next generation of mobile communication systems to improve the access efficiency by allowing multiple users to share the same spectrum in a non-orthogonal way. Due to the strong co-channel interference among mobile users introduced by NOMA, it poses significant challenges for system design and resource management. This article reviews resource management issues in NOMA systems. The main taxonomy of NOMA is presented by focusing on the following two categories: power-domain NOMA and code-domain NOMA. Then a novel radio resource management framework is presented based on game-theoretic models for uplink and downlink transmissions. Finally, potential applications and open research directions in the area of resource management for NOMA are provided.
Motivated by the recently launched mobile data trading markets (e.g., China Mobile Hong Kong's 2nd exChange Market), in this paper we study the mobile data trading problem under the future data demand uncertainty. We introduce a brokerage-based market, where sellers and buyers propose their selling and buying quantities, respectively, to the trading platform that matches the market supply and demand. To understand the users' realistic trading behaviors, a prospect theory (PT) model from behavioral economics is proposed, which includes the widely adopted expected utility theory (EUT) as a special case. Although the PT modeling leads to a challenging non-convex optimization problem, the optimal solution can be characterized by exploiting the unimodal structure of the objective function. Building upon our analysis, we design an algorithm to help estimate the user's risk preference and provide trading recommendations dynamically, considering the latest market and usage information. It is shown in our simulation that the risk preferences have a significant impact on the user's decision and outcome: a risk-averse dominant user can guarantee a higher minimum profit in the trading, while a risk-seeking dominant user can achieve a higher maximum profit. By comparing with the EUT benchmark, it is shown that a PT user with a low reference point is more willing to buy mobile data. Moreover, when the probability of high future data demand is low, a PT user is more willing to buy mobile data due to the probability distortion comparing with an EUT user.
This paper considers the joint design of user power allocation and relay beamforming in relaying communications, in which multiple pairs of single-antenna users exchange information with each other via multiple-antenna relays in two time slots. All users transmit their signals to the relays in the first time slot while the relays broadcast the beamformed signals to all users in the second time slot. The aim is to maximize the system's energy efficiency (EE) subject to quality-of-service (QoS) constraints in terms of exchange throughput requirements. The QoS constraints are nonconvex with many nonlinear cross-terms, so finding a feasible point is already computationally challenging. The sum throughput appears in the numerator while the total consumption power appears in the denominator of the EE objective function. The former is a nonconcave function and the latter is a nonconvex function, making fractional programming useless for EE optimization. Nevertheless, efficient iterations of low complexity to obtain its optimized solutions are developed. The performances of the multiple-user and multiple-relay networks under various scenarios are evaluated to show the merit of the paper development.
Considering a multiple-user multiple-input multiple-output (MIMO) channel with an eavesdropper, this letter develops a beamformer design to optimize the energy efficiency in terms of secrecy bits per Joule under secrecy quality-of-service constraints. This is a very difficult design problem with no available exact solution techniques. A path-following procedure, which iteratively improves its feasible points by using a simple quadratic program of moderate dimension, is proposed. Under any fixed computational tolerance the procedure terminates after finitely many iterations, yielding at least a locally optimal solution. Simulation results show the superior performance of the obtained algorithm over other existing methods.
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.) samples drawn from a distribution p, whereas each anomalous sequence contains m i.i.d. samples drawn from a distribution q that is distinct from p. The distributions p and q are assumed to be unknown in advance. Distribution-free tests are constructed using maximum mean discrepancy as the metric, which is based on mean embeddings of distributions into a reproducing kernel Hilbert space. The probability of error is bounded as a function of the sample size m, the number s of anomalous sequences and the number n of sequences. It is then shown that with s known, the constructed test is exponentially consistent if m is greater than a constant factor of log n, for any p and q, whereas with s unknown, m should has an order strictly greater than log n. Furthermore, it is shown that no test can be consistent for arbitrary p and q if m is less than a constant factor of log n, thus the order-level optimality of the proposed test is established. Numerical results are provided to demonstrate that our tests outperform (or perform as well as) the tests based on other competitive approaches under various cases.
Large scale power failures induced by severe weather have become frequent and damaging in recent years, causing millions of people to be without electricity service for days. Although the power industry has been battling weather-induced failures for years, it is largely unknown how resilient the energy infrastructure and services really are to severe weather disruptions. What fundamental issues govern the resilience? Can advanced approaches such as modeling and data analytics help industry to go beyond empirical methods? This paper discusses the research to date and open issues related to these questions. The focus is on identifying fundamental challenges and advanced approaches for quantifying resilience. In particular, a first aspect of this problem is how to model large-scale failures, recoveries and impacts, involving the infrastructure, service providers, customers, and weather. A second aspect is how to identify generic vulnerability (i.e., non-resilience) in the infrastructure and services through large-scale data analytics. And, a third is to understand what resilience metrics are needed and how to develop them.
An outage detection framework for power distribution networks is proposed. Given the tree structure of the distribution system, a method is developed combining the use of real-time power flow measurements on edges of the tree with load forecasts at the nodes of the tree. A maximum a posteriori detector {\color{black} (MAP)} is formulated for arbitrary number and location of outages on trees which is shown to have an efficient detector. A framework relying on the maximum missed detection probability is used for optimal sensor placement and is solved for tree networks. Finally, a set of case studies is considered using feeder data from the Pacific Northwest National Laboratories. We show that a 10\% loss in mean detection reliability network wide reduces the required sensor density by 60 \% for a typical feeder if efficient use of measurements is performed.
This paper considers the application of non-orthogonal multiple access (NOMA) to a multi-user network with mixed multicasting and unicasting traffic. The proposed design of beamforming and power allocation ensures that the unicasting performance is improved while maintaining the reception reliability of multicasting. Both analytical and simulation results are provided to demonstrate that the use of the NOMA assisted multicast-unicast scheme yields a significant improvement in spectral efficiency compared to orthogonal multiple access (OMA) schemes which realize multicasting and unicasting services separately. Since unicasting messages are broadcasted to all the users, how the use of NOMA can prevent those multicasting receivers intercepting the unicasting messages is also investigated, where it is shown that the secrecy unicasting rate achieved by NOMA is always larger than or equal to that of OMA. This security gain is mainly due to the fact that the multicasting messages can be used as jamming signals to prevent potential eavesdropping when the multicasting and unicasting messages are superimposed together following the NOMA principle.
As the latest member of the multiple access family, non-orthogonal multiple access (NOMA) has been recently proposed for 3GPP Long Term Evolution (LTE) and envisioned to be an essential component of 5th generation (5G) mobile networks. The key feature of NOMA is to serve multiple users at the same time/frequency/code, but with different power levels, which yields a significant spectral efficiency gain over conventional orthogonal MA. This article provides a systematic treatment of this newly emerging technology, from its combination with multiple-input multiple-output (MIMO) technologies, to cooperative NOMA, as well as the interplay between NOMA and cognitive radio. This article also reviews the state of the art in the standardization activities concerning the implementation of NOMA in LTE and 5G networks.
Physical security of power networks under power injection attacks that alter generation and loads is studied. The system operator employs Phasor Measurement Units (PMUs) for detecting such attacks, while attackers devise attacks that are unobservable by such PMU networks. It is shown that, given the PMU locations, the solution to finding the sparsest unobservable attacks has a simple form with probability one, namely, $κ(G^M) + 1$, where $κ(G^M)$ is defined as the vulnerable vertex connectivity of an augmented graph. The constructive proof allows one to find the entire set of the sparsest unobservable attacks in polynomial time. Furthermore, a notion of the potential impact of unobservable attacks is introduced. With optimized PMU deployment, the sparsest unobservable attacks and their potential impact as functions of the number of PMUs are evaluated numerically for the IEEE 30, 57, 118 and 300-bus systems and the Polish 2383, 2737 and 3012-bus systems. It is observed that, as more PMUs are added, the maximum potential impact among all the sparsest unobservable attacks drops quickly until it reaches the minimum sparsity.
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.) time-series consisting of a nonlinear function of the true but unknown parameter corrupted by noise. A distributed recursive estimator of the \emph{consensus} + \emph{innovations} type, namely $\mathcal{CIWNLS}$, is proposed, in which the agents update their parameter estimates at each observation sampling epoch in a collaborative way by simultaneously processing the latest locally sensed information~(\emph{innovations}) and the parameter estimates from other agents~(\emph{consensus}) in the local neighborhood conforming to a pre-specified inter-agent communication topology. Under rather weak conditions on the connectivity of the inter-agent communication and a \emph{global observability} criterion, it is shown that at every network agent, the proposed algorithm leads to consistent parameter estimates. Furthermore, under standard smoothness assumptions on the local observation functions, the distributed estimator is shown to yield order-optimal convergence rates, i.e., as far as the order of pathwise convergence is concerned, the local parameter estimates at each agent are as good as the optimal centralized nonlinear least squares estimator which would require access to all the observations across all the agents at all times. In order to benchmark the performance of the proposed distributed $\mathcal{CIWNLS}$ estimator with that of the centralized nonlinear least squares estimator, the asymptotic normality of the estimate sequence is established and the asymptotic covariance of the distributed estimator is evaluated. Finally, simulation results are presented which illustrate and verify the analytical findings.
The proliferation of distributed generation and storage units is leading to the development of local, small-scale distribution grids, known as microgrids (MGs). In this paper, the problem of optimizing the energy trading decisions of MG operators (MGOs) is studied using game theory. In the formulated game, each MGO chooses the amount of energy that must be sold immediately or stored for future emergencies, given the prospective market prices which are influenced by other MGOs' decisions. The problem is modeled using a Bayesian game to account for the incomplete information that MGOs have about each others' levels of surplus. The proposed game explicitly accounts for each MGO's subjective decision when faced with the uncertainty of its opponents' energy surplus. In particular, the so-called framing effect, from the framework of prospect theory (PT), is used to account for each MGO's valuation of its gains and losses with respect to an individual utility reference point. The reference point is typically different for each individual and originates from its past experiences and future aspirations. A closed-form expression for the Bayesian Nash equilibrium is derived for the standard game formulation. Under PT, a best response algorithm is proposed to find the equilibrium. Simulation results show that, depending on their individual reference points, MGOs can tend to store more or less energy under PT compared to classical game theory. In addition, the impact of the reference point is found to be more prominent as the emergency price set by the power company increases.
This paper investigates secrecy rate optimization for a multicasting network, in which a transmitter broadcasts the same information to multiple legitimate users in the presence of multiple eavesdroppers. In order to improve the achievable secrecy rates, private jammers are employed to generate interference to confuse the eavesdroppers. These private jammers charge the legitimate transmitter for their jamming services based on the amount of interference received at the eavesdroppers. Therefore, this secrecy rate maximization problem is formulated as a Stackelberg game, in which the private jammers and the transmitter are the leaders and the follower of the game, respectively. A fixed interference price scenario is considered first, in which a closed-form solution is derived for the optimal amount of interference generated by the jammers to maximize the revenue of the legitimate transmitter. Based on this solution, the Stackelberg equilibrium of the proposed game, at which both legitimate transmitter and the private jammers achieve their maximum revenues, is then derived. Simulation results are also provided to validate these theoretical derivations.
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matches the algebraic structure of the channel and the joint source distribution fulfills certain conditions, the secrecy computation-capacity equals the computation capacity, which is the supremum of all achievable computation rates without secrecy constraints. Unlike the case of securely transmitting messages, no additional randomness is needed at the encoders nor does the legitimate receiver need any advantage over the eavesdropper. The results therefore show that the problem of securely computing a function over a multiple-access wiretap channel may significantly differ from the one of securely communicating messages.
The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the asymptotic ratio of its rate-distortion function $R(D)$ to $\log {1\over D}$ as the distortion $D$ approaches zero, is equal to its information dimension (ID). This generalizes an earlier result by Kawabata and Dembo and provides an operational approach to evaluate the ID of a process, which previously was shown to be closely related to the effective dimension of the underlying process and also to the fundamental limits of compressed sensing. The relation between RDD and ID is illustrated for a piecewise constant process.