arXiv subjects

K. G. Nagananda

Publications and source records attributed to K. G. Nagananda.

At least 19 recordsLinked to original sources

arXiv2020

Tight Bounds on the Weighted Sum of MMSEs with Applications in Distributed Estimation

In this paper, tight upper and lower bounds are derived on the weighted sum of minimum mean-squared errors for additive Gaussian noise channels. The bounds are obtained by constraining the input distribution to be close to a Gaussian reference distribution in terms of the Kullback--Leibler divergence. The distributions that attain these bounds are shown to be Gaussian whose covariance matrices are defined implicitly via systems of matrix equations. Furthermore, the estimators that attain the upper bound are shown to be minimax robust against deviations from the assumed input distribution. The lower bound provides a potentially tighter alternative to well-known inequalities such as the Cramér--Rao lower bound. Numerical examples are provided to verify the theoretical findings of the paper. The results derived in this paper can be used to obtain performance bounds, robustness guarantees, and engineering guidelines for the design of local estimators for distributed estimation problems which commonly arise in wireless communication systems and sensor networks.

cs.IT↗

arXiv2019

Secure Communication in Dynamic Wireless Ad hoc Networks

We consider a wireless ad hoc network in the presence of eavesdroppers (EDs), where the nodes are distributed according to independent Poisson point processes (PPPs). The legitimate nodes follow the half-duplex mode of operation employing the slotted ALOHA protocol for transmission. For such a network, a novel communication scheme that induces a time-varying secure connectivity graph (SCG) is proposed, and the connectivity behavior of this induced SCG is studied. In particular, for a legitimate node in the network, we analyze (i) the average number of incoming edges and the average number of outgoing edges; (ii) the time to nearest-neighbor secure connectivity; and (iii) a condition on the EDs' density that allows information percolation, {\ie}, a condition for the existence of a `giant' component. The average time for secure connectivity among the nodes in this giant component is shown to scale linearly with the Euclidean distance. Further, we show that by splitting the packets into two sub-packets and routing each sub-packet along paths that are sufficiently far apart can (a) potentially improve secure connectivity and (b) reduce the overall delay incurred in exchanging packets between any two legitimate nodes in the giant component.

cs.IT↗

arXiv2019

Reduced-rank Analysis of the Total Least Squares

The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of the solution at the expense of introducing a little distortion. In the context of parameter estimation, this yields an estimator whose sum of distortion plus variance is smaller than the variance of its undistorted counterpart. The method intrinsically results in an ordering mechanism for the singular vectors of the system matrix in the measurement model used for estimating the parameter of interest. According to this ordering rule, only a few \emph{dominant} singular vectors need to be selected to construct the reduced-rank solution while the rest can be discarded. The reduced-rank estimator is less sensitive to measurement errors. In this paper, we attempt to derive the reduced-rank estimator for the total least squares (TLS) problem, including the order selection rule. It will be shown that, due to the inherent structure of the problem, it is not possible to exploit the distortion-variance tradeoff in TLS formulations using existing techniques, except in some special cases. This result has not been reported previously and warrants a new viewpoint to achieve rank reduction for the TLS estimation problem. The work is motivated by the problems arising in practical applications such as channel estimation in wireless communication systems and time synchronization in wireless sensor networks.

cs.IT↗

arXiv2018

Energy-efficient Decision Fusion for Distributed Detection in Wireless Sensor Networks

This paper proposes an energy-efficient counting rule for distributed detection by ordering sensor transmissions in wireless sensor networks. In the counting rule-based detection in an $N-$sensor network, the local sensors transmit binary decisions to the fusion center, where the number of all $N$ local-sensor detections are counted and compared to a threshold. In the ordering scheme, sensors transmit their unquantized statistics to the fusion center in a sequential manner; highly informative sensors enjoy higher priority for transmission. When sufficient evidence is collected at the fusion center for decision making, the transmissions from the sensors are stopped. The ordering scheme achieves the same error probability as the optimum unconstrained energy approach (which requires observations from all the $N$ sensors) with far fewer sensor transmissions. The scheme proposed in this paper improves the energy efficiency of the counting rule detector by ordering the sensor transmissions: each sensor transmits at a time inversely proportional to a function of its observation. The resulting scheme combines the advantages offered by the counting rule (efficient utilization of the network's communication bandwidth, since the local decisions are transmitted in binary form to the fusion center) and ordering sensor transmissions (bandwidth efficiency, since the fusion center need not wait for all the $N$ sensors to transmit their local decisions), thereby leading to significant energy savings. As a concrete example, the problem of target detection in large-scale wireless sensor networks is considered. Under certain conditions the ordering-based counting rule scheme achieves the same detection performance as that of the original counting rule detector with fewer than $N/2$ sensor transmissions; in some cases, the savings in transmission approaches $(N-1)$.

cs.IT↗

arXiv2018

Caching With Time-Varying Popularity Profiles: A Learning-Theoretic Perspective

Content caching at the small-cell base stations (sBSs) in a heterogeneous wireless network is considered. A cost function is proposed that captures the backhaul link load called the `offloading loss', which measures the fraction of the requested files that are not available in the sBS caches. As opposed to the previous approaches that consider time-invariant and perfectly known popularity profile, caching with non-stationary and statistically dependent popularity profiles (assumed unknown, and hence, estimated) is studied from a learning-theoretic perspective. A probably approximately correct result is derived, which presents a high probability bound on the offloading loss difference, i.e., the error between the estimated and the optimal offloading loss. The difference is a function of the Rademacher complexity, the $β-$mixing coefficient, the number of time slots, and a measure of discrepancy between the estimated and true popularity profiles. A cache update algorithm is proposed, and simulation results are presented to show its superiority over periodic updates. The performance analyses for Bernoulli and Poisson request models are also presented.

cs.IT↗

arXiv2017

Sequential joint signal detection and signal-to-noise ratio estimation

The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance. This optimization problem is reduced to a more tractable formulation by transforming the observed signal and noise sequences to a single sequence of Bernoulli random variables; joint detection and estimation is then performed on the Bernoulli sequence. This transformation renders the problem easily solvable, and results in a computationally simpler sufficient statistic compared to the one based on the (untransformed) observation sequences. Experimental results demonstrate the advantages of the proposed method, making it feasible for applications having strict constraints on data storage and computation.

cs.IT↗

arXiv2016

A Learning-Based Approach to Caching in Heterogenous Small Cell Networks

A heterogenous network with base stations (BSs), small base stations (SBSs) and users distributed according to independent Poisson point processes is considered. SBS nodes are assumed to possess high storage capacity and to form a distributed caching network. Popular files are stored in local caches of SBSs, so that a user can download the desired files from one of the SBSs in its vicinity. The offloading-loss is captured via a cost function that depends on the random caching strategy proposed here. The popularity profile of cached content is unknown and estimated using instantaneous demands from users within a specified time interval. An estimate of the cost function is obtained from which an optimal random caching strategy is devised. The training time to achieve an $ε>0$ difference between the achieved and optimal costs is finite provided the user density is greater than a predefined threshold, and scales as $N^2$, where $N$ is the support of the popularity profile. A transfer learning-based approach to improve this estimate is proposed. The training time is reduced when the popularity profile is modeled using a parametric family of distributions; the delay is independent of $N$ and scales linearly with the dimension of the distribution parameter.

cs.IT↗

arXiv2015

An Approximately Optimal Algorithm for Scheduling Phasor Data Transmissions in Smart Grid Networks

In this paper, we devise a scheduling algorithm for ordering transmission of synchrophasor data from the substation to the control center in as short a time frame as possible, within the realtime hierarchical communications infrastructure in the electric grid. The problem is cast in the framework of the classic job scheduling with precedence constraints. The optimization setup comprises the number of phasor measurement units (PMUs) to be installed on the grid, a weight associated with each PMU, processing time at the control center for the PMUs, and precedence constraints between the PMUs. The solution to the PMU placement problem yields the optimum number of PMUs to be installed on the grid, while the processing times are picked uniformly at random from a predefined set. The weight associated with each PMU and the precedence constraints are both assumed known. The scheduling problem is provably NP-hard, so we resort to approximation algorithms which provide solutions that are suboptimal yet possessing polynomial time complexity. A lower bound on the optimal schedule is derived using branch and bound techniques, and its performance evaluated using standard IEEE test bus systems. The scheduling policy is power grid-centric, since it takes into account the electrical properties of the network under consideration.

cs.IT↗

arXiv2015

Caching with Unknown Popularity Profiles in Small Cell Networks

A heterogenous network is considered where the base stations (BSs), small base stations (SBSs) and users are distributed according to independent Poisson point processes (PPPs). We let the SBS nodes to posses high storage capacity and are assumed to form a distributed caching network. Popular data files are stored in the local cache of SBS, so that users can download the desired files from one of the SBS in the vicinity subject to availability. The offloading-loss is captured via a cost function that depends on a random caching strategy proposed in this paper. The cost function depends on the popularity profile, which is, in general, unknown. In this work, the popularity profile is estimated at the BS using the available instantaneous demands from the users in a time interval $[0,τ]$. This is then used to find an estimate of the cost function from which the optimal random caching strategy is devised. The main results of this work are the following: First it is shown that the waiting time $τ$ to achieve an $ε>0$ difference between the achieved and optimal costs is finite, provided the user density is greater than a predefined threshold. In this case, $τ$ is shown to scale as $N^2$, where $N$ is the support of the popularity profile. Secondly, a transfer learning-based approach is proposed to obtain an estimate of the popularity profile used to compute the empirical cost function. A condition is derived under which the proposed transfer learning-based approach performs better than the random caching strategy.

cs.IT↗

arXiv2015

An Electrical Structure-Based Approach to PMU Placement in the Electric Power Grid

The phasor measurement unit (PMU) placement problem is revisited by taking into account a stronger characterization of the electrical connectedness between various buses in the grid. To facilitate this study, the placement problem is approached from the perspective of the \emph{electrical structure} which, unlike previous work on PMU placement, accounts for the sensitivity between power injections and nodal phase angle differences between various buses in the power network. The problem is formulated as a binary integer program with the objective to minimize the number of PMUs for complete network observability in the absence of zero injection measurements. The implication of the proposed approach on static state estimation and fault detection algorithms incorporating PMU measurements is analyzed. Results show a significant improvement in the performance of estimation and detection schemes by employing the electrical structure-based PMU placement compared to its topological counterpart. In light of recent advances in the electrical structure of the grid, our study provides a more realistic perspective of PMU placement in the electric power grid.

eess.SY↗

arXiv2014

A PMU Scheduling Scheme for Transmission of Synchrophasor Data in Electric Power Systems

With the proposition to install a large number of phasor measurement units (PMUs) in the future power grid, it is essential to provide robust communications infrastructure for phasor data across the network. We make progress in this direction by devising a simple time division multiplexing scheme for transmitting phasor data from the PMUs to a central server: Time is divided into frames and the PMUs take turns to transmit to the control center within the time frame. The main contribution of this work is a scheduling policy based on which PMU transmissions are ordered during a time frame. The scheduling scheme is independent of the approach taken to solve the PMU placement problem, and unlike strategies devised for conventional communications, it is intended for the power network since it is fully governed by the measure of electrical connectedness between buses in the grid. To quantify the performance of the scheduling scheme, we couple it with a fault detection algorithm used to detect changes in the susceptance parameters in the grid. Results demonstrate that scheduling the PMU transmissions leads to an improved performance of the fault detection scheme compared to PMUs transmitting at random.

cs.IT↗

arXiv2013

A Unifying Framework for the Electrical Structure-Based Approach to PMU Placement in Electric Power Systems

The electrical structure of the power grid is utilized to address the phasor measurement unit (PMU) placement problem. First, we derive the connectivity matrix of the network using the resistance distance metric and employ it in the linear program formulation to obtain the optimal number of PMUs, for complete network observability without zero injection measurements. This approach was developed by the author in an earlier work, but the solution methodology to address the location problem did not fully utilize the electrical properties of the network, resulting in an ambiguity. In this paper, we settle this issue by exploiting the coupling structure of the grid derived using the singular value decomposition (SVD)-based analysis of the resistance distance matrix to solve the location problem. Our study, which is based on recent advances in complex networks that promote the electrical structure of the grid over its topological structure and the SVD analysis which throws light on the electrical coupling of the network, results in a unified framework for the electrical structure-based PMU placement. The proposed method is tested on IEEE bus systems, and the results uncover intriguing connections between the singular vectors and average resistance distance between buses in the network.

eess.SY↗

arXiv2013

Impact of system state dynamics on PMU placement in the electric power grid

The goal of this paper is to study the impact of the dynamic nature of bus voltage magnitudes and phase angles, which constitute the state of the power system, on the phasor measurement unit (PMU) placement problem. To facilitate this study, the placement problem is addressed from the perspective of the electrical structure which, unlike existing work on PMU placement, accounts for the sensitivity between power injections and nodal phase angle differences between various buses in the power network. A linear dynamic model captures the time evolution of system states, and a simple procedure is devised to estimate the state transition function at each time instant. The placement problem is formulated as a series (time steps) of binary integer programs, with the goal to obtain the minimum number of PMUs at each time step for complete network observability in the absence of zero injection measurements. Experiments are conducted on several standard IEEE test bus systems. The main thesis of this study is that, owing to the dynamic nature of the system states, for optimal power system operation the best one could do is to install a PMU on each bus of the given network, though it is undesirable from an economic standpoint.

eess.SY↗

arXiv2013

Electrical Structure-Based PMU Placement in Electric Power Systems

Recent work on complex networks compared the topological and electrical structures of the power grid, taking into account the underlying physical laws that govern the electrical connectivity between various components in the network. A distance metric, namely, resistance distance was introduced to provide a more comprehensive description of interconnections in power systems compared with the topological structure, which is based only on geographic connections between network components. Motivated by these studies, in this paper we revisit the phasor measurement unit (PMU) placement problem by deriving the connectivity matrix of the network using resistance distances between buses in the grid, and use it in the integer program formulations for several standard IEEE bus systems. The main result of this paper is rather discouraging: more number of PMUs are required, compared with those obtained using the topological structure, to meet the desired objective of complete network observability without zero injection measurements. However, in light of recent advances in the electrical structure of the grid, our study provides a more realistic perspective of PMU placement in power systems. By further exploring the connectivity matrix derived using the electrical structure, we devise a procedure to solve the placement problem without resorting to linear programming.

eess.SY↗

arXiv2012

Capacity Bounds for State-Dependent Broadcast Channels

In this paper, we derive information-theoretic performance limits for three classes of two-user state-dependent discrete memoryless broadcast channels, with noncausal side-information at the encoder. The first class of channels comprises a sender broadcasting two independent messages to two non-cooperating receivers; for channels of the second class, each receiver is given the message it need not decode; and the third class comprises channels where the sender is constrained to keep each message confidential from the unintended receiver. We derive inner bounds for all the three classes of channels. For the first and second class of channels, we discuss the rate penalty on the achievable region for having to deal with side-information. For channels of third class, we characterize the rate penalties for having to deal not only with side-information, but also to satisfy confidentiality constraints. We then derive outer bounds, where we present an explicit characterization of sum-rate bounds for the first and third class of channels. For channels of the second class, we show that our outer bounds are within a fixed gap away from the achievable rate region, where the gap is independent of the distribution characterizing this class of channels. The channel models presented in this paper are useful variants of the classical broadcast channel, and provide fundamental building blocks for cellular downlink communications with side-information, such as fading in the wireless medium, interference caused by neighboring nodes in the network, {\etc}. at the encoder; two-way relay communications; and secure wireless broadcasting.

cs.IT↗

arXiv2011

Two Classes of Broadcast Channels With Side-Information: Capacity Outer Bounds

In this paper, we derive outer bounds on the capacity region of two classes of the general two-user discrete memoryless broadcast channels with side-information at the transmitter. The first class comprises the classical broadcast channel where a sender transmits two independent messages to two receivers. A constraint that each message must be kept confidential from the unintended receiver constitutes the second class. For both classes, the conditional distribution characterizing the channel depends on a state process and the encoder has side-information provided to it in a noncausal manner. For the first class of channels, an outer bound is derived employing techniques used to prove the converse theorem for the Gel'fand-Pinsker's channel with random parameters; the bounds are tight for individual rate constraints, but can be improved upon for the sum rate. The technique for deriving outer bounds for the second class of channels hinges on the confidentiality requirements; we also derive a genie-aided outer bound, where a hypothetical genie gives the unintended message to a receiver which treats it as side-information during equivocation computation. For both classes of channels, Csiszár's sum identity plays a central role in establishing the capacity outer bounds.

cs.IT↗

arXiv2011

Secure Broadcasting With Side-Information

In this paper, we derive information-theoretic performance limits for secure and reliable communications over the general two-user discrete memoryless broadcast channel with side-information at the transmitter. The sender wishes to broadcast two independent messages to two receivers, under the constraint that each message should be kept confidential from the unintended receiver. Furthermore, the encoder has side-information - for example, fading in the wireless medium, interference caused by neighboring nodes in the network, etc. - provided to it in a noncausal manner, i.e., before the process of transmission. We derive an inner bound on the capacity region of this channel, by employing an extension of Marton's coding technique used for the classical two-user broadcast channel, in conjunction with a stochastic encoder to satisfy confidentiality constraints. Based on previously known results, we discuss a procedure to present a schematic of the achievable rate region. The rate-penalties for dealing with side-information and confidentiality constraints make the achievable region for this channel strictly smaller than the rate regions of those channels where one or both of these constraints are relaxed.

cs.IT↗

arXiv2011

Asymmetric Transmitter Cooperation in Multiuser Wireless Networks: Achievable Rate Regions

In this work, we derive achievable rate regions for the three-user interference channels with asymmetric transmitter cooperation and various decoding capabilities at the receivers. The three-user channel facilitates different ways of message sharing between the transmitters. We introduce two natural ways of extending the concept of unidirectional message sharing from two users to three users - (i) cumulative message sharing and (ii) primary-only message sharing. In addition, we define several cognitive interference channels based on the decoding capability of the receivers. We employ a coding technique, which is a combination of superposition and Gel'fand-Pinsker coding techniques, to derive an achievable rate region for each of the cognitive interference channels. Simulation results, by considering the Gaussian channel case, enables a visual comparison of the two message-sharing schemes considered in this paper. It also provides useful insights into the effect of message-splitting at the transmitters and the decoding capability of the receivers on the achievable rates.

cs.IT↗