Due to their effectiveness in capturing similarities between different entities, graphical models are widely used to represent datasets that reside on irregular and complex manifolds. Graph signal processing offers support to handle such complex datasets. In this paper, we propose a novel graph filter design method for semi-supervised data classification. The proposed design uses multiple graph shift matrices, one for each feature, and is shown to provide improved performance when the feature qualities are uneven. We introduce three methods to optimize for the graph filter coefficients and the graph combining coefficients. The first method uses the alternating minimization approach. In the second method, we optimize our objective function by convex relaxation that provides a performance benchmark. The third method adopts a genetic algorithm, which is computationally efficient and better at controlling overfitting. In our simulation experiments, we use both synthetic and real datasets with informative and non-informative features. Monte Carlo simulations demonstrate the effectiveness of multiple graph shift operators in the graph filters. Significant improvements in comparison to conventional graph filters are shown, in terms of average error rate and confidence scores. Furthermore, we perform cross validation to show how our approach can control overfitting and improve generalization performance.

This study considers a federated learning setup where cost-sensitive and strategic agents train a learning model with a server. During each round, each agent samples a minibatch of training data and sends his gradient update. As an increasing function of his minibatch size choice, the agent incurs a cost associated with the data collection, gradient computation and communication. The agents have the freedom to choose their minibatch size and may even opt out from training. To reduce his cost, an agent may diminish his minibatch size, which may also cause an increase in the noise level of the gradient update. The server can offer rewards to compensate the agents for their costs and to incentivize their participation but she lacks the capability of validating the true minibatch sizes of the agents. To tackle this challenge, the proposed reward mechanism evaluates the quality of each agent's gradient according to the its distance to a reference which is constructed from the gradients provided by other agents. It is shown that the proposed reward mechanism has a cooperative Nash equilibrium in which the agents determine the minibatch size choices according to the requests of the server.

A relationship between the growth-rate of log-optimal portfolios and capacity of fading single-input multiple output (SIMO) channels are established. Using this relation, stock vector stochastic processes that model the investment environments are stochastically ordered using different criteria. The presence of side information (SI) is considered, and a bound on the gains in the growth-rate due to SI is derived along with data processing inequality and convexity properties. A statistical test on the usefulness of SI that does not require the computation of the optimal portfolio vector in the presence of SI is introduced and its several variants are discussed.

Using graphs to represent data sets that reside on irregular and complex structures can bring special advantages. Graph signal processing (DSP G ) converts traditional DSP operators, such as time shift, linear filters and Fourier transform, from time and frequency domain to the graph domain. In machine learning applications, DSP G provides an approach for semi-supervised classification. Different from conventional graph-filter-based classifiers, we propose a new graph filter with multiple graph shift matrices that can provide better classification performance when the feature quality is uneven. To solve the resulting non-convex problem, a tight and efficient convex relaxation approach is introduced. Through a branch and bound optimization method, we can find the mapping from the optimum relaxed parameter set to original parameter set, which technically provides the globally optimum solution. Simulation experiments corroborate our results.

We study a system with a full-duplex (FD) amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay and a single antenna at the source and the destination. The residual self-interference (RSI) is shown to behave as inter-symbol interference (ISI) at the destination. Assuming Rayleigh fading on all the channels, we derive the end-to-end impulse response and consider diversity combining schemes including Equal Gain Transmission (EGT), Maximal Ratio Transmission (MRT) and Antenna Selection (AS) strategies at the relay. The performances of the proposed techniques are analyzed based on the outage probability that is computed at the output of the equalizer at the destination.

A fully distributed algorithm for estimating the center and the radius of the smallest sphere that contains a wireless sensor network is proposed. The center finding problem is formulated as a convex optimization problem in summation form by using a soft-max approximation to the maximum function. Diffusion adaptation method is used where states of nodes converge to the estimated center distributively. Then, distributed max consensus is used to compute the radius. The proposed algorithm is fully distributed in the sense that each node in the network only needs to know its own location and nodes do not need to be pre-labeled. The algorithm works for any connected graph structure. The performance of the proposed algorithm is analyzed and it is shown that there is a tradeoff: a larger design parameter results in a more accurate center estimation but also makes the convergence speed of the distributed algorithm slower. It is also shown that the proposed algorithm can also be used to estimate the center and radius of the (not necessarily location-based) data at sensor nodes in a distributed way, thereby providing information and insights about the global data at each sensor. Simulation results corroborating the theory are also provided.

Channel estimation and optimal training sequence design for full-duplex one-way relays are investigated. We propose a training scheme to estimate the residual self-interference (RSI) channel and the channels between nodes simultaneously. A maximum likelihood estimator is implemented with the Broyden-Fletcher-Goldfarb-Shanno algorithm. In the presence of RSI, the overall source-to-destination channel becomes an inter-symbol-interference (ISI) channel. With the help of estimates of the RSI channel, the destination is able to cancel the ISI through equalization. We derive and analyze the Cramer-Rao bound (CRB) in closed-form by using the asymptotic properties of Toeplitz matrices. The optimal training sequence is obtained by minimizing the CRB. Extensions for the fundamental one-way relay model to the frequency-selective fading channels and the multiple relays case are also considered. For the former, we propose a training scheme to estimate the overall channel, and for the latter the CRB and the optimal number of relays are derived when the distance between the source and the destination is fixed. Simulations using LTE parameters corroborate our theoretical results.

Estimation of both cascaded and residual self-interference (RSI) channels and a new training frame structure are considered for full-duplex (FD) amplify-and-forward (AF) one-way relay networks with rapidly time-varying individual channels. To estimate the RSI and the rapidly time-varying cascaded channels, we propose a new training frame structure in which orthogonal training blocks are sent by the source node and delivered to the destination over an FD-AF relay. Exploiting the orthogonality of the training blocks, we obtain two decoupled training signal models for the estimation of the RSI and the cascaded channels. We apply linear minimum mean square error (MMSE) based estimators to the cascaded channel as well as RSI channel. In order to investigate the mean square error (MSE) performance of the system, we also derive the Bayesian Cramer-Rao lower bound. As another performance benchmark, we also assess the symbol error rate (SER) performances corresponding to the estimated and the perfect channel state information available at the receiver side. Computer simulations exhibit the proposed training frame structure and the linear MMSE estimator MSE and SER performances are shown.

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte-Carlo simulations are used to supplement our analytical results.

In this work we study the problem of hard-deadline constrained data offloading in cellular networks. A single-Base-Station (BS) single-frequency-channel down-link system is studied where users request the same packet from the BS at the beginning of each time slot. Packets have a hard deadline of one time slot. The slot is divided into two phases. Out of those users having high channel gain allowing them to decode the packet in the first phase, one is chosen to rebroadcast it to the remaining users in the second phase. This gives the remaining users a second opportunity to potentially decode this packet before the deadline passes. By this, the BS has offloaded the packet to a “local network of users” which eliminates unnecessary BS retransmissions. The problem is modeled as a rate-adaptation and scheduling optimization problem to maximize the duration of this second phase such that each user receives a certain percentage of the packets. We show that the proposed algorithm has a polynomial complexity in the number of users with optimal performance.

The analysis of a distributed consensus algorithm for estimating the maximum of the node initial state values in a network is considered in the presence of communication noise. Conventionally, the maximum is estimated by updating the node state value with the largest received measurements in every iteration at each node. However, due to additive channel noise, the estimate of the maximum at each node has a positive drift at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used to study this ergodic process, wherein, at each iteration, the state values are multiplied by a random matrix characterized by the noise distribution. The growth rate of the state values due to noise is studied by analyzing the Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is bounded by a constant which depends on the spectral radius of the network and the noise variance. Simulation results supporting the theory are also presented.

We consider a joint scheduling-and-power-allocation problem of a downlink cellular system. The system consists of two groups of users: real-time (RT) and non-real-time (NRT) users. Given an average power constraint on the base station, the problem is to find an algorithm that satisfies the RT hard deadline constraint and NRT queue stability constraint. We propose two sum-rate-maximizing algorithms that satisfy these constraints as well as achieving the system's capacity region. In both algorithms, the power allocation policy has a closed-form expression for the two groups of users. However, interestingly, the power policy of the RT users differ in structure from that of the NRT users. The first algorithm is optimal for the on-off channel model with a polynomial-time scheduling complexity in the number of RT users. The second, on the other hand, works for any channel fading model which is shown, through simulations, to have an average complexity that is close-to-linear. We also show the superiority of the proposed algorithms over existing approaches using extensive simulations.

Distributed node counting in wireless sensor networks can be important in various applications, such as network maintenance and information aggregation. In this paper, a distributed consensus algorithm for estimating the number of nodes in a wireless sensor network in the presence of communication noise is introduced. In networks with a fusion center, counting the number of nodes can easily be done by letting each node to transmit a fixed constant value to the fusion center. In a network without a fusion center, where nodes do not know the graph structure, estimating the number of nodes is not straightforward. The proposed algorithm is based on distributed average consensus and norm estimation. Different sources of error are explicitly discussed; the Fisher information and the distribution of the final estimate are derived. Several design parameters and how they affect the performance of the algorithm are studied, which provide guidelines toward making the estimation error smaller. Simulation results corroborating the theory are also provided.

We consider a joint scheduling-and-power-allocation problem of a downlink cellular system. The system consists of two groups of users: real-time (RT) and non-real-time (NRT) users. Given an average power constraint on the base station, the problem is to find an algorithm that satisfies the RT hard deadline constraint and NRT queue stability constraint. We propose a sum-rate-maximizing algorithm that satisfies these constraints. We also show, through simulations, that the proposed algorithm has an average complexity that is close-to-linear in the number of RT users. The power allocation policy in the proposed algorithm has a closed-form expression for the two groups of users. However, interestingly, the power policy of the RT users differ in structure from that of the NRT users. We also show the superiority of the proposed algorithms over existing approaches using extensive simulations.

This paper proposes to unify fading distributions by modeling the instantaneous SNR as an infinitely divisible random variable, which is a known class of random variables from the probability theory literature. A random variable is said to be infinitely divisible if it can be written as a sum of n >= 1 independent and identically distributed random variables for each n. The proposed unification subsumes several classes of multipath and shadowing fading distributions previously proposed in the wireless communication literature. We show that infinitely divisible random variables have many useful mathematical properties that are applied in the performance analysis of wireless systems. Specific applications include diversity analysis and partial ordering of fading distributions.

A relay-aided cooperative underlay cognitive radio system with an interference constraint at the primary receiver (PR) is considered. When the primary user (PU) is active, those secondary users (SUs) whose interference at the PR is above a threshold will amplify-and-forward PU's signal to enhance the PU's performance, and those SUs below this threshold will proceed with their own transmission in an underlay fashion. As the number of relay SUs increases, the PU's performance will be improved but cause degradation of SU's performance concurrently. With our overall average bit error rate and the average combined sum achievable rate metrics, we analytically quantify this fundamental performance trade-off in the large number of SUs regime. Both deterministic and random number of SUs scenarios are considered. Monte-Carlo simulations are provided to verify our analytical results.

A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state value with the largest received measurements in every iteration at each sensor. In the presence of communication noise, however, the maximum estimate will incorrectly drift and the estimate at each sensor will diverge. As a result, a soft-max approximation together with a non-linear consensus algorithm is introduced herein. A design parameter controls the tradeoff between the soft-max error and convergence speed. An analysis of this tradeoff gives a guideline toward how to choose the design parameter for the max estimate. We also show that if some prior knowledge of the initial measurements is available, the consensus process can converge faster by using an optimal step size in the iterative algorithm. A shifted non-linear bounded transmit function is also introduced for faster convergence when sensor nodes have some prior knowledge of the initial measurements. Simulation results corroborating the theory are also provided.

A cooperative underlay cognitive radio system with an instantaneous interference constraint at the primary receiver is considered. Secondary users (SU) whose interference above this threshold will relay primary user's (PU) signal, and the rest will fulfill their own underlay transmissions. Hence the numbers of relay and underlay SUs are random at a time instant. As the mean number of relay SUs increases, the PU's performance will be improved which causes degradation of underlay SUs' performance concurrently. We will quantify this fundamental performance trade-off by deriving the optimal ratio between the mean number of relay and underlay SUs in closed form.

An uplink cognitive radio system with a single primary user (PU) and multiple secondary users (SUs) is considered. The SUs have an individual average delay constraint and an aggregate average interference constraint to the PU. If the interference channels between the SUs and the PU are statistically different due to the different physical locations of the SUs, the SUs will experience different delay performances. This is because SUs located closer to the PU transmit with lower power levels. A dynamic scheduling-and-power-allocation policy that uses the dynamic programming, is proposed. The proposed policy can provide the required average delay guarantees to all SUs irrespective of their location as well as protect the PU from harmful interference. The policy is shown to be asymptotically delay optimal in the light traffic regime. Motivated, by the high complexity of the dynamic programming algorithm in the optimal policy we exploit the structure of the problem's solution to present an alternative suboptimal policy. Through simulations we show that in both light and heavy traffic regimes, the delay performance of the suboptimal policy is within 0.3 % from the optimal policy and both outperforming existing methods.

Monitoring utility-scale solar arrays was shown to minimize cost of maintenance and help optimize the performance of the array under various conditions. In this paper, we describe the design of an 18 kW experimental facility that consists of 104 panels fitted with smart monitoring devices. Each of these devices embeds sensors, wireless transceivers, and relays that enable continuous monitoring, fault detection, and real-time connection topology changes. The facility enables networked data exchanges via the use of wireless data sharing with servers, fusion and control centers, and mobile devices. Research planned at this stage includes developing machine learning methods for fault detection. Preliminary simulation results on fault detection using machine learning are given in this paper.