Hoi-To Wai

Transmit Solutions for MIMO Wiretap Channels using Alternating Optimization

This paper considers transmit optimization in multi-input multi-output (MIMO) wiretap channels, wherein we aim at maximizing the secrecy capacity or rate of an MIMO channel overheard by one or multiple eavesdroppers. Such optimization problems are nonconvex, and appear to be difficult especially in the multi-eavesdropper scenario. In this paper, we propose an alternating optimization (AO) approach to tackle these secrecy optimization problems. We first consider the secrecy capacity maximization (SCM) problem in the single eavesdropper scenario. An AO algorithm is derived through a judicious SCM reformulation. The algorithm conducts some kind of reweighting and water-filling in an alternating fashion, and thus is computationally efficient to implement. We also prove that the AO algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point of the SCM problem. Then, we turn our attention to the multiple eavesdropper scenario, where the artificial noise (AN)-aided secrecy rate maximization (SRM) problem is considered. Although the AN-aided SRM problem has a more complex problem structure than the previous SCM, we show that AO can be extended to deal with the former, wherein the problem is handled by solving convex problems in an alternating fashion. Again, the resulting AO method is proven to have KKT point convergence guarantee. For fast implementation, a custom-designed AO algorithm based on smoothing and projected gradient is also derived. The secrecy rate performance and computational efficiency of the proposed algorithms are demonstrated by simulations.

Active Sensing of Social Networks

This paper develops an active sensing method to estimate the relative weight (or trust) agents place on their neighbors’ information in a social network. The model used for the regression is based on the steady state equation in the linear DeGroot model under the influence of stubborn agents; i.e., agents whose opinions are not influenced by their neighbors. This method can be viewed as a social RADAR, where the stubborn agents excite the system and the latter can be estimated through the reverberation observed from the analysis of the agents’ opinions. The social network sensing problem can be interpreted as a blind compressed sensing problem with a sparse measurement matrix. We prove that the network structure will be revealed when a sufficient number of stubborn agents independently influence a number of ordinary (non-stubborn) agents. We investigate the scenario with a deterministic or randomized DeGroot model and propose a consistent estimator of the steady states for the latter scenario. Simulation results on synthetic and real world networks support our findings.

Cheap semidefinite relaxation MIMO detection using row-by-row block coordinate descent

This paper considers the problem of low complexity implementation of high-performance semidefinite relaxation (SDR) MIMO detection methods. Currently, most SDR MIMO detectors are implemented using interior-point methods. Although such implementations have worst-case polynomial complexity (approximately cubic in the problem size), they can be quite computationally costly in practice. Here we depart from the interior-point method framework and investigate the use of other low per-iteration-complexity techniques for SDR MIMO detection. Specifically, we employ the row-by-row (RBR) method, which is a particular version of block coordinate descent, to solve the semidefinite programs that arise in the SDR MIMO context with an emphasis on the QPSK scenario. In each iteration of the RBR method, only matrix-vector multiplications are needed, and hence it can be implemented in a very efficient manner. Our simulation results show that the RBR method can indeed offer a significant speedup in runtime, while providing bit error rate performance on par with the interior-point methods.

Optimal Pricing to Manage Electric Vehicles in Coupled Power and Transportation Networks

We study the system-level effects of the introduction of large populations of Electric Vehicles (EVs) on the power and transportation networks. We assume that each EV owner solves a decision problem to pick a cost-minimizing charge and travel plan. This individual decision takes into account traffic congestion in the transportation network, affecting travel times, as well as congestion in the power grid, resulting in spatial variations in electricity prices for battery charging. We show that this decision problem is equivalent to finding the shortest path on an “extended” transportation graph, with virtual arcs that represent charging options. Using this extended graph, we study the collective effects of a large number of EV owners individually solving this path planning problem. We propose a scheme in which independent power and transportation system operators can collaborate to manage each network towards a socially optimum operating point while keeping the operational data of each system private. We further study the optimal reserve capacity requirements for pricing in the absence of such collaboration. We showcase numerically that a lack of attention to interdependencies between the two infrastructures can have adverse operational effects.

A convex approximation method for multiuser MISO sum rate maximization under discrete rate constraints

This paper considers a discrete sum rate maximization (DSRM) problem for transmit optimization in multiuser MISO downlink. Unlike many existing sum rate maximization designs, DSRM focuses on a scenario where each users achievable rate can only be chosen from a given discrete rate set. This discrete rate-based design is motivated by the fact that practical communication systems can support only a finite number of combinations of modulation and coding schemes. We tackle the DSRM problem first by deriving a novel reformulation of DSRM, in which the discrete rate variables are absorbed by the objective function. Then, from this reformulation, an approximation algorithm based on convex optimization and iterative solution refinement is developed. Simulations results are provided to demonstrate the performance of the proposed algorithm compared with some state-of-the-art algorithms.

Consensus on State and Time: Decentralized Regression With Asynchronous Sampling

An implicit assumption made in several studies on sensor systems is that the time and frequency at which sensor measurements are taken is consistent across all the distributed sensing sites. In reality, the times of measurement often lack consistency and integrity, and this is an intrinsic vulnerability of wide area sensor system. Data logs coming from different analog to digital converters (ADCs) are not in phase and may differ also in the sampling rate, in some cases because heterogeneity in the sensors and in others because the data are simply not refreshed in the data historians with the same frequency. Lack of good synchronization in sensing may be the result of a malfunction or also due to intentional delay attacks. This premise motivates our work, where we advance the area of decentralized signal processing and consider explicitly timing errors and nonhomogenous sampling rates in least square estimation problems with distributed sensing. For linear observations models, we provide a necessary and sufficient condition for identifiability of the time offsets. We propose an algorithm for the joint regression on the state vector and time offsets. The algorithm also exploits the asynchrony and redundancy in the spatial sampling to attain sub-Nyquist sampling resolution of the slow sensor feeds. Importantly, this also leads to the development of a novel decentralized algorithm. The efficacies of the proposed decentralized algorithm are shown by both convergence analysis and numerical simulations.

Data Injection Attacks in Randomized Gossiping

The subject of this paper is the detection and mitigation of data injection attacks in randomized average consensus gossip algorithms. It is broadly known that the main advantages of randomized average consensus gossip are its fault tolerance and distributed nature. Unfortunately, the flat architecture of the algorithm also increases the attack surface for a data injection attack. Even though we cast our problem in the context of sensor network security, the attack scenario is identical to existing models for opinion dynamics (the so-called DeGroot model) with stubborn agents steering the opinions of the group toward a final state that is not the average of the network initial states. We specifically propose two novel strategies for detecting and locating attackers and study their detection and localization performance numerically and analytically. Our detection and localization methods are completely decentralized and, therefore, nodes can directly act on their conclusions and stop receiving information from nodes identified as attackers. As we show by simulation, the network can often recover in this fashion, leveraging the resilience of randomized gossiping to reduced network connectivity.

An alternating optimization algorithm for the MIMO secrecy capacity problem under sum power and per-antenna power constraints

This paper considers transmit covariance optimization for a multi-input multi-output (MIMO) Gaussian wiretap channel. Specifically, we aim to maximize the MIMO secrecy capacity by judiciously designing the transmit covariance under the sum power and per-antenna power constraints. The MIMO secrecy capacity maximization (SCM) problem is nonconvex, and so far there is no tractable solution available. We propose an alternating optimization (AO) approach to handle the SCM problem. In particular, our development consists of two steps: First, we show that the SCM problem can be reexpressed to a form that can be conveniently processed by AO. Second, we develop a custom-designed fast algorithm for each AO iteration. Interestingly, with this fast implementation, the overall AO algorithm can be viewed as performing iterative reweighting and water-filling. Finally, the convergence of the proposed algorithm to a stationary solution of SCM is shown, and numerical results are provided to demonstrate its efficacy.

D-FW: Communication efficient distributed algorithms for high-dimensional sparse optimization

We propose distributed algorithms for high-dimensional sparse optimization. In many applications, the parameter is sparse but high-dimensional. This is pathological for existing distributed algorithms as the latter require an information exchange stage involving transmission of the full parameter, which may not be sparse during the intermediate steps of optimization. The novelty of this work is to develop communication efficient algorithms using the stochastic Frank-Wolfe (sFW) algorithm, where the gradient computation is inexact but controllable. For star network topology, we propose an algorithm with low communication cost and establishes its convergence. The proposed algorithm is then extended to perform decentralized optimization on general network topology. Numerical experiments are conducted to verify our findings.

Detection of data injection attacks in decentralized learning

Gossip based optimization and learning are appealing methods that solve big data learning problems sharing computation and network resources when data are distributed. The main advantage these methods offer is that they are fault tolerant. Their flat architecture, however, expands the attack surface in the case of a data injection attack. We analyze the effects of data injection on the asymptotic behavior of the network and draw a parallel with the case of opinion dynamics in a network where zealots inject opinions to mislead a community. We further propose a possible decentralized detection of such attacks and analyze its performance.