Abstract-We consider Kalman filtering in a network with packet losses, and use a two state Markov chain to describe the normal operating condition of packet delivery and transmission failure. We analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance, which describes the upper envelope of the sequence of error covariance matrices {Pt, t ≥ 1} for the case of an unstable scalar model. We give sufficient conditions for the stability of the peak covariance process in the general vector case; for the scalar case we obtain a sufficient and necessary condition, and derive upper and lower bounds for the tail distribution of the peak variance. For practically verifying the stability condition, we further introduce a suboptimal estimator and develop a numerical procedure to generate tighter estimate for the constants involved in the stability criterion.

Abstract-A data rate theorem for stabilization of a linear, discrete-time, dynamical system with arbitrarily large disturbances, over a rate-limited, time-varying communication channel is presented. Necessary and sufficient conditions for stabilization are derived, their implications and relationships with related results in the literature are discussed. The proof techniques rely on both information-theoretic and control-theoretic tools.

We study stochastic stability of centralized Kalman filtering for linear time-varying systems equipped with wireless sensors. Transmission is over fading channels where variable channel gains are counteracted by power control to alleviate the effects of packet drops. We establish sufficient conditions for the expected value of the Kalman filter covariance matrix to be exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing power control policies which minimize the total sensor power budget. In deriving the optimal power control laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases.

In this paper we provide a study of channel-aware decision fusion (DF) over a "virtual" multiple-input multipleoutput (MIMO) channel in the large-array regime at the DF center (DFC). The considered scenario takes into account channel estimation and inhomogeneous large-scale fading between the sensors and the DFC. The aim is the development of (widely) linear fusion rules, as opposed to the unsuitable optimum loglikelihood ratio (LLR). The proposed rules can effectively benefit from performance improvement via a large-array, differently from existing sub-optimal alternatives. Performance evaluation, along with theoretical achievable performance and complexity analysis, is presented. Simulation results are provided to confirm the findings. Analogies and differences with uplink communication in a multiuser (massive) MIMO scenario are underlined. Index Terms-Decision fusion, distributed detection, largescale MIMO, wireless sensor networks. Recently, DF over MACs is becoming increasingly attractive, since it exploits both the interfering nature of the broadcast wireless medium (for spectral-efficiency purposes) and the correlated nature of decisions, all regarding the same unknown event being observed. Also, deep fading scenarios

We consider remote state estimation of cyberphysical systems under signal-to-interference-plus-noise ratio-based denial-of-service attacks. A sensor sends its local estimate to a remote estimator through a wireless network that may suffer interference from an attacker. Both the sensor and the attacker have energy constraints. We first study an associated two-player game when multiple power levels are available. Then, we build a Markov game framework to model the interactive decision-making process based on the current state and information collected from previous time steps. To solve the associated optimality (Bellman) equations, a modified Nash Q-learning algorithm is applied to obtain the optimal solutions. Numerical examples and simulations are provided to demonstrate our results.

We seek distributed protocols that attain the global optimum allocation of link transmitter powers and source rates in a cross-layer design of a mobile ad hoc network. Although the underlying network utility maximization is nonconvex, convexity plays a major role in our development. We provide new convexity results surrounding the Shannon capacity formula, allowing us to abandon suboptimal high-SIR approximations that have almost become entrenched in the literature. More broadly, these new results can be back-substituted into many existing problems for similar benefit.Three protocols are developed. The first is based on a convexification of the underlying problem, relying heavily on our new convexity results. We provide conditions under which it produces a globally optimum resource allocation. We show how it may be distributed through message passing for both rate-and power-allocation. Our second protocol relaxes this requirement and involves a novel sequence of convex approximations, each exploiting existing TCP protocols for source rate allocation. Message passing is only used for power control. Our convexity results again provide sufficient conditions for global optimality. Our last protocol, motivated by a desire of power control devoid of message passing, is a near optimal scheme that makes use of noise measurements and enjoys a convergence rate that is orders of magnitude faster than existing methods.Index Terms-Congestion control, cross-layer optimization, mobile ad hoc network, network utility maximization, outage probability, power control, Rayleigh fading.

How can we achieve the conflicting goals of reduced transmission power and increased capacity in a wireless network, without attempting to follow the instantaneous state of a fading channel? In this paper, we address this problem by jointly considering power control and multiuser detection (MUD) with outage-probability constraints in a Rayleigh fast-fading environment. The resulting power-control algorithms (PCAs) utilize the statistics of the channel and operate on a much slower timescale than traditional schemes. We propose an optimal iterative solution that is conceptually simple and finds the minimum sum power of all users while meeting their outage targets. Using a derived bound on outage probability, we introduce a mapping from outage to average signal-to-interference ratio (SIR) constraints. This allows us to propose a suboptimal iterative scheme that is a variation of an existing solution to a joint power control and MUD problem involving SIR constraints. We further use a recent result that transforms complex SIR expressions into a compact and decoupled form, to develop a noniterative and computationally inexpensive PCA for large systems of users. Simulation results are presented showing the closeness of the optimal and mapped schemes, speed of convergence, and performance comparisons. Index Terms-Code division multiple access (CDMA), large system analysis (LSA), multiuser detection (MUD), outage probability, power control, Rayleigh fading.

We consider a decentralized multi-sensor estimation problem where L sensor nodes observe noisy versions of a correlated random source vector. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source. We optimize the amplification factor (or equivalently transmission power) at each sensor node in two different scenarios: a) with the objective of total power minimization subject to mean square error (MSE) of source estimation constraint, and b) with the objective of minimizing MSE subject to total power constraint. For this purpose, based on the well-known favorable propagation condition (when L ≪ N) achieved in massive multiple-input multiple-output (MIMO), we apply an asymptotic approximation on the MSE, and use convex optimization techniques to solve for the optimal sensor power allocation in a) and b). In a), we show that the total power consumption at the sensors decays as 1/N , replicating the power savings obtained in massive MIMO mobile communications literature. We also show several extensions of the aforementioned scenarios to the cases where sensor-to-FC fading channels are correlated, and channel coefficients are subject to estimation error. Through numerical studies, we also illustrate the superiority of the proposed optimal power allocation methods over uniform power allocation.