Athina P. Petropulu

Spilios Evmorfos, Athina P. Petropulu, H. Vincent Poor

The paper studies the problem of designing the Intelligent Reflecting Surface (IRS) phase shifters for Multiple Input Single Output (MISO) communication systems in spatiotemporally correlated channel environments, where the destination can move within a confined area. The objective is to maximize the expected sum of SNRs at the receiver over infinite time horizons. The problem formulation gives rise to a Markov Decision Process (MDP). We propose a deep actor-critic algorithm that accounts for channel correlations and destination motion by constructing the state representation to include the current position of the receiver and the phase shift values and receiver positions that correspond to a window of previous time steps. The channel variability induces high frequency components on the spectrum of the underlying value function. We propose the preprocessing of the critic's input with a Fourier kernel which enables stable value learning. Finally, we investigate the use of the destination SNR as a component of the designed MDP state, which is common practice in previous work. We provide empirical evidence that, when the channels are spatiotemporally correlated, the inclusion of the SNR in the state representation interacts with function approximation in ways that inhibit convergence.

Dionysios S. Kalogerias, Athina P. Petropulu

We consider stochastic motion planning in single-source single-destination robotic relay networks, under a cooperative beamforming framework. Assuming that the communication medium constitutes a spatiotemporal stochastic field, we propose a 2-stage stochastic programming formulation of the problem of specifying the positions of the relays, such that the expected reciprocal of their total beamforming power is maximized. Stochastic decision making is made on the basis of random causal CSI. Recognizing the intractability of the original problem, we propose a lower bound relaxation, resulting to a nontrivial optimization problem with respect to the relay locations, which is equivalent to a small set of simple, tractable subproblems. Our formulation results in spatial controllers with a predictive character; at each time slot, the new relay positions should be such that the expected power reciprocal at the next time slot is maximized. Quite interestingly, the optimal control policy to the relaxed problem is purely selective; under a certain sense, only the best relay should move.

Dionysios S. Kalogerias, Athina P. Petropulu

We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More specifically, we consider a class of nonlinear, partially observable stochastic systems, comprised by a (possibly nonstationary) hidden stochastic process (the state), observed through another conditionally Gaussian stochastic process (the observations). Under general assumptions, we show that, given an approximating process which, for each time step, is stochastically convergent to the state process, an approximate filtering operator can be defined, which converges to the true optimal nonlinear filter of the state in a strong and well defined sense. In particular, the convergence is compact in time and uniform in a completely characterized measurable set of probability measure almost unity, also providing a purely quantitative justification of Egoroff's Theorem for the problem at hand. The results presented in this paper can form a common basis for the analysis and characterization of a number of heuristic approaches for approximating optimal nonlinear filters, such as approximate grid based techniques, known to perform well in a variety of applications.

Anastasios Dimas, Dionysios S. Kalogerias, Athina P. Petropulu

While millimeter wave (mmWave) communications promise high data rates, their sensitivity to blockage and severe signal attenuation presents challenges in their deployment in urban settings. To overcome these effects, we consider a distributed cooperative beamforming system, which relies on static relays deployed in clusters with similar channel characteristics, and where, at every time instance, only one relay from each cluster is selected to participate in beamforming to the destination. To meet the quality-of-service guarantees of the network, a key prerequisite for beamforming is relay selection. However, as the channels change with time, relay selection becomes a resource demanding task. Indeed, estimation of channel state information for all candidate relays, essential for relay selection, is a process that takes up bandwidth, wastes power and introduces latency and interference in the network. We instead propose a unique, predictive scheme for resource efficient relay selection, which exploits the special propagation patterns of the mmWave medium, and can be executed distributively across clusters, and in parallel to optimal beamforming-based communication. The proposed predictive scheme efficiently exploits spatiotemporal channel correlations with current and past networkwide Received Signal Strength (RSS), the latter being invariant to relay cluster size, measured sequentially during the operation of the system. Our numerical results confirm that our proposed relay selection strategy outperforms any randomized selection policy that does not exploit channel correlations, whereas, at the same time, it performs very close to an ideal scheme that uses complete, cluster size dependent RSS, and offers significant savings in terms of channel estimation overhead, providing substantially better network utilization, especially in dense topologies, typical in mmWave networks.

Dionysios S. Kalogerias, Athina P. Petropulu

We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state quantization: The \textit{Markovian} type and the \textit{marginal} type. We propose a set of novel, relaxed sufficient conditions, ensuring strong and fully characterized pathwise convergence of these filters to the respective MMSE state estimator. In particular, for marginal state quantizations, we introduce the notion of \textit{conditional regularity of stochastic kernels}, which, to the best of our knowledge, constitutes the most relaxed condition proposed, under which asymptotic optimality of the respective grid based filters is guaranteed. Further, we extend our convergence results, including filtering of bounded and continuous functionals of the state, as well as recursive approximate state prediction. For both Markovian and marginal quantizations, the whole development of the respective grid based filters relies more on linear-algebraic techniques and less on measure theoretic arguments, making the presentation considerably shorter and technically simpler.

Dionysios S. Kalogerias, Athina P. Petropulu

In this work, we study stability of distributed filtering of Markov chains with finite state space, partially observed in conditionally Gaussian noise. We consider a nonlinear filtering scheme over a Distributed Network of Agents (DNA), which relies on the distributed evaluation of the likelihood part of the centralized nonlinear filter and is based on a particular specialization of the Alternating Direction Method of Multipliers (ADMM) for fast average consensus. Assuming the same number of consensus steps between any two consecutive noisy measurements for each sensor in the network, we fully characterize a minimal number of such steps, such that the distributed filter remains uniformly stable with a prescribed accuracy level, {\varepsilon} \in (0,1], within a finite operational horizon, T, and across all sensors. Stability is in the sense of the \ell_1-norm between the centralized and distributed versions of the posterior at each sensor, and at each time within T. Roughly speaking, our main result shows that uniform {\varepsilon}-stability of the distributed filtering process depends only loglinearly on T and (roughly) the size of the network, and only logarithmically on 1/{\varepsilon}. If this total loglinear bound is fulfilled, any additional consensus iterations will incur a fully quantified further exponential decay in the consensus error. Our bounds are universal, in the sense that they are independent of the particular structure of the Gaussian Hidden Markov Model (HMM) under consideration.