This paper investigates distributionally robust filtering for state-space models subject to exogenous disturbances in state evolution and observation processes. The joint probability distribution of the disturbance process over an arbitrary horizon is unknown but is assumed to reside within a Wasserstein-2 ambiguity set centered around a nominal distribution. We seek to develop a causal estimator that minimizes the worst-case mean squared error (MSE) among all distributions in this ambiguity set. Unlike prior works, our framework accommodates disturbances with arbitrary temporal correlations. In the finite-horizon setting, this problem reduces to a semi-definite program (SDP) whose complexity scales with the time horizon. Consequently, we focus on the infinite-horizon case, where we derive the optimal linear time-invariant (LTI) filter using the Karush-Kuhn-Tucker (KKT) conditions and propose an efficient frequency-domain algorithm to compute it. While the optimal LTI filter generally has a non-rational transfer function, we provide a minimax rational approximation method to approximate the optimal non-rational filter, in the H∞-norm, with a near-optimal finite-order state-space estimator. This approach avoids the computational challenges associated with horizon-dependent scaling in the finite-horizon case. Numerical simulations demonstrate the effectiveness of the proposed method.

We study the scalar quantization of random information sources with unknown probability distributions through the lens of distributional robustness. Assuming the true source distribution resides within an ambiguity set of plausible distributions, we formulate the problem of distributionally robust scalar quantization (DRQ) as finding a minimax optimal quantizer that minimizes the mean-squared quantization error (MSQE) under the least favorable distribution in the ambiguity set. Specifically, we define the ambiguity set using the Wasserstein-2 ($\mathrm{W}_{2}$) distance, a statistical measure of distribution shift, as a statistical ball centered around a nominal source distribution. We derive a tractable dual reformulation and establish the necessary optimality conditions for$\mathrm{W}_{2}$-DRQ. Building on these results, we propose a novel fixedpoint iteration algorithm, inspired by the classical Lloyd-Max algorithm, to compute locally optimal DR quantizers. We prove the monotonic convergence of the algorithm and demonstrate its effectiveness through numerical simulations. Our results highlight the performance advantages of the proposed approach under distributional uncertainty, particularly in comparison to the classical Lloyd-Max algorithm.

We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret—the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting.

We consider the rate-distortion function for lossy source compression, as well as the channel capacity for error cor-rection, through the lens of distributional robustness. We assume that the distribution of the source or of the additive channel noise is unknown and lies within a Wasserstein-2 ambiguity set of a given radius centered around a specified nominal distribution, and we look for the worst-case asymptotically optimal coding rate over such an ambiguity set. Varying the radius of the ambiguity set allows us to interpolate between the worst-case and stochastic scenarios using probabilistic tools. Our problem setting fits into the paradigm of compound source / channel models introduced by Sakrison [1] and Blackwell [2], respectively. This paper shows that if the nominal distribution is Gaussian, then so is the worst-case source / noise distribution, and the compound rate-distortion / channel capacity functions admit convex formulations with Linear Matrix Inequality (LMI) constraints. These formulations yield simple closed-form expressions in the scalar case, offering insights into the behavior of Shannon limits with the changing radius of the Wasserstein-2 ambiguity set.

In mmWave networks, a large or nearby object can obstruct multiple communication links, which results in spatial correlation in the blocking probability between a user and two or more base stations (BSs). This paper characterizes this blocking correlation and derives its impact on the signal-to-interference-plus-noise ratio (SINR) of a mmWave cellular network. We first present an exact analysis of a 1D network and highlight the impact of blocking correlation in the derived expressions. Gaining insights from the 1D analysis, we develop an analytical framework for a 2D network where we characterize the sum interference at the user by considering the correlation between the blocking of serving and interfering links. Using this, we derive the SINR coverage probability. Via simulations, we demonstrate that including blockage correlation in the analysis is required for accurate characterization of the system performance, in particular when the blocking objects tend to be large.

Wireless communications aided by reconfigurable intelligent surfaces (RISs) is a promising way to improve the coverage for cellular users. The controlled reflection of the signal from RISs is especially useful in mm-wave networks when the direct link between a cellular user and its serving base station (BS) is weak or unavailable due to blockages. But the joint blockage of the user-RIS and the user-BS links may significantly degrade the performance of RIS-aided transmissions. This paper aims to study the effect of joint blockages on downlink performance. When the RIS locations are coupled with BS locations, using tools from stochastic geometry, we obtain an optimal placement of RISs either to minimize the joint blockage probability of the user-RIS and the user-BS links or to maximize the downlink coverage probability. The results show that installing RISs on the street intersections improves the coverage probability. For users associated with BSs that are deployed sufficiently close to intersections, the intersection-mounted RISs offer a better coverage performance compared to BS-coupled RISs.