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The asymptotic distribution of a wide class of V- and U-statistics with estimated parameters is derived in the case when the kernel is not necessarily differentiable along the parameter. The results have their application in goodness-of-fit problems.

The accurate estimation of Channel State Information (CSI) is of crucial importance for the successful operation of Multiple-Input Multiple-Output (MIMO) communication systems, especially in a Multi-User (MU) time-varying environment and when employing the emerging technology of Reconfigurable Intelligent Surfaces (RISs). Their predominantly passive nature renders the estimation of the channels involved in the user-RIS-base station link a quite challenging problem. Moreover, the time-varying nature of most of the realistic wireless channels drives up the cost of real-time channel tracking significantly, especially when RISs of massive size are deployed. In this paper, we develop a channel tracking scheme for the uplink of RIS-enabled MU MIMO systems in the presence of channel fading. The starting point is a tensor representation of the received signal and we rely on its PARAllel FACtor (PARAFAC) analysis to both get the initial estimate and track the channel time variation. Simulation results for various system settings are reported, which validate the feasibility and effectiveness of the proposed channel tracking approach.

Machine learning algorithms have recently been considered for many tasks in the field of wireless communications. Previously, we have proposed the use of a deep fully convolutional neural network (CNN) for receiver processing and shown it to provide considerable performance gains. In this study, we focus on machine learning algorithms for the transmitter. In particular, we consider beamforming and propose a CNN which, for a given uplink channel estimate as input, outputs downlink channel information to be used for beamforming. The CNN is trained in a supervised manner considering both uplink and downlink transmissions with a loss function that is based on UE receiver performance. The main task of the neural network is to predict the channel evolution between uplink and downlink slots, but it can also learn to handle inefficiencies and errors in the whole chain, including the actual beamforming phase. The provided numerical experiments demonstrate the improved beamforming performance.

This paper studies the sample complexity of learning the $k$ unknown centers of a balanced Gaussian mixture model (GMM) in $\mathbb{R}^d$ with spherical covariance matrix $\sigma^2\mathbf{I}$. In particular, we are interested in the following question: what is the maximal noise level $\sigma^2$, for which the sample complexity is essentially the same as when estimating the centers from labeled measurements? To that end, we restrict attention to a Bayesian formulation of the problem, where the centers are uniformly distributed on the sphere $\sqrt{d}\mathcal{S}^{d-1}$. Our main results characterize the exact noise threshold $\sigma^2$ below which the GMM learning problem, in the large system limit $d,k\to\infty$, is as easy as learning from labeled observations, and above which it is substantially harder. The threshold occurs at $\frac{\log k}{d} = \frac12\log\left( 1+\frac{1}{\sigma^2} \right)$, which is the capacity of the additive white Gaussian noise (AWGN) channel. Thinking of the set of $k$ centers as a code, this noise threshold can be interpreted as the largest noise level for which the error probability of the code over the AWGN channel is small. Previous works on the GMM learning problem have identified the minimum distance between the centers as a key parameter in determining the statistical difficulty of learning the corresponding GMM. While our results are only proved for GMMs whose centers are uniformly distributed over the sphere, they hint that perhaps it is the decoding error probability associated with the center constellation as a channel code that determines the statistical difficulty of learning the corresponding GMM, rather than just the minimum distance.

Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks and without the knowing closed form distribution of the data. This class of estimators is referred to as neural mutual information estimators. Although very promising, such techniques have yet to be rigorously bench-marked so as to establish their efficacy, ease of implementation, and stability for capacity estimation which is joint maximization frame-work. In this paper, we compare the different techniques proposed in the literature for estimating capacity and provide a practitioner perspective on their effectiveness. In particular, we study the performance of mutual information neural estimator (MINE), smoothed mutual information lower-bound estimator (SMILE), and directed information neural estimator (DINE) and provide insights on InfoNCE. We evaluated these algorithms in terms of their ability to learn the input distributions that are capacity approaching for the AWGN channel, the optical intensity channel, and peak power-constrained AWGN channel. For both scenarios, we provide insightful comments on various aspects of the training process, such as stability, sensitivity to initialization.

As physical layer security evolves to multi-user systems, multi-user interference (MUI) becomes an unavoidable issue. Recently, rate-splitting multiple access (RSMA) emerges as a powerful non-orthogonal transmission framework and interference management strategy with high spectral efficiency. Unlike most works fully treating MUI as noise, we take all users' secrecy rate requirements into consideration and propose an RSMA-based secure beamforming approach to maximize the weighted sum-rate (WSR), where MUI is partially decoded and partially treated as noise. User messages are split and encoded into common and private streams. Each user not only decodes the common stream and the intended private stream, but also tries to eavesdrop other users' private streams. A successive convex approximation (SCA)-based approach is proposed to maximize the instantaneous WSR under perfect channel state information at the transmitter (CSIT). We then propose a joint weighted minimum mean square error and SCA-based alternating optimization algorithm to maximize the weighted ergodic sum-rate under imperfect CSIT. Numerical results demonstrate RSMA achieves better WSR and is more robust to channel errors than conventional multi-user linear precoding technique while ensuring all users' security requirements. Besides, RSMA can satisfy all users' secrecy rate requirements without introducing WSR loss thanks to its powerful interference management capability.

How to manage the interference introduced by the enormous wireless devices is a crucial issue to address in the prospective sixth-generation (6G) communications. The treating interference as noise (TIN) optimality conditions are commonly used for interference management and thus attract significant interest in existing wireless systems. Cell-free massive multiple-input multiple-output (CF mMIMO) is a promising technology in 6G that exhibits high system throughput and excellent interference management by exploiting a large number of access points (APs) to serve the users collaboratively. In this paper, we take the first step on studying TIN in CF mMIMO systems from a stochastic geometry perspective by investigating the probability that the TIN conditions hold with spatially distributed network nodes. We propose a novel analytical framework for TIN in a CF mMIMO system with both Binomial Point Process (BPP) and Poisson Point Process (PPP) approximations. We derive the probability that the TIN conditions hold in close form using the PPP approximation. Numerical results validate our derived expressions and illustrate the impact of various system parameters on the probability that the TIN conditions hold.

In this paper, we investigate the problem of pilot optimization and channel estimation of two-way relaying network (TWRN) aided by an intelligent reflecting surface (IRS) with finite discrete phase shifters. In a TWRN, there exists a challenging problem that the two cascading channels from source-to-IRS-to-Relay and destination-to-IRS-to-relay interfere with each other. Via designing the initial phase shifts of IRS and pilot pattern, the two cascading channels are separated by using simple arithmetic operations like addition and subtraction. Then, the least-squares estimator is adopted to estimate the two cascading channels and two direct channels from source to relay and destination to relay. The corresponding mean square errors (MSE) of channel estimators are derived. By minimizing MSE, the optimal phase shift matrix of IRS is proved. Then, two special matrices Hadamard and discrete Fourier transform (DFT) matrix is shown to be two optimal training matrices for IRS. Furthermore, the IRS with discrete finite phase shifters is taken into account. Using theoretical derivation and numerical simulations, we find that 3-4 bits phase shifters are sufficient for IRS to achieve a negligible MSE performance loss. More importantly, the Hadamard matrix requires only one-bit phase shifters to achieve the optimal MSE performance while the DFT matrix requires at least three or four bits to achieve the same performance. Thus, the Hadamard matrix is a perfect choice for channel estimation using low-resolution phase-shifting IRS.

Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov developed an accelerated gradient search algorithm for convex optimization problems. This has been recently extended for non-convex and also stochastic optimization. We use Nesterov's acceleration for policy gradient search in the well-known actor-critic algorithm and show the convergence using ODE method. We tested this algorithm on a scheduling problem. Here an incoming job is scheduled into one of the four queues based on the queue lengths. We see from experimental results that algorithm using Nesterov's acceleration has significantly better performance compared to algorithm which do not use acceleration. To the best of our knowledge this is the first time Nesterov's acceleration has been used with actor-critic algorithm.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.