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Learning of the cell-load in radio access networks (RANs) has to be performed within a short time period. Therefore, we propose a learning framework that is robust against uncertainties resulting from the need for learning based on a relatively small training sample set. To this end, we incorporate prior knowledge about the cell-load in the learning framework. For example, an inherent property of the cell-load is that it is monotonic in downlink (data) rates. To obtain additional prior knowledge we first study the feasible rate region, i.e., the set of all vectors of user rates that can be supported by the network. We prove that the feasible rate region is compact. Moreover, we show the existence of a Lipschitz function that maps feasible rate vectors to cell-load vectors. With these results in hand, we present a learning technique that guarantees a minimum approximation error in the worst-case scenario by using prior knowledge and a small training sample set. Simulations in the network simulator NS3 demonstrate that the proposed method exhibits better robustness and accuracy than standard multivariate learning techniques, especially for small training sample sets., Comment: Published in IEEE Transactions on Signal Processing ( Volume: 68)

We propose a novel utility optimization algorithm for wireless networks modeled by systems of nonlinear equations based on the load at the base stations. Unlike previous studies, the algorithm solves a max-min utility optimization problem over the joint space of network load, transmit power, and rates. In more detail, our first main contribution is to show that, in the optimum, users operate at the same rate, base stations are fully loaded, and at least one base station transmits at the maximum power. This characterization of the optimal solution enables a reformulation of the optimization task as a conditional eigenvalue problem associated with a concave mapping that relates the transmit power to the network load. With this reformulation, an efficient iterative solver becomes readily available. Our second main contribution is the derivation of a simple lower bound for conditional eigenvalues of general positive concave mappings. These bounds are of particular interest to network designers, because conditional eigenvalues can often be related to the optimal rates (or the optimal signal-to-interference-noise ratio) of a large class of utility optimization problems, and, in this paper, these bounds are used to derive performance limits of load coupled networks.

This study investigates the interplay between load and power in load coupled interference networks. In more detail, the first objective of this study is to derive a positive concave mapping having as its fixed point the power allocation inducing a desired network load. Knowledge of this mapping is important for many theoretical and practical reasons. First, it opens up the possibility of applying many existing algorithms to compute the power inducing a desired load, which is an estimation problem typically used to obtain energy efficient network configurations. With the results in this study, systems designers can now select an algorithm based on practical considerations such as the computational complexity, memory requirements, and convergence speed. In particular, we show that algorithms based on simple fixed point iterations already have many advantages over the previously only known method for the power estimation problem. Second, knowledge of specific properties of the mapping, such as concavity, enables us to use standard tools in convex analysis to analyze the network, and it may also give rise to novel optimization tools for self-organizing networks. The second main objective of this study is the development of a truly distributed algorithm for power estimation in real networks. This algorithm uses only information that is readily available at base stations, and it does not require any additional signaling overhead. These two characteristics make the proposed algorithm especially useful in ultra-dense wireless networks, one of the main visions for 5G networks.

In this paper, we address the problem of reconstructing coverage maps from path-loss measurements in cellular networks. We propose and evaluate two kernel-based adaptive online algorithms as an alternative to typical offline methods. The proposed algorithms are application-tailored extensions of powerful iterative methods such as the adaptive projected subgradient method and a state-of-the-art adaptive multikernel method. Assuming that the moving trajectories of users are available, it is shown how side information can be incorporated in the algorithms to improve their convergence performance and the quality of the estimation. The complexity is significantly reduced by imposing sparsity-awareness in the sense that the algorithms exploit the compressibility of the measurement data to reduce the amount of data which is saved and processed. Finally, we present extensive simulations based on realistic data to show that our algorithms provide fast, robust estimates of coverage maps in real-world scenarios. Envisioned applications include path-loss prediction along trajectories of mobile users as a building block for anticipatory buffering or traffic offloading., Comment: IEEE Transactions on Vehicular Technology; revised and extended version with new simulation scenario

The densification and expansion of wireless networks pose new challenges on energy efficiency. With a drastic increase of infrastructure nodes (e.g. ultradense deployment of small cells), the total energy consumption may easily exceed an acceptable level. While most studies focus on the energy radiated by the antennas, the bigger part of the total energy budget is actually consumed by the hardware (e.g., coolers and circuit energy consumption). The ability to shut down infrastructure nodes (or parts of it) or to adapt the transmission strategy according to the traffic will therefore become an important design aspect of energy-efficient wireless ?architectures. Network infrastructure should be ?regarded as a resource that can be occupied or released on demand, and the modeling and optimization of such systems are highly nontrivial problems. In particular, elements of the network infrastructure should be released by taking into account traffic forecasts to avoid losing the required coverage and capacity. However, even if traffic profiles were perfectly known, the determination of the elements to be released is complicated by the potential interference coupling between active elements and the sheer size of the optimization problems in dense networks.

We consider a convex optimization problem for non-hierarchical agent networks where each agent has access to a local or private time-varying function, and the network-wide objective is to find a time-invariant minimizer of the sum of these functions, provided that such a minimizer exists. Problems of this type are common in dynamic systems where the objective function is time-varying because of, for instance, the dependency on measurements that arrive continuously to each agent. A typical outer-loop optimization iteration for optimization problems of this type consists of a local optimization step based on the information provided by neighboring agents, followed by a consensus step to exchange and fuse local estimates of the agents. A great deal of research effort has been directed towards developing and better understanding such algorithms, which find many applications in distinct areas such as cognitive radio networks, distributed acoustic source localization, coordination of unmanned vehicles, and environmental modeling. Contrasting with existing work, which considers either dynamic systems or noisy links (but not both jointly), in this study we devise and analyze a novel distributed online algorithm for dynamic optimization problems in noisy communication environments. The main result of the study proves sufficient conditions for almost sure convergence of the algorithm as the number of iterations tends to infinity. The algorithm is applicable to a wide range of distributed optimization problems with time-varying cost functions and consensus updates corrupted by additive noise. Our results therefore extend previous work to include recently proposed schemes that merge the processes of computation and data transmission over noisy wireless networks for fast and efficient consensus protocols. To give a concrete example of an application, we show how to apply our general technique to the problem of distributed detection with adaptive filters.

We propose a non-hierarchical decentralized algorithm for the asymptotic minimization of possibly time-varying convex functions. In our method, each agent in a network has a private, local (possibly time-varying) cost function, and the objective is to minimize asymptotically the sum of these local functions in every agent (this problem appears in many different applications such as, among others, motion planning, acoustic source localization, and environmental modeling). The algorithm consists of two main steps. First, to improve the estimate of a minimizer, agents apply a particular version of the adaptive projected subgradient method to their local functions. Then the agents exchange and mix their estimates using a communication model based on recent results of consensus algorithms. We show formally the convergence of the resulting scheme, which reproduces as particular cases many existing methods such as gossip consensus algorithms and recent decentralized adaptive s ubgradient methods (which themselves include as particular cases many distributed adaptive filtering algorithms). To illustrate two possible applications, we consider the problems of acoustic source localization and environmental modeling via network gossiping with mobile agents.

In many distributed systems, the objective is to reach agreement on values acquired by the nodes in a network. A common approach to solve such problems is the iterative, weighted linear combination of those values to which each node has access. Methods to compute appropriate weights have been extensively studied, but the resulting iterative algorithms still require many iterations to provide a fairly good estimate of the consensus value. In this study we show that a good estimate of the consensus value can be obtained with few iterations of conventional consensus algorithms by filtering the output of each node with set-theoretic adaptive filters. We use the adaptive projected subgradient method to derive a set-theoretic filter requiring only local information available to each node and being robust to topology changes and erroneous information about the network. Numerical simulations show the good performance of the proposed method.

This paper proposes a novel linear estimator named stochastic MV-PURE estimator, developed for the stochastic linear model, and designed to provide improved performance over the linear minimum mean square error (MMSE) Wiener estimator in cases prevailing in practical, real-world settings, where at least some of the second-order statistics of the random vectors under consideration are only imperfectly known. The proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE), developed for the linear regression model. The proposed stochastic MV-PURE estimator minimizes the mean square error (MSE) of its estimates subject to rank constraint and inducing minimum distortion to the target random vector. Therefore, the stochastic MV-PURE combines the techniques of the reduced rank Wiener filter (named in this paper RR-MMSE) and the distortionless-constrained estimator (named in this paper C-MMSE), in order to achieve greater robustness against noise or model errors than RR-MMSE and C-MMSE. Furthermore, to ensure that the stochastic MV-PURE estimator combines the reduced-rank and minimum-distortion approaches in the MSE-optimal way, we propose a rank selection criterion which minimizes the MSE of the estimates obtained by the stochastic MV-PURE. As a numerical example, we employ the stochastic MV-PURE, RR-MMSE, C-MMSE, and MMSE estimators as linear receivers in a MIMO wireless communication system. This example is chosen as a typical signal processing scenario, where the statistical information on the data, on which the estimates are built, is only imperfectly known. We verify that the stochastic MV-PURE achieves the lowest MSE and symbol error rate (SER) in such settings by employing the proposed rank selection criterion.

This paper introduces adaptive filters that are effective to suppress multiple access interference (MAI) in orthogonal space-time block coded/ multiple-input multiple-output (OSTBC-MIMO) systems. We define an optimal linear filter that minimizes the mean-square error between the filter output and a scaled version of the desired output under a constraint defined by the available channel state information (CSI). The adaptive filters refine a given estimate of the optimal filter by suppressing a sequence of closed convex functions with the adaptive projected subgradient method (APSM) at each iteration. To provide robustness against imperfect CSI, the adaptive filters use not only the available CSI but also estimates of previously transmitted symbols, which usually belong to a small finite set in digital communication systems. The resulting algorithms employ computationally efficient projections onto hyperplanes or hyperslabs and do not require any matrix inversion. An efficient recursive scheme based on such an algorithm is also presented. Convergence analysis and simulation results show the excellent performance of the proposed schemes.