Robust set-theoretic distributed detection in diffusion networks

We propose novel set-theoretic distributed adaptive filters for cooperative signal detection in diffusion networks, a problem that has been gaining attention owing to its application to cooperative cognitive radio networks. In the proposed method, nodes in a network detect the presence of a signal of interest by means of an inner product between the current term of a series and a known reference vector. Each term of the series is computed from information fusion among neighboring nodes and projections onto closed convex sets, which are constructed with a priori knowledge of the signal of interest and measurements obtained by nodes. In particular, we show that sets based on a priori knowledge are useful to decrease the communication overhead and to provide good detection performance. Our results are rigorous in the sense that no approximations are used to prove convergence properties. In particular, we show conditions to guarantee that the series converge to a point that can reliably identify the signal of interest. Furthermore, we also show that recent results in distributed optimization for dynamic systems can be used to derive algorithms where nodes exchange not only the current vectors of their sequences (as in previous distributed set-theoretic filters), but also side information that influences the above-mentioned sets

Peak load minimization in load coupled interference networks

We propose a novel power control algorithm for the minimization of the peak load in the widely used load coupled network model, which is an abstract model able to capture the behavior of current and possibly future wireless networks. We first prove that the solution to the optimization problem we pose here requires all base stations with the same load. This necessary condition for optimality gives rise to a solver based on a bisection algorithm that requires an oracle able to answer whether a probed load is greater than the optimal value. By exploiting known properties of concave mappings, we devise an iterative oracle that, with a very mild assumption, provably gives the correct answer with a finite number of iterations. Simulations in an ultra-dense network show that the proposed algorithm can decrease the peak load by around 40% when compared to the peak load induced by the common approach of fixing the power of every base station to the maximum value

Spectral Radii of Asymptotic Mappings and the Convergence Speed of the Standard Fixed Point Algorithm

Important problems in wireless networks can often be solved by computing fixed points of standard or contractive interference mappings, and the conventional fixed point algorithm is widely used for this purpose. Knowing that the mapping used in the algorithm is not only standard but also contractive (or only contractive) is valuable information because we obtain a guarantee of geometric convergence rate, and the rate is related to a property of the mapping called modulus of contraction. To date, contractive mappings and their moduli of contraction have been identified with case-by-case approaches that can be difficult to generalize. To address this limitation of existing approaches, we show in this study that the spectral radii of asymptotic mappings can be used to identify an important subclass of contractive mappings and also to estimate their moduli of contraction. In addition, if the fixed point algorithm is applied to compute fixed points of positive concave mappings, we show that the spectral radii of asymptotic mappings provide us with simple lower bounds for the estimation error of the iterates. An immediate application of this result proves that a known algorithm for load estimation in wireless networks becomes slower with increasing traffic

Weakly Standard Interference Mappings: Existence of Fixed Points and Applications to Power Control in Wireless Networks

We propose novel approaches to identify the existence of fixed points of the so-called weakly standard interference mappings, which include the well-known standard and general interference mappings as particular cases. The approaches are based on the concept of spectral radius of asymptotic mappings, a mathematical tool recently introduced to study the behavior of wireless networks. We show that, for arbitrary weakly standard interference mappings, knowledge of the spectral radius of an associated asymptotic mapping gives a sufficient condition to determine the existence of fixed points or their absence in the positive orthant. If the mapping has a fixed point, we further prove that the set of fixed points has a minimal element that can be easily computed with a simple fixed point algorithm. The theory developed here is applied to the problem of power control for load planning in LTE networks. Unlike previous approaches in the literature, the proposed solution takes into account the limited number of modulation and coding schemes of practical transceivers

Connections between Spectral Properties of Asymptotic Mappings and Solutions to Wireless Network Problems

In this study, we establish connections between asymptotic functions and properties of solutions to important problems in wireless networks. We start by introducing a class of self-mappings (called asymptotic mappings) constructed with asymptotic functions, and we show that spectral properties of these mappings explain the behavior of solutions to some max-min utility optimization problems. For example, in a common family of max-min utility power control problems, we prove that the optimal utility as a function of the power available to transmitters is approximately linear in the low power regime. However, as we move away from this regime, there exists a transition point, easily computed from the spectral radius of an asymptotic mapping, from which gains in utility become increasingly marginal. From these results we derive analogous properties of the transmit energy efficiency. In this study, we also generalize and unify existing approaches for feasibility analysis in wireless networks. Feasibility problems often reduce to determining the existence of the fixed point of a standard interference mapping, and we show that the spectral radius of an asymptotic mapping provides a necessary and sufficient condition for the existence of such a fixed point. We further present a result that determines whether the fixed point satisfies a constraint given in terms of a monotone norm

Distributed RAN and backhaul optimization for energy efficient wireless networks

In this study, we address the problem of minimizing the energy consumption in future 5G networks by means of a joint optimization of radio access network (RAN) and multi-hop wireless backhaul network. The objective of the optimization is to operate the network with the smallest set of base stations while meeting the quality of service (QoS) requirements of users. We first pose the optimization problem as a convex optimization problem. We use a Lagrangian decomposition method to separate the problem in smaller subproblems, which are then solved using minimax primal-dual optimization in a distributed manner. By using the proposed method both the primal and dual problems can be solved at each base station with minimal information exchange between the neighboring base stations. Therefore, the solution proposed is suitable for solving the problems of similar nature in a completely distributed manner in large-scale ultra-dense networks (UDNs) with wireless backhaul infrastructure, which are extensively discussed in the context of 5G

Robust Cell-Load Learning With a Small Sample Set

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 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 learning techniques, especially for small training sample sets

Interference identification in cellular networks via adaptive projected subgradient methods

We develop an adaptive algorithm to estimate a channel gain matrix in cellular heterogeneous networks. This algorithm has the objective of providing important information to interference coordination and management schemes, a crucial functionality of 'beyond 2020 networks'. In more detail, we pose the estimation problem as a set-theoretic adaptive filtering problem. In the proposed scheme, the channel gain matrix is tracked with the adaptive projected subgradient method (APSM), a powerful iterative tool that can seamlessly use prior information and information gained by measurements. More precisely, we construct multiple closed convex sets, each of which containing estimates that are consistent with a piece of information about the channel gain matrix. The intersection of these sets corresponds to estimates that are consistent with all available information. In particular, we use the following information to construct the sets: i) physical upper and lower bounds of the path gains, ii) interference bounds for the downlink and uplink communication, and iii) received signal received power (RSRP) measurements. The algorithm produces a sequence of estimates where each term is an estimate that approaches the intersection of the multiple sets available at a given time instant. Simulations show that the proposed algorithm is able to track the channel gain matrix in scenarios with mobile users, and it outperforms standard adaptive filters that do not use prior information