Data Offloading in Load Coupled Networks: A Utility Maximization Framework

We provide a general framework for the problem of data offloading in a heterogeneous wireless network, where some demand of cellular users is served by a complementary network. The complementary network is either a small-cell network that shares the same resources as the cellular network, or a WiFi network that uses orthogonal resources. For a given demand served in a cellular network, the load, or the level of resource usage, of each cell depends in a non-linear manner on the load of other cells due to the mutual coupling of interference seen by one another. With load coupling, we optimize the demand to be served in the cellular or the complementary networks, so as to maximize a utility function. We consider three representative utility functions that balance, to varying degrees, the revenue from serving the users vs the user fairness. We establish conditions for which the optimization problem has a feasible solution and is convex, and hence tractable to numerical computations. Finally, we propose a strategy with theoretical justification to constrain the load to some maximum value, as required for practical implementation. Numerical studies are conducted for both under-loaded and over-loaded networks.Comment: 12 pages, accepted for publication in IEEE Transactions on Wireless Communication

Multivariate Bernoulli and Euler polynomials via L\'evy processes

By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to this representation, which could be easily implemented in any symbolic manipulation system. A very simple relation between these two families of multivariate polynomials is provided

Power and Channel Allocation for Non-orthogonal Multiple Access in 5G Systems: Tractability and Computation

Network capacity calls for significant increase for 5G cellular systems. A promising multi-user access scheme, non-orthogonal multiple access (NOMA) with successive interference cancellation (SIC), is currently under consideration. In NOMA, spectrum efficiency is improved by allowing more than one user to simultaneously access the same frequency-time resource and separating multi-user signals by SIC at the receiver. These render resource allocation and optimization in NOMA different from orthogonal multiple access in 4G. In this paper, we provide theoretical insights and algorithmic solutions to jointly optimize power and channel allocation in NOMA. For utility maximization, we mathematically formulate NOMA resource allocation problems. We characterize and analyze the problems' tractability under a range of constraints and utility functions. For tractable cases, we provide polynomial-time solutions for global optimality. For intractable cases, we prove the NP-hardness and propose an algorithmic framework combining Lagrangian duality and dynamic programming (LDDP) to deliver near-optimal solutions. To gauge the performance of the obtained solutions, we also provide optimality bounds on the global optimum. Numerical results demonstrate that the proposed algorithmic solution can significantly improve the system performance in both throughput and fairness over orthogonal multiple access as well as over a previous NOMA resource allocation scheme.Comment: IEEE Transactions on Wireless Communications, revisio

Optimal Cell Clustering and Activation for Energy Saving in Load-Coupled Wireless Networks

Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study optimal cell clustering and scheduling of activation duration for each cluster, with the objective of minimizing the sum energy, subject to a time constraint of delivering the users' traffic demand. The cells within a cluster are simultaneously in transmission and napping modes, with cluster activation and deactivation, respectively. Our optimization framework accounts for the coupling relation among cells due to the mutual interference. Thus, the users' achievable rates in a cell depend on the cluster composition. On the theoretical side, we provide mathematical formulation and structural characterization for the energy-efficient cell clustering and scheduling optimization problem, and prove its NP hardness. On the algorithmic side, we first show how column generation facilitates problem solving, and then present our notion of local enumeration as a flexible and effective means for dealing with the trade-off between optimality and the combinatorial nature of cluster formation, as well as for the purpose of gauging the deviation from optimality. Numerical results demonstrate that our solutions achieve more than 60% energy saving over existing schemes, and that the solutions we obtain are within a few percent of deviation from global optimum.Comment: Revision, IEEE Transactions on Wireless Communication

On Power and Load Coupling in Cellular Networks for Energy Optimization

We consider the problem of minimization of sum transmission energy in cellular networks where coupling occurs between cells due to mutual interference. The coupling relation is characterized by the signal-to-interference-and-noise-ratio (SINR) coupling model. Both cell load and transmission power, where cell load measures the average level of resource usage in the cell, interact via the coupling model. The coupling is implicitly characterized with load and power as the variables of interest using two equivalent equations, namely, non-linear load coupling equation (NLCE) and non-linear power coupling equation (NPCE), respectively. By analyzing the NLCE and NPCE, we prove that operating at full load is optimal in minimizing sum energy, and provide an iterative power adjustment algorithm to obtain the corresponding optimal power solution with guaranteed convergence, where in each iteration a standard bisection search is employed. To obtain the algorithmic result, we use the properties of the so-called standard interference function; the proof is non-standard because the NPCE cannot even be expressed as a closed-form expression with power as the implicit variable of interest. We present numerical results illustrating the theoretical findings for a real-life and large-scale cellular network, showing the advantage of our solution compared to the conventional solution of deploying uniform power for base stations.Comment: Accepted for publication in IEEE Transactions on Wireless Communication